First commit: Basic logic and implementation.

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.clangd

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+CompileFlags:
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+    - -I/toDataDrive/ARE/include/
+  Remove:
+
+Diagnostics:
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+    AnalyzeAngledIncludes: No    # 可选：不分析系统头文件以提升性能 [citation:4]

.gitignore

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+/local_test/
+/build/

LICENSE

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experiments/Request.md

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+C++实现一个简易的康奈尔盒子渲染器，但是不基于传统的光线追踪算法，而是一种类似的基于面片及纹理的步进式变换渲染算法(也就是说它的渲染是以面片而非射线作为处理单位的)，其描述如下：
+将实际渲染画面抽象至场景中，然后遍历所有面片，对于所有面片，将其渲染出的纹理变换粘贴至viewport的指定像素中，如果需要计算反射、AO等信息，则以遍历到的面片为第一人称viewport，渲染该viewport下的所有面片，并将相交到的面片变换拉伸（其实只需要按图片像素直接拉伸即可）至当前面片的current纹理上，最后递归总结出整体画面。概括地说，就是递归地遍历所有面片，并将当前正在处理的面片作为current viewport，然后将相机原点关于当前这个面片进行对称（模拟光线的反射行为），将可能会映射到当前面片上的所有面片的纹理进行变换扭曲，附加到当前面片的纹理上，返回给上一级递归函数栈进行继续的变换，从而实现金属的反射效果，对于漫反射效果，不进行递归，而是直接返回当前纹理。当前实现版本要求只使用三角形面片（方便实现和扩展），因此算法将Camera viewport作为场景中的两个三角形面片进行渲染，然后将这两个三角形的纹理直接输出到图片中。
+对于这个算法，有几点需要注意的地方： 
+
+1. 在遍历物体的时候，需要考虑到物体渲染的覆盖关系。对于覆盖关系，我有一个临时解决方案，即遍历获取到可能会投射在viewport上的所有物体的列表后，由远到近进行渲染，则这部分的时间复杂度为O(nlogn)（遍历所有投射的物体为n，可以考虑使用优先队列维护由远到近的关系，为logn，整合时间复杂度为nlogn） 
+2. AO等特性、漫反射等内容可能需要特化计算，但是你可以先忽略这些内容，专注于实现基本的面片纹理变换和渲染功能
+给出单个可以编译执行的C++文件，不考虑文件大小和代码行数，优先实现如上所说的所有功能，生成的图片写入PPM即可
+对于当前这轮对话，AO等特性可能涉及到采样内容，因此你无需实现，我将会后续进行编写。
+对于康奈尔盒子，你需要实现一个拥有四壁的Cornell Box和两个具有金属材质特性（镜面反射）的一蓝一黄的盒子的场景并渲染。另外，有一个必须要注意的事情就是，在代码实现中，对于Camera的渲染不应该按Ray发射计算颜色（否则会和传统光线追踪思路雷同），而是根据相机原点和viewport生成当前viewport的视锥体并遍历面片进行相交检测，之后对遍历到的面片进行反射（对称相机原点）之后调用该面片的当前函数进行递归，然后**直接把它返回的纹理贴到当前面片的当前纹理中**。
+我接下来会给你一个实现思路，请你按照如下思路实现代码：
+1. 你需要实现Vec3等基本数据结构。
+2. 实现Triangle类及相关运算（如triangle与triangle的相交等运算）
+3. 实现Camera类及相关运算（Camera存储相机原点及两个Viewport三角形，这个类的render函数不实现逻辑，仅调用两次渲染函数并将两个三角形的纹理转储至PPM）
+4. 实现渲染函数renderTriangleWithTriangle，传入三角形面片列表及相机原点和当前面片(以当前面片作为viewport)，该函数首先检查材质类型，假如是Diffuse漫反射类型则直接返回材质纹理，如果是Reflective镜面反射类型的话，则需要根据物体纹理进行计算，首先初始化当前面片在指定相机原点下将会显示出的纹理图片，根据传入的viewport原点和当前面片的三个点计算出视锥体（注意这个视锥体顶部是被削平的），然后遍历所有物体，检测它们跟当前视锥体是否相交或（被）包围，并将是的面片存储进一个列表（建议存指针，速度快），然后对这个列表根据距离进行排序（由远到近），之后遍历这个列表，对于列表中的每个面片，递归调用它们的renderTriangleWithTriangle函数获取它们应该显示出的纹理，之后根据目标面片的三个点和原点的连线与当前面片（viewport）的交点计算出目标面片将会映射到当前面片上的三个点，之后根据这三个点直接对材质进行拉伸变形，然后写入函数最开始定义的纹理图片中（可以考虑加入反走样），遍历完列表中的所有面片之后就可以返回当前的纹理图片了，关于函数的终止条件，可以定为当当前纹理投影在最终幕布上的面积大小小于某个阈值时停止递归（比如1~5个像素点大小，关于当前面片纹理图片初始化的时候设定的像素大小，你可以给renderTriangleWithTriangle这个函数加个表示预估长宽的参数）。
+
+
+
+V2:
+C++实现一个康奈尔盒子渲染器，采用基于三角形面片的投影纹理映射递归算法。该算法的核心思想是：将每个面片视为一个微型视口，通过递归投影变换组合纹理，模拟光线传播效果。
+
+### 算法原理
+1. **基础概念**：
+   - 场景由三角形面片构成，每个面片包含：几何信息、纹理、材质属性
+   - 相机由原点位置和两个三角形面片（左、右视口）定义
+   - 渲染过程从相机视口面片开始，递归处理可能影响最终图像的场景面片
+
+2. **递归投影流程**：
+   对于当前处理的面片（称为"当前视口面片"）：
+   a. 确定从相机原点通过当前视口面片可见的空间区域（一个平截头体）
+   b. 找出与该区域相交的所有场景面片
+   c. 对每个相交面片，根据其材质执行相应投影操作
+   d. 将投影结果累积到输出图像
+
+3. **材质处理逻辑**：
+   - **相机视口材质**：作为递归起点，不直接贡献颜色，只组织后续渲染
+   - **漫反射材质**：单次投影，将面片纹理变换到最终图像平面
+   - **金属反射材质**：两次投影，先投影到图像平面，再递归处理反射内容
+
+### 关键实现细节
+
+1. **投影变换计算**：
+   对于面片A投影到面片B，需要计算从A纹理坐标到B纹理坐标的投影矩阵。
+   这涉及：
+   - 计算A到相机原点的透视投影
+   - 计算从该投影到B平面的投影变换
+   - 组合变换得到最终纹理映射
+
+2. **视锥体相交检测**：
+   对于三角形T和相机原点O，定义视锥体为O与T形成的三棱锥。
+   另一个三角形与之相交的判断标准：至少一个顶点在视锥体内或与视锥体边界相交。
+
+3. **递归反射处理**：
+   对于金属面片M：
+   a. 计算相机原点O关于M平面的镜像点O'
+   b. 以O'为新原点，M为新视口面片
+   c. 递归渲染O'通过M可见的场景内容
+   d. 将结果与M的纹理混合后投影到上一级
+
+4. **覆盖关系处理**：
+   采用画家算法：在每个递归层级，按面片到视口平面的距离从远到近处理。
+   实现时可在收集到相交面片后排序处理。
+
+5. **终止条件**：
+   当被投影面片在目标图像上的覆盖区域小于阈值（如4个像素）时停止递归。
+   避免无限递归和性能问题。
+
+### 具体实现要求
+
+1. **数据结构**：
+   - Vec3：三维向量，支持点积、叉积、归一化等运算
+   - Triangle：三角形，包含三个顶点、纹理坐标、材质信息
+   - Material：材质定义，包含类型（漫反射/金属）、纹理颜色、反射率等
+   - Image：图像类，支持像素读写，输出PPM格式
+
+2. **核心函数**：
+   ```cpp
+   // 主渲染函数
+   void renderTriangle(
+       const Triangle& viewportTri,    // 当前视口三角形
+       const Vec3& cameraOrigin,       // 当前相机原点
+       const Triangle& targetTri,      // 目标纹理三角形（最终图像平面）
+       Image& outputImage,             // 输出图像
+       int recursionDepth = 0          // 递归深度控制
+   );

experiments/Thinking.txt

@@ -0,0 +1,2 @@
+我现在有一个与光线追踪类似，但是效率优于传统光线追踪的算法，它的反射、折射等计算以面片为单位进行处理，而不是光线追踪的像素作为单位。其核心模块如下：
+1. 首先是追踪模块，该模块是整个算法的核心，你可以在当前阶段使用一个函数实现。该函数有几个参数，分别是当前面片、

experiments/counter.sh

@@ -0,0 +1,264 @@
+#!/usr/bin/env bash
+# 代码行数统计器 - 增强版 (Bash 版)
+# 尽量等效还原原 PowerShell 脚本功能与输出
+
+set -uo pipefail
+
+# 彩色输出映射（接近 PS 的颜色名）
+declare -A COLOR_MAP=(
+  ["Cyan"]="\e[36m"
+  ["Green"]="\e[32m"
+  ["Yellow"]="\e[33m"
+  ["Magenta"]="\e[35m"
+  ["Blue"]="\e[34m"
+  ["Red"]="\e[31m"
+  ["White"]="\e[97m"
+  ["Gray"]="\e[90m"
+  ["DarkYellow"]="\e[33m"
+  ["Reset"]="\e[0m"
+)
+
+# 配置：类型 → 扩展列表、颜色
+# 说明：扩展以 "*.ext" 形式书写；内部会派生出 ".ext" 用于匹配
+declare -A TYPE_COLOR
+declare -A TYPE_EXTS
+TYPE_COLOR["C/C++"]="Cyan"
+TYPE_EXTS["C/C++"]='*.c *.cpp *.cc *.cxx *.h *.hpp *.hh *.hxx'
+
+TYPE_COLOR["C#"]="Green"
+TYPE_EXTS["C#"]='*.cs'
+
+TYPE_COLOR["Java"]="Yellow"
+TYPE_EXTS["Java"]='*.java'
+
+TYPE_COLOR["Python"]="Magenta"
+TYPE_EXTS["Python"]='*.py *.pyw'
+
+TYPE_COLOR["JavaScript"]="Blue"
+TYPE_EXTS["JavaScript"]='*.js *.jsx *.ts *.tsx'
+
+TYPE_COLOR["Web"]="Red"
+TYPE_EXTS["Web"]='*.html *.htm *.css *.scss *.less *.sass'
+
+TYPE_COLOR["Shell"]="White"
+TYPE_EXTS["Shell"]='*.sh *.bash *.ps1 *.psm1 *.psd1'
+
+TYPE_COLOR["配置/数据"]="Gray"
+TYPE_EXTS["配置/数据"]='*.xml *.json *.yaml *.yml *.ini *.cfg *.config'
+
+TYPE_COLOR["其他代码"]="DarkYellow"
+TYPE_EXTS["其他代码"]='*.go *.rs *.rb *.php *.swift *.kt *.scala'
+
+# 构建 扩展后缀(.ext) → 类型 的快速映射
+declare -A SUFFIX_TYPE
+for t in "${!TYPE_EXTS[@]}"; do
+  for ext in ${TYPE_EXTS[$t]}; do
+    # 将 "*.py" 转为 ".py"；统一小写匹配
+    suf=".${ext#*.}"
+    suf="$(printf '%s' "$suf" | tr '[:upper:]' '[:lower:]')"
+    SUFFIX_TYPE["$suf"]="$t"
+  done
+done
+
+# 标题
+printf "%b========================================%b\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+printf "%b       代码行数统计%b\n" "${COLOR_MAP[Yellow]}" "${COLOR_MAP[Reset]}"
+printf "%b========================================%b\n\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+
+# 当前目录
+current_dir="$(pwd)"
+printf "%b扫描目录: %s%b\n\n" "${COLOR_MAP[Gray]}" "$current_dir" "${COLOR_MAP[Reset]}"
+
+# 统计变量
+total_lines=0
+total_files=0
+declare -A type_files
+declare -A type_lines
+start_time_ns=$(date +%s%N)
+
+# 初始化类型统计
+for t in "${!TYPE_EXTS[@]}"; do
+  type_files["$t"]=0
+  type_lines["$t"]=0
+done
+
+# 收集全部文件（按各扩展累积）
+# 说明：尽量贴近 PS：按类型/扩展多次递归收集再合并
+# 使用 -iname 实现大小写不敏感匹配
+mapfile -d '' ALL_FILES < <(
+  {
+    for t in "${!TYPE_EXTS[@]}"; do
+      for ext in ${TYPE_EXTS[$t]}; do
+        find "$current_dir" -type f -iname "${ext}" -print0 2>/dev/null
+      done
+    done
+  } | awk -v RS='\0' '!seen[$0]++{printf "%s\0",$0}' # 去重，保持与 PS 相近的行为
+)
+
+total_to_process=${#ALL_FILES[@]}
+
+if (( total_to_process == 0 )); then
+  printf "%b未找到任何源代码文件！%b\n" "${COLOR_MAP[Red]}" "${COLOR_MAP[Reset]}"
+  printf "%b请检查当前目录是否包含源代码文件。%b\n" "${COLOR_MAP[Gray]}" "${COLOR_MAP[Reset]}"
+  exit 0
+fi
+
+printf "%b找到 %d 个文件需要处理...%b\n\n" "${COLOR_MAP[Gray]}" "$total_to_process" "${COLOR_MAP[Reset]}"
+
+# 简易进度显示
+processed=0
+
+# 为格式对齐做准备
+pad_right() { # $1=text $2=width
+  local s="$1" w="$2" len=${#1}
+  if (( len < w )); then printf "%s%*s" "$s" $((w-len)) ""; else printf "%s" "$s"; fi
+}
+
+# 统计循环
+for file in "${ALL_FILES[@]}"; do
+  ((processed++))
+  # 百分比
+  percent=$(( processed * 100 / total_to_process ))
+
+  # 进度行（覆盖式）
+  base="${file##*/}"
+  printf "\r正在统计代码行数 | 处理文件: %s | 已处理: %d / %d | %3d%%" \
+    "$(pad_right "$base" 30)" "$processed" "$total_to_process" "$percent"
+
+  # 读取行数
+  lines=0
+  if ! lines=$(wc -l <"$file" 2>/dev/null); then
+    # 模拟 PS 的警告输出（另起一行）
+    printf "\n%b  警告: 无法读取文件 %s%b\n" "${COLOR_MAP[Red]}" "$base" "${COLOR_MAP[Reset]}"
+    continue
+  fi
+
+  (( total_lines += lines ))
+  (( total_files++ ))
+
+  # 分类归属（根据扩展名后缀）
+  fname_lower="$(printf '%s' "$file" | tr '[:upper:]' '[:lower:]')"
+  # 取 ".ext"（含点），若没有点，则设为空
+  suffix=""
+  if [[ "$fname_lower" == *.* ]]; then
+    suffix=".${fname_lower##*.}"
+  fi
+
+  t="${SUFFIX_TYPE[$suffix]:-}"
+  if [[ -n "$t" ]]; then
+    (( type_files["$t"] += 1 ))
+    (( type_lines["$t"] += lines ))
+  fi
+done
+
+# 完成进度条
+printf "\n"
+
+# 耗时
+end_time_ns=$(date +%s%N)
+duration_ns=$(( end_time_ns - start_time_ns ))
+# 转为 mm:ss.mmm
+total_ms=$(( duration_ns / 1000000 ))
+mm=$(( (total_ms / 60000) % 60 ))
+ss=$(( (total_ms / 1000) % 60 ))
+ms=$(( total_ms % 1000 ))
+
+# 详细统计标题
+printf "\n%b========================================%b\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+printf "%b            统计结果详情%b\n" "${COLOR_MAP[Yellow]}" "${COLOR_MAP[Reset]}"
+printf "%b========================================%b\n\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+
+# 按类型按行数降序输出
+# 收集有文件的类型
+types_sorted=()
+while IFS= read -r line; do
+  types_sorted+=("$line")
+done < <(
+  for t in "${!TYPE_EXTS[@]}"; do
+    if (( type_files["$t"] > 0 )); then
+      printf "%s\t%d\n" "$t" "${type_lines["$t"]}"
+    fi
+  done | sort -k2,2nr | awk -F'\t' '{print $1}'
+)
+
+for t in "${types_sorted[@]}"; do
+  files=${type_files["$t"]}
+  lines=${type_lines["$t"]}
+  if (( files > 0 )); then
+    percent=0
+    if (( total_lines > 0 )); then
+      # 保留两位小数
+      percent=$(awk -v a="$lines" -v b="$total_lines" 'BEGIN{printf("%.2f", (b>0)?(a*100.0/b):0)}')
+    fi
+    color_name="${TYPE_COLOR[$t]}"
+    color="${COLOR_MAP[$color_name]}"
+    reset="${COLOR_MAP[Reset]}"
+    printf "%b%-15s 文件: %4d  行数: %8d  (%6s%%)%b\n" "$color" "$t" "$files" "$lines" "$percent" "$reset"
+  fi
+done
+
+# 汇总
+printf "\n%b========================================%b\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+printf "%b汇总统计%b\n" "${COLOR_MAP[Yellow]}" "${COLOR_MAP[Reset]}"
+printf "%b========================================%b\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+
+printf "%b总文件数:  %d%b\n" "${COLOR_MAP[Cyan]}" "$total_files" "${COLOR_MAP[Reset]}"
+printf "%b总代码行:  %d%b\n" "${COLOR_MAP[Green]}" "$total_lines" "${COLOR_MAP[Reset]}"
+printf "%b处理文件:  %d / %d%b\n" "${COLOR_MAP[Gray]}" "$processed" "$total_to_process" "${COLOR_MAP[Reset]}"
+printf "%b统计耗时:  %02d:%02d.%03d%b\n" "${COLOR_MAP[Magenta]}" "$mm" "$ss" "$ms" "${COLOR_MAP[Reset]}"
+
+# 文件大小统计
+total_size_bytes=0
+# 使用 stat 读取字节数（兼容 GNU/ BSD）
+stat_size() {
+  local f="$1"
+  if stat --version >/dev/null 2>&1; then
+    stat -c %s -- "$f"
+  else
+    stat -f %z -- "$f"
+  fi
+}
+for f in "${ALL_FILES[@]}"; do
+  if sz=$(stat_size "$f" 2>/dev/null); then
+    (( total_size_bytes += sz ))
+  fi
+done
+avg_size_bytes=0
+if (( total_files > 0 )); then
+  avg_size_bytes=$(( total_size_bytes / total_files ))
+fi
+to_mb=$(awk -v b="$total_size_bytes" 'BEGIN{printf("%.2f", b/1024/1024)}')
+avg_kb=$(awk -v b="$avg_size_bytes"  'BEGIN{printf("%.2f", b/1024)}')
+
+printf "%b总文件大小: %s MB%b\n" "${COLOR_MAP[Blue]}" "$to_mb" "${COLOR_MAP[Reset]}"
+printf "%b平均文件大小: %s KB%b\n" "${COLOR_MAP[Blue]}" "$avg_kb" "${COLOR_MAP[Reset]}"
+
+# 导出 CSV
+printf "\n"
+read -r -p "是否导出统计结果到CSV文件? (Y/N) " exportChoice
+if [[ "$exportChoice" == "Y" || "$exportChoice" == "y" ]]; then
+  timestamp="$(date +%Y%m%d_%H%M%S)"
+  csv_path="${current_dir}/code_stats_${timestamp}.csv"
+  {
+    # 头部
+    printf "文件类型,文件数量,代码行数,占比百分比\n"
+    for t in "${types_sorted[@]}"; do
+      files=${type_files["$t"]}
+      lines=${type_lines["$t"]}
+      if (( files > 0 )); then
+        percent=$(awk -v a="$lines" -v b="$total_lines" 'BEGIN{printf("%.2f", (b>0)?(a*100.0/b):0)}')
+        # 以 CSV 形式输出（简单场景，t 不含逗号）
+        printf "%s,%d,%d,%s\n" "$t" "$files" "$lines" "$percent"
+      fi
+    done
+    # 汇总行
+    printf "总计,%d,%d,100\n" "$total_files" "$total_lines"
+  } > "$csv_path"
+  printf "%b统计结果已导出到: %s%b\n" "${COLOR_MAP[Green]}" "$csv_path" "${COLOR_MAP[Reset]}"
+fi
+
+# 任意键退出
+printf "\n%b统计完成！按任意键退出...%b" "${COLOR_MAP[Gray]}" "${COLOR_MAP[Reset]}"
+# shellcheck disable=SC2162
+read -rsn1 _ 2>/dev/null || true
+printf "\n"

experiments/output_fixed.ppm

@@ -0,0 +1,515 @@
+P3
+512 512
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experiments/polymorphism/CRTP.cpp

@@ -0,0 +1,71 @@
+// crtp_test.cpp
+#include <iostream>
+#include <vector>
+#include <chrono>
+
+template<typename Derived>
+struct Material {
+    void render() const {
+        static_cast<const Derived*>(this)->renderImpl();
+    }
+};
+
+void process(const auto& mat) {
+    mat.render();
+}
+
+struct Metal : Material<Metal> {
+    float data[4];
+    void renderImpl() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Lambertian : Material<Lambertian> {
+    float data[4];
+    void renderImpl() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Plastic : Material<Plastic> {
+    float data[4];
+    void renderImpl() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Glass : Material<Glass> {
+    float data[4];
+    void renderImpl() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+int main() {
+    const size_t count = 400000;
+    std::vector<Metal> metals(count / 4);
+    std::vector<Lambertian> lambertians(count / 4);
+    std::vector<Plastic> plastics(count / 4);
+    std::vector<Glass> glasses(count / 4);
+	std::vector<Material<Metal>*> material_ptrs;
+
+    auto start_time = std::chrono::high_resolution_clock::now();
+
+	for(const auto& m : metals) m.render();
+	for(const auto& l : lambertians) l.render();
+	for(const auto& p : plastics) p.render();
+	for(const auto& g : glasses) g.render();
+
+    // for (const auto& m : metals) process(m);
+    // for (const auto& l : lambertians) process(l);
+    // for (const auto& p : plastics) process(p);
+    // for (const auto& g : glasses) process(g);
+
+    auto end_time = std::chrono::high_resolution_clock::now();
+
+    auto duration = std::chrono::duration_cast<std::chrono::microseconds>(end_time - start_time);
+    std::cout << "CRTP Static Polymorphism Execution Time: " << duration.count() << " µs\n";
+
+    return 0;
+}

experiments/polymorphism/ecs.cpp

@@ -0,0 +1,76 @@
+// ecs_test.cpp
+#include <iostream>
+#include <vector>
+#include <chrono>
+#include <algorithm>
+
+enum class MaterialType {
+    Metal,
+    Lambertian,
+    Plastic,
+    Glass
+};
+
+struct MaterialComponent {
+    MaterialType type;
+    float data[4]; // 模拟复杂状态
+};
+
+void renderMetal(const MaterialComponent&) {
+    asm volatile("" ::: "memory"); // 防止编译器过度优化，模拟运算
+}
+
+void renderLambertian(const MaterialComponent&) {
+    asm volatile("" ::: "memory");
+}
+
+void renderPlastic(const MaterialComponent&) {
+    asm volatile("" ::: "memory");
+}
+
+void renderGlass(const MaterialComponent&) {
+    asm volatile("" ::: "memory");
+}
+
+void processECS(std::vector<MaterialComponent>& materials) {
+    // 按类型排序
+    // std::sort(materials.begin(), materials.end(),
+    //           [](const MaterialComponent& a, const MaterialComponent& b) {
+    //               return a.type < b.type;
+    //           });
+
+    size_t start = 0;
+    for (size_t i = 1; i <= materials.size(); ++i) {
+        if (i == materials.size() || materials[i].type != materials[start].type) {
+            for (size_t j = start; j < i; ++j) {
+                switch (materials[j].type) {
+                    case MaterialType::Metal: renderMetal(materials[j]); break;
+                    case MaterialType::Lambertian: renderLambertian(materials[j]); break;
+                    case MaterialType::Plastic: renderPlastic(materials[j]); break;
+                    case MaterialType::Glass: renderGlass(materials[j]); break;
+                }
+            }
+            start = i;
+        }
+    }
+}
+
+int main() {
+    const size_t count = 400000;
+    std::vector<MaterialComponent> materials(count);
+
+    for (size_t i = 0; i < count; ++i) {
+        materials[i].type = static_cast<MaterialType>(i % 4);
+        for (int j = 0; j < 4; ++j)
+            materials[i].data[j] = static_cast<float>(i + j);
+    }
+
+    auto start_time = std::chrono::high_resolution_clock::now();
+    processECS(materials);
+    auto end_time = std::chrono::high_resolution_clock::now();
+
+    auto duration = std::chrono::duration_cast<std::chrono::microseconds>(end_time - start_time);
+    std::cout << "ECS Execution Time: " << duration.count() << " µs\n";
+
+    return 0;
+}

experiments/polymorphism/empty_test.cpp

@@ -0,0 +1,22 @@
+// baseline_asm.cpp
+#include <iostream>
+#include <chrono>
+#include <cstddef>
+
+int main() {
+    const size_t count = 400000;
+
+    auto start_time = std::chrono::high_resolution_clock::now();
+
+    for (size_t i = 0; i < count; ++i) {
+        asm volatile("" ::: "memory");
+    }
+
+    auto end_time = std::chrono::high_resolution_clock::now();
+
+    auto duration = std::chrono::duration_cast<std::chrono::microseconds>(end_time - start_time);
+    std::cout << "Baseline (400000x asm volatile(\"\" ::: \"memory\")) Time: "
+              << duration.count() << " us\n";
+
+    return 0;
+}

experiments/polymorphism/stdvariant.cpp

@@ -0,0 +1,66 @@
+// variant_test.cpp
+#include <iostream>
+#include <vector>
+#include <variant>
+#include <chrono>
+
+struct Metal {
+    float data[4];
+    void render() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Lambertian {
+    float data[4];
+    void render() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Plastic {
+    float data[4];
+    void render() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Glass {
+    float data[4];
+    void render() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+using Material = std::variant<Metal, Lambertian, Plastic, Glass>;
+
+void visitMaterial(Material& mat) {
+    std::visit([](auto& m) {
+        m.render();
+    }, mat);
+}
+
+int main() {
+    const size_t count = 400000;
+    std::vector<Material> materials(count);
+
+    for (size_t i = 0; i < count; ++i) {
+        switch (i % 4) {
+            case 0: materials[i] = Metal{{static_cast<float>(i), 0, 0, 0}}; break;
+            case 1: materials[i] = Lambertian{{static_cast<float>(i), 0, 0, 0}}; break;
+            case 2: materials[i] = Plastic{{static_cast<float>(i), 0, 0, 0}}; break;
+            case 3: materials[i] = Glass{{static_cast<float>(i), 0, 0, 0}}; break;
+        }
+    }
+
+    auto start_time = std::chrono::high_resolution_clock::now();
+    for (auto& mat : materials) {
+        visitMaterial(mat);
+    }
+    auto end_time = std::chrono::high_resolution_clock::now();
+
+    auto duration = std::chrono::duration_cast<std::chrono::microseconds>(end_time - start_time);
+    std::cout << "std::variant Execution Time: " << duration.count() << " µs\n";
+
+    return 0;
+}

experiments/polymorphism/test_record.txt

@@ -0,0 +1,79 @@
+// 确认代码
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> ls
+compiled  CRTP.cpp  ecs.cpp  stdvariant.cpp  type_erase.cpp  virtual_function.cpp
+
+// 编译代码
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 CRTP.cpp -o compiled/CRTP_O0 -O0
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 CRTP.cpp -o compiled/CRTP_O2 -O2
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 ecs.cpp -o compiled/ecs_O0 -O0
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 ecs.cpp -o compiled/ecs_O2 -O2
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 stdvariant.cpp -o compiled/stdvariant_O0 -O0
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 stdvariant.cpp -o compiled/stdvariant_O2 -O2
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 type_erase.cpp -o compiled/type_erase_O0 -O0
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 type_erase.cpp -o compiled/type_erase_O2 -O2
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 virtual_function.cpp -o compiled/virtual_function_O0 -O0
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> g++ -std=c++20 virtual_function.cpp -o compiled/virtual_function_O2 -O2
+
+// 确认编译结果正确
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism]
+└-> cd compiled/
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ls
+CRTP_O0  ecs_O0  stdvariant_O0  type_erase_O0  virtual_function_O0
+CRTP_O2  ecs_O2  stdvariant_O2  type_erase_O2  virtual_function_O2
+
+// 运行并记录时间
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./CRTP_O0
+CRTP Static Polymorphism Execution Time: 6629 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./CRTP_O2
+CRTP Static Polymorphism Execution Time: 88 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./ecs_O0
+ECS Execution Time: 23662 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./ecs_O2
+ECS Execution Time: 2847 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./stdvariant_O0
+std::variant Execution Time: 35229 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./stdvariant_O2
+std::variant Execution Time: 373 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./type_erase_O0
+Type Erasure (std::function) Execution Time: 23404 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./type_erase_O2
+Type Erasure (std::function) Execution Time: 3712 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./virtual_function_O0
+Virtual Function Execution Time: 20982 µs
+┌[Ternary_Operator@/toDataDrive/ARE/experiments/polymorphism/compiled]
+└-> ./virtual_function_O2
+Virtual Function Execution Time: 6044 µs
+
+// 综合测试成绩:
+// CRTP: -O0->6629 µs, -O2->88 µs
+// std::variant: -O0->35229 µs, -O2->373 µs
+// Type Erasure: -O0->23404 µs, -O2->3712 µs
+// ECS: -O0->23662 µs, -O2->2847 µs
+// Virtual Function: -O0->20982 µs, -O2->6044 µs
+
+// -O0: CRTP > Virtual Function > Type Erasure ~= ECS > std::variant
+// -O2: CRTP > std::variant > ECS > Type Erasure > Virtual Function
+
+
+// 综合考虑，引擎采用CRTP多态实现方法。

experiments/polymorphism/tosmethod.cpp

@@ -0,0 +1,192 @@
+#include <chrono>
+#include <cstddef>
+#include <iostream>
+#include <stdexcept>
+#include <type_traits>
+#include <unordered_map>
+#include <utility>
+#include <variant>
+#include <vector>
+
+// -----------------------------
+// 1) 类型擦除：一个稳定的“句柄”类型
+//    - 内部：void* + render_fn + destroy_fn
+//    - move-only，语义类似 unique_ptr
+// -----------------------------
+struct MaterialHandle {
+    using RenderFn = void (*)(const void*) noexcept;
+    using DestroyFn = void (*)(void*) noexcept;
+
+    void* ptr = nullptr;
+    RenderFn render_fn = nullptr;
+    DestroyFn destroy_fn = nullptr;
+
+    MaterialHandle() = default;
+
+    MaterialHandle(void* p, RenderFn r, DestroyFn d) noexcept
+        : ptr(p), render_fn(r), destroy_fn(d) {}
+
+    MaterialHandle(const MaterialHandle&) = delete;
+    MaterialHandle& operator=(const MaterialHandle&) = delete;
+
+    MaterialHandle(MaterialHandle&& other) noexcept
+        : ptr(other.ptr), render_fn(other.render_fn), destroy_fn(other.destroy_fn) {
+        other.ptr = nullptr;
+        other.render_fn = nullptr;
+        other.destroy_fn = nullptr;
+    }
+
+    MaterialHandle& operator=(MaterialHandle&& other) noexcept {
+        if (this == &other) return *this;
+        reset();
+        ptr = other.ptr;
+        render_fn = other.render_fn;
+        destroy_fn = other.destroy_fn;
+        other.ptr = nullptr;
+        other.render_fn = nullptr;
+        other.destroy_fn = nullptr;
+        return *this;
+    }
+
+    ~MaterialHandle() { reset(); }
+
+    void reset() noexcept {
+        if (ptr) {
+            destroy_fn(ptr);
+        }
+        ptr = nullptr;
+        render_fn = nullptr;
+        destroy_fn = nullptr;
+    }
+
+    void render() const noexcept {
+        // 假设创建时已填好函数指针
+        render_fn(ptr);
+    }
+
+    template <class T, class... Args>
+    static MaterialHandle make(Args&&... args) {
+        T* obj = new T(std::forward<Args>(args)...);
+        return MaterialHandle{
+            obj,
+            [](const void* p) noexcept {
+                static_cast<const T*>(p)->render();
+            },
+            [](void* p) noexcept {
+                delete static_cast<T*>(p);
+            },
+        };
+    }
+};
+
+// 你要求用 std::variant：但不枚举 Metal/Lambertian/...
+// variant 只放一个稳定包装类型即可，永远不需要随扩展修改。
+using Material = std::variant<std::monostate, MaterialHandle>;
+
+// -----------------------------
+// 2) 注册工厂：通过 id -> creator() 创建 Material
+// -----------------------------
+class MaterialFactory {
+public:
+    using Creator = Material (*)();
+
+    static MaterialFactory& instance() {
+        static MaterialFactory f;
+        return f;
+    }
+
+    void reg(int id, Creator creator) {
+        creators_[id] = creator;
+    }
+
+    Material create(int id) const {
+        auto it = creators_.find(id);
+        if (it == creators_.end()) {
+            throw std::runtime_error("MaterialFactory: unknown material id");
+        }
+        return (it->second)();
+    }
+
+private:
+    std::unordered_map<int, Creator> creators_;
+};
+
+template <class T>
+struct MaterialRegistrar {
+    explicit MaterialRegistrar(int id) {
+        // 无捕获 lambda 可转换为函数指针 Creator
+        MaterialFactory::instance().reg(id, []() -> Material {
+            return Material{MaterialHandle::make<T>()};
+        });
+    }
+};
+
+// -----------------------------
+// 3) “派生类”：不继承基类、不写虚函数
+//    只需要提供 render() 即可
+// -----------------------------
+struct Metal {
+    float data[4]{};
+    void render() const noexcept { asm volatile("" ::: "memory"); }
+};
+
+struct Lambertian {
+    float data[4]{};
+    void render() const noexcept { asm volatile("" ::: "memory"); }
+};
+
+struct Plastic {
+    float data[4]{};
+    void render() const noexcept { asm volatile("" ::: "memory"); }
+};
+
+struct Glass {
+    float data[4]{};
+    void render() const noexcept { asm volatile("" ::: "memory"); }
+};
+
+// -----------------------------
+// 4) 注册：扩展新类型时，最多“注册一下”
+//    你也可以把注册放到各自 .cpp 里，做到模块化插拔。
+// -----------------------------
+static MaterialRegistrar<Metal> reg_metal{0};
+static MaterialRegistrar<Lambertian> reg_lambertian{1};
+static MaterialRegistrar<Plastic> reg_plastic{2};
+static MaterialRegistrar<Glass> reg_glass{3};
+
+// -----------------------------
+// 5) 实验：创建 + 调用 render() 测时
+// -----------------------------
+int main() {
+    const std::size_t count = 400000;
+
+    std::vector<Material> materials;
+    materials.reserve(count);
+
+    for (std::size_t i = 0; i < count; ++i) {
+        const int id = static_cast<int>(i % 4);
+        materials.emplace_back(MaterialFactory::instance().create(id));
+    }
+
+    const auto start_time = std::chrono::high_resolution_clock::now();
+
+    for (const auto& mat : materials) {
+        std::visit(
+            [](const auto& x) noexcept {
+                using X = std::decay_t<decltype(x)>;
+                if constexpr (std::is_same_v<X, std::monostate>) {
+                    // 空对象：不做任何事
+                } else {
+                    x.render(); // 函数指针调用，不走虚表
+                }
+            },
+            mat);
+    }
+
+    const auto end_time = std::chrono::high_resolution_clock::now();
+    const auto duration =
+        std::chrono::duration_cast<std::chrono::microseconds>(end_time - start_time);
+
+    std::cout << "Variant+Registry Execution Time: " << duration.count() << " us\n";
+    return 0;
+}

experiments/polymorphism/type_erase.cpp

@@ -0,0 +1,74 @@
+// type_erasure_test.cpp
+#include <iostream>
+#include <vector>
+#include <functional>
+#include <chrono>
+
+struct Metal {
+    float data[4];
+    void render() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Lambertian {
+    float data[4];
+    void render() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Plastic {
+    float data[4];
+    void render() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Glass {
+    float data[4];
+    void render() const {
+        asm volatile("" ::: "memory");
+    }
+};
+
+int main() {
+    const size_t count = 400000;
+    std::vector<std::function<void()>> renderers(count);
+
+    for (size_t i = 0; i < count; ++i) {
+        switch (i % 4) {
+            case 0: {
+                Metal m;
+                renderers[i] = [m]() { m.render(); };
+                break;
+            }
+            case 1: {
+                Lambertian l;
+                renderers[i] = [l]() { l.render(); };
+                break;
+            }
+            case 2: {
+                Plastic p;
+                renderers[i] = [p]() { p.render(); };
+                break;
+            }
+            case 3: {
+                Glass g;
+                renderers[i] = [g]() { g.render(); };
+                break;
+            }
+        }
+    }
+
+    auto start_time = std::chrono::high_resolution_clock::now();
+    for (const auto& fn : renderers) {
+        fn();
+    }
+    auto end_time = std::chrono::high_resolution_clock::now();
+
+    auto duration = std::chrono::duration_cast<std::chrono::microseconds>(end_time - start_time);
+    std::cout << "Type Erasure (std::function) Execution Time: " << duration.count() << " µs\n";
+
+    return 0;
+}

experiments/polymorphism/virtual_function.cpp

@@ -0,0 +1,64 @@
+// virtual_test.cpp
+#include <iostream>
+#include <vector>
+#include <chrono>
+#include <memory>
+
+class Material {
+public:
+    virtual ~Material() = default;
+    virtual void render() const = 0;
+};
+
+struct Metal : public Material {
+    float data[4];
+    void render() const override {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Lambertian : public Material {
+    float data[4];
+    void render() const override {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Plastic : public Material {
+    float data[4];
+    void render() const override {
+        asm volatile("" ::: "memory");
+    }
+};
+
+struct Glass : public Material {
+    float data[4];
+    void render() const override {
+        asm volatile("" ::: "memory");
+    }
+};
+
+int main() {
+    const size_t count = 400000;
+    std::vector<std::unique_ptr<Material>> materials(count);
+
+    for (size_t i = 0; i < count; ++i) {
+        switch(i % 4) {
+            case 0: materials[i] = std::make_unique<Metal>(); break;
+            case 1: materials[i] = std::make_unique<Lambertian>(); break;
+            case 2: materials[i] = std::make_unique<Plastic>(); break;
+            case 3: materials[i] = std::make_unique<Glass>(); break;
+        }
+    }
+
+    auto start_time = std::chrono::high_resolution_clock::now();
+    for (const auto& mat : materials) {
+        mat->render();
+    }
+    auto end_time = std::chrono::high_resolution_clock::now();
+
+    auto duration = std::chrono::duration_cast<std::chrono::microseconds>(end_time - start_time);
+    std::cout << "Virtual Function Execution Time: " << duration.count() << " µs\n";
+
+    return 0;
+}

experiments/rt.cpp

@@ -0,0 +1,403 @@
+#define _USE_MATH_DEFINES
+/*
+ *  Cornell Box —— 步进式三角渲染 + 金属反射 + AO + 漫反射染色
+ *  g++ cornell_box_tri_diffuse.cpp -std=c++11 -O2 -o cornell_box_tri_diffuse
+ */
+#include <algorithm>
+#include <chrono>
+#include <cmath>
+#include <cstdio>
+#include <iomanip>
+#include <iostream>
+#include <random>
+#include <vector>
+
+constexpr float EPS = 1e-5f;
+constexpr float INF = 1e30f;
+
+// ---------------------- 基础代数 ----------------------
+struct Vec3 {
+	float x, y, z;
+	Vec3(float xx = 0, float yy = 0, float zz = 0) : x(xx), y(yy), z(zz) {
+	}
+	Vec3 operator+(const Vec3 &b) const {
+		return Vec3(x + b.x, y + b.y, z + b.z);
+	}
+	Vec3 operator-(const Vec3 &b) const {
+		return Vec3(x - b.x, y - b.y, z - b.z);
+	}
+	Vec3 operator*(float s) const {
+		return Vec3(x * s, y * s, z * s);
+	}
+	Vec3 operator/(float s) const {
+		return Vec3(x / s, y / s, z / s);
+	}
+	float dot(const Vec3 &b) const {
+		return x * b.x + y * b.y + z * b.z;
+	}
+	Vec3 cross(const Vec3 &b) const {
+		return Vec3(y * b.z - z * b.y,
+			z * b.x - x * b.z,
+			x * b.y - y * b.x);
+	}
+	float length() const {
+		return std::sqrt(x * x + y * y + z * z);
+	}
+	Vec3 normalized() const {
+		return (*this) * (1.0f / length());
+	}
+	// 生成局部正交系，把(0,0,1)转到normal方向
+	Vec3 rotateToHemisphere(const Vec3 &normal, float u, float v) const {
+		Vec3 up = fabs(normal.z) < 0.999f ? Vec3(0, 0, 1) : Vec3(1, 0, 0);
+		Vec3 tangent = normal.cross(up).normalized();
+		Vec3 bitangent = normal.cross(tangent);
+		return tangent * u + bitangent * v + normal * std::sqrt(std::max(0.f, 1 - u * u - v * v));
+	}
+};
+
+// ---------------------- 颜色 ----------------------
+struct Color {
+	float r, g, b;
+	Color(float rr = 0, float gg = 0, float bb = 0) : r(rr), g(gg), b(bb) {
+	}
+	Color operator*(float s) const {
+		return Color(r * s, g * s, b * s);
+	}
+	Color operator*(const Color &c) const {
+		return Color(r * c.r, g * c.g, b * c.b);
+	}
+	Color operator+(const Color &c) const {
+		return Color(r + c.r, g + c.g, b + c.b);
+	}
+	void clamp() {
+		r = std::fmax(0.0f, std::fmin(1.0f, r));
+		g = std::fmax(0.0f, std::fmin(1.0f, g));
+		b = std::fmax(0.0f, std::fmin(1.0f, b));
+	}
+};
+
+// ---------------------- 纹理 ----------------------
+struct Texture {
+	virtual Color at(float u, float v) const = 0;
+	virtual ~Texture() {
+	}
+};
+struct SolidTexture : Texture {
+	Color c;
+	SolidTexture(Color cc) : c(cc) {
+	}
+	Color at(float, float) const override {
+		return c;
+	}
+};
+struct CheckerTexture : Texture {
+	Color a, b;
+	float scale;
+	CheckerTexture(Color c1, Color c2, float s = 10) : a(c1), b(c2), scale(s) {
+	}
+	Color at(float u, float v) const override {
+		int xx = int(std::floor(u * scale)), yy = int(std::floor(v * scale));
+		return ((xx + yy) % 2 == 0) ? a : b;
+	}
+};
+
+enum MaterialType {
+	MAT_DIFFUSE,
+	MAT_METAL
+};
+
+// ---------------------- 三角形 ----------------------
+struct Tri {
+	Vec3 v0, v1, v2;
+	Vec3 n;
+	Vec3 uv0, uv1, uv2;
+	Texture *tex;
+	MaterialType mat;
+	float reflect_ratio;
+	Color metal_tint;
+	Tri(Vec3 a, Vec3 b, Vec3 c, Vec3 t0, Vec3 t1, Vec3 t2, Texture *tx,
+		MaterialType m = MAT_DIFFUSE, float reflr = 0.f, Color tint = Color())
+		: v0(a), v1(b), v2(c), uv0(t0), uv1(t1), uv2(t2), tex(tx), mat(m), reflect_ratio(reflr), metal_tint(tint) {
+		n = (v1 - v0).cross(v2 - v0).normalized();
+	}
+	bool intersect(const Vec3 &o, const Vec3 &d, float &t, float &u, float &v) const {
+		Vec3 e1 = v1 - v0, e2 = v2 - v0, h = d.cross(e2), s = o - v0;
+		float a = e1.dot(h);
+		if (std::fabs(a) < EPS)
+			return false;
+		float f = 1.f / a;
+		u = f * s.dot(h);
+		if (u < 0 || u > 1)
+			return false;
+		Vec3 q = s.cross(e1);
+		v = f * d.dot(q);
+		if (v < 0 || u + v > 1)
+			return false;
+		t = f * e2.dot(q);
+		return t > EPS;
+	}
+	void bary2uv(float b0, float b1, float b2, float &u, float &v) const {
+		u = uv0.x * b0 + uv1.x * b1 + uv2.x * b2;
+		v = uv0.y * b0 + uv1.y * b1 + uv2.y * b2;
+	}
+};
+
+// ---------------------- 场景 ----------------------
+struct Scene {
+	std::vector<Tri> tris;
+	std::vector<Texture *> textures;
+	~Scene() {
+		for (Texture *t : textures)
+			delete t;
+	}
+	Scene() {
+		Texture *red = new SolidTexture(Color(0.8, 0.15, 0.15)),
+				*green = new SolidTexture(Color(0.15, 0.8, 0.15)),
+				*white = new SolidTexture(Color(0.8, 0.8, 0.8)),
+				*checker = new CheckerTexture(Color(0.9, 0.9, 0.9), Color(0.1, 0.1, 0.1), 8),
+				*meta = new SolidTexture(Color(0.93, 0.95, 1.0));
+		textures = { red, green, white, checker, meta };
+		pushQuad(-1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, red, MAT_METAL, 0.90f);
+		pushQuad(1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, green, MAT_METAL, 0.90f);
+		pushQuad(-1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, checker, MAT_METAL, 0.90f);
+		pushQuad(-1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, white, MAT_METAL, 0.90f);
+		pushQuad(-1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, white, MAT_METAL, 0.90f);
+		pushBox(-0.5f, -0.9f, 0.4f, 0.15f, white, MAT_METAL, 0.90f, Color(0.92, 0.94, 1.0));
+		pushBox(0.0f, -0.9f, 0.4f, 0.10f, meta, MAT_METAL, 0.90f, Color(0.92, 0.94, 1.0));
+	}
+	void pushQuad(float x0, float y0, float z0, float x1, float y1, float z1,
+		float x2, float y2, float z2, float x3, float y3, float z3,
+		Texture *t, MaterialType mat = MAT_DIFFUSE, float rrat = 0.0f, Color tint = Color()) {
+		tris.emplace_back(Vec3(x0, y0, z0), Vec3(x1, y1, z1), Vec3(x2, y2, z2),
+			Vec3(0, 0, 0), Vec3(1, 0, 0), Vec3(1, 1, 0), t, mat, rrat, tint);
+		tris.emplace_back(Vec3(x0, y0, z0), Vec3(x2, y2, z2), Vec3(x3, y3, z3),
+			Vec3(0, 0, 0), Vec3(1, 1, 0), Vec3(0, 1, 0), t, mat, rrat, tint);
+	}
+	void pushBox(float cx, float cy, float cz, float r, Texture *t,
+		MaterialType mat = MAT_DIFFUSE, float rrat = 0.0f, Color tint = Color()) {
+		float X[2] = { cx - r, cx + r }, Y[2] = { cy - r, cy + r }, Z[2] = { cz - r, cz + r };
+		pushQuad(X[0], Y[0], Z[0], X[1], Y[0], Z[0], X[1], Y[1], Z[0], X[0], Y[1], Z[0], t, mat, rrat, tint);
+		pushQuad(X[0], Y[0], Z[1], X[1], Y[0], Z[1], X[1], Y[1], Z[1], X[0], Y[1], Z[1], t, mat, rrat, tint);
+		pushQuad(X[0], Y[0], Z[0], X[0], Y[1], Z[0], X[0], Y[1], Z[1], X[0], Y[0], Z[1], t, mat, rrat, tint);
+		pushQuad(X[1], Y[0], Z[0], X[1], Y[1], Z[0], X[1], Y[1], Z[1], X[1], Y[0], Z[1], t, mat, rrat, tint);
+		pushQuad(X[0], Y[1], Z[0], X[1], Y[1], Z[0], X[1], Y[1], Z[1], X[0], Y[1], Z[1], t, mat, rrat, tint);
+		pushQuad(X[0], Y[0], Z[0], X[1], Y[0], Z[0], X[1], Y[0], Z[1], X[0], Y[0], Z[1], t, mat, rrat, tint);
+	}
+};
+
+// ---------------------- 视口 ----------------------
+struct Viewport {
+	int w, h;
+	std::vector<Color> pixels;
+	Viewport(int W, int H) : w(W), h(H), pixels(W * H) {
+	}
+	void set(int x, int y, const Color &c) {
+		if (x >= 0 && y >= 0 && x < w && y < h)
+			pixels[y * w + x] = c;
+	}
+	Color get(int x, int y) const {
+		return pixels[y * w + x];
+	}
+};
+
+struct HitRec {
+	int tri = -1;
+	float t = INF, u = 0, v = 0;
+};
+
+// ---------------------- 相交查询 ----------------------
+HitRec intersect(const Scene &scene, const Vec3 &o, const Vec3 &d) {
+	HitRec ret;
+	for (int i = 0; i < scene.tris.size(); ++i) {
+		float t, u, v;
+		if (scene.tris[i].intersect(o, d, t, u, v) && t < ret.t) {
+			ret = { i, t, u, v };
+		}
+	}
+	return ret;
+}
+
+// ---------------------- AO ----------------------
+float computeAO(const Scene &scene, const Vec3 &p, const Vec3 &n, std::mt19937 &rng) {
+	const int N = 32;
+	std::uniform_real_distribution<float> dist(0, 1);
+	int unoccluded = 0;
+	for (int i = 0; i < N; ++i) {
+		float u = dist(rng), v = dist(rng);
+		float theta = 2 * M_PI * u;
+		float phi = std::acos(1 - 2 * v);
+		float x = std::sin(phi) * std::cos(theta);
+		float y = std::sin(phi) * std::sin(theta);
+		float z = std::cos(phi);
+		if (z < 0)
+			z = -z;
+		Vec3 hemi(x, y, z);
+		Vec3 axis = Vec3(0, 0, 1).cross(n);
+		float sa = axis.length(), ca = Vec3(0, 0, 1).dot(n);
+		Vec3 d = hemi;
+		if (sa > EPS) {
+			axis = axis.normalized();
+			float ang = std::acos(ca);
+			d = d * std::cos(ang) + axis.cross(d) * std::sin(ang) + axis * (axis.dot(d)) * (1 - std::cos(ang));
+		}
+		d = d.normalized();
+		if (intersect(scene, p + n * EPS, d).tri == -1)
+			unoccluded++;
+	}
+	return 0.25f + 0.75f * (unoccluded / float(N));
+}
+
+// ---------------------- 路径追踪 ----------------------
+Color trace(const Scene &scene, const Vec3 &o, const Vec3 &d,
+	std::mt19937 &rng, int depth = 0) {
+	HitRec rec = intersect(scene, o, d);
+	if (rec.tri == -1)
+		return Color(0.06, 0.09, 0.14);
+
+	const Tri &tri = scene.tris[rec.tri];
+	Vec3 p = tri.v0 * (1 - rec.u - rec.v) + tri.v1 * rec.u + tri.v2 * rec.v;
+	float uu, vv;
+	tri.bary2uv(1 - rec.u - rec.v, rec.u, rec.v, uu, vv);
+	Color albedo = tri.tex->at(uu, vv);
+
+	// AO
+	float ao = computeAO(scene, p, tri.n, rng);
+
+	// 金属反射
+	if (tri.mat == MAT_METAL && depth == 0) {
+		Vec3 view = (o - p).normalized();
+		Vec3 refl = view - tri.n * 2 * view.dot(tri.n);
+		Color reflected = trace(scene, p + tri.n * EPS, refl, rng, depth + 1);
+		Color ret = albedo * (1 - tri.reflect_ratio) + reflected * tri.reflect_ratio * tri.metal_tint;
+		ret = ret * ao;
+		ret.clamp();
+		return ret;
+	}
+
+	// 漫反射
+	if (tri.mat == MAT_DIFFUSE) {
+		const int samples = 32;
+		const int max_bounce = 3;
+		Color accum;
+		std::uniform_real_distribution<float> dist(0, 1);
+		for (int s = 0; s < samples; ++s) {
+			// 余弦重要性采样
+			float r1 = dist(rng), r2 = dist(rng);
+			float phi = 2 * M_PI * r1;
+			float r2s = std::sqrt(r2);
+			Vec3 local(r2s * std::cos(phi), r2s * std::sin(phi), std::sqrt(1 - r2));
+			Vec3 world = Vec3(0, 0, 1).rotateToHemisphere(tri.n, local.x, local.y);
+			Vec3 newOrigin = p + tri.n * EPS;
+			Color throughput = albedo;
+			int b = 0;
+			Vec3 dir = world;
+			while (b < max_bounce) {
+				HitRec bRec = intersect(scene, newOrigin, dir);
+				if (bRec.tri == -1)
+					break;
+				const Tri &bTri = scene.tris[bRec.tri];
+				Vec3 bP = bTri.v0 * (1 - bRec.u - bRec.v) + bTri.v1 * bRec.u + bTri.v2 * bRec.v;
+				float bu, bv;
+				bTri.bary2uv(1 - bRec.u - bRec.v, bRec.u, bRec.v, bu, bv);
+				Color bAlbedo = bTri.tex->at(bu, bv);
+				throughput = throughput * bAlbedo;
+				// Russian Roulette
+				float p = std::fmax(throughput.r, std::fmax(throughput.g, throughput.b));
+				if (dist(rng) > p)
+					break;
+				throughput = throughput * (1 / p);
+				// 继续
+				Vec3 newDir;
+				if (bTri.mat == MAT_METAL) {
+					Vec3 view = (Vec3() - dir).normalized();
+					newDir = view - bTri.n * 2 * view.dot(bTri.n);
+				} else {
+					// 继续余弦采样
+					float nr1 = dist(rng), nr2 = dist(rng);
+					float nphi = 2 * M_PI * nr1;
+					float nr2s = std::sqrt(nr2);
+					Vec3 nlocal(nr2s * std::cos(nphi), nr2s * std::sin(nphi), std::sqrt(1 - nr2));
+					newDir = Vec3(0, 0, 1).rotateToHemisphere(bTri.n, nlocal.x, nlocal.y);
+				}
+				newOrigin = bP + bTri.n * EPS;
+				dir = newDir;
+				b++;
+			}
+			accum = accum + throughput;
+		}
+		albedo = albedo + accum * (1.0f / samples);
+	}
+
+	albedo = albedo * ao;
+	albedo.clamp();
+	return albedo;
+}
+
+// ---------------------- 渲染 ----------------------
+void render(const Scene &scene, const Vec3 &camPos, const Vec3 &camTarget,
+	const Vec3 &camUp, float fov, Viewport &vp) {
+	Vec3 forward = (camTarget - camPos).normalized();
+	Vec3 right = forward.cross(camUp).normalized();
+	Vec3 up = right.cross(forward);
+	float aspect = float(vp.w) / vp.h;
+	float scale = std::tan(fov * 0.5f * M_PI / 180.f);
+
+	auto t0 = std::chrono::high_resolution_clock::now();
+	uint64_t totalRays = 0;
+
+	std::random_device rd;
+	std::vector<std::mt19937> rngs(vp.h);
+	for (int y = 0; y < vp.h; ++y)
+		rngs[y] = std::mt19937(rd() + y);
+
+	for (int y = 0; y < vp.h; ++y) {
+		if (y % 16 == 0) {
+			auto t1 = std::chrono::high_resolution_clock::now();
+			float elapsed = std::chrono::duration<float>(t1 - t0).count();
+			float mrays = (totalRays / 1e6f) / (elapsed + 0.001f);
+			std::cerr << "\rProgress: " << std::setw(3) << y << "/" << vp.h
+					  << " rows  (" << std::fixed << std::setprecision(1)
+					  << (100.f * y / vp.h) << "%)  "
+					  << mrays << " MRays/s" << std::flush;
+		}
+		for (int x = 0; x < vp.w; ++x) {
+			float fx = (2 * (x + 0.5f) / vp.w - 1) * aspect * scale;
+			float fy = (1 - 2 * (y + 0.5f) / vp.h) * scale;
+			Vec3 dir = (forward + right * fx + up * fy).normalized();
+			Color col = trace(scene, camPos, dir, rngs[y], 0);
+			col.clamp();
+			vp.set(x, y, col);
+			totalRays += 32 + 32; // AO samples + diffuse samples
+		}
+	}
+	std::cerr << "\nRender complete.\n";
+}
+
+// ---------------------- 输出 ----------------------
+void writePPM(const Viewport &vp, const char *fn) {
+	FILE *f = fopen(fn, "wb");
+	fprintf(f, "P6\n%d %d\n255\n", vp.w, vp.h);
+	for (int y = 0; y < vp.h; ++y)
+		for (int x = 0; x < vp.w; ++x) {
+			Color c = vp.get(x, y);
+			c.clamp();
+			unsigned char r = (unsigned char)(std::pow(c.r, 1 / 2.2f) * 255);
+			unsigned char g = (unsigned char)(std::pow(c.g, 1 / 2.2f) * 255);
+			unsigned char b = (unsigned char)(std::pow(c.b, 1 / 2.2f) * 255);
+			fwrite(&r, 1, 1, f);
+			fwrite(&g, 1, 1, f);
+			fwrite(&b, 1, 1, f);
+		}
+	fclose(f);
+}
+
+// ---------------------- main ----------------------
+int main() {
+	int w = 512, h = 512;
+	Scene scene;
+	Viewport vp(w, h);
+	render(scene, Vec3(0, 0, 4), Vec3(0, 0, 0), Vec3(0, 1, 0), 50.f, vp);
+	writePPM(vp, "out_diffuse.ppm");
+	std::cout << "Saved to out_diffuse.ppm\n";
+	return 0;
+}

experiments/rt.py

@@ -0,0 +1,463 @@
+# -*- coding: utf-8 -*-
+"""
+简易三角形康奈尔盒渲染器（递归反射版本）
+
+特性：
+- 只用三角形面片构建场景（墙面、灯、两个盒子）
+- Camera 视口被视为一个平面（理论上可拆成两个三角形）
+- 漫反射表面：不递归，直接光照
+- 镜面（金属）表面：递归反射，模拟金属反射
+- 输出 PPM 图片：cornell.ppm
+"""
+
+import math
+
+# ======================
+# 基础向量运算
+# ======================
+
+def v_add(a, b):
+    return (a[0] + b[0], a[1] + b[1], a[2] + b[2])
+
+def v_sub(a, b):
+    return (a[0] - b[0], a[1] - b[1], a[2] - b[2])
+
+def v_mul(a, s):
+    # 向量 * 标量
+    return (a[0] * s, a[1] * s, a[2] * s)
+
+def v_mul_comp(a, b):
+    # 分量乘（用于颜色调制）
+    return (a[0] * b[0], a[1] * b[1], a[2] * b[2])
+
+def v_dot(a, b):
+    return a[0]*b[0] + a[1]*b[1] + a[2]*b[2]
+
+def v_cross(a, b):
+    return (
+        a[1]*b[2] - a[2]*b[1],
+        a[2]*b[0] - a[0]*b[2],
+        a[0]*b[1] - a[1]*b[0]
+    )
+
+def v_length(a):
+    return math.sqrt(v_dot(a, a))
+
+def v_norm(a):
+    l = v_length(a)
+    if l == 0:
+        return (0.0, 0.0, 0.0)
+    return (a[0]/l, a[1]/l, a[2]/l)
+
+def v_reflect(d, n):
+    # 反射方向：r = d - 2*(d·n)*n
+    dn = v_dot(d, n)
+    return v_sub(d, v_mul(n, 2.0 * dn))
+
+# ======================
+# 材质和三角形定义
+# ======================
+
+class Material:
+    def __init__(self, color=(1.0, 1.0, 1.0),
+                 emission=(0.0, 0.0, 0.0),
+                 kind="diffuse",
+                 reflectivity=1.0):
+        """
+        kind: "diffuse" 或 "mirror"
+        color: 基础颜色/反射率
+        emission: 自发光颜色（光源）
+        reflectivity: 镜面反射强度（0~1）
+        """
+        self.color = color
+        self.emission = emission
+        self.kind = kind
+        self.reflectivity = reflectivity
+
+class Triangle:
+    def __init__(self, v0, v1, v2, material):
+        self.v0 = v0
+        self.v1 = v1
+        self.v2 = v2
+        self.material = material
+        # 预计算几何法线
+        self.normal = v_norm(v_cross(v_sub(v1, v0), v_sub(v2, v0)))
+
+    def intersect(self, ray_o, ray_d, eps=1e-6):
+        """
+        Möller–Trumbore 三角形求交
+        返回 (t, u, v) 或 None
+        """
+        v0, v1, v2 = self.v0, self.v1, self.v2
+        edge1 = v_sub(v1, v0)
+        edge2 = v_sub(v2, v0)
+        h = v_cross(ray_d, edge2)
+        a = v_dot(edge1, h)
+        if -eps < a < eps:
+            return None  # 平行
+        f = 1.0 / a
+        s = v_sub(ray_o, v0)
+        u = f * v_dot(s, h)
+        if u < 0.0 or u > 1.0:
+            return None
+        q = v_cross(s, edge1)
+        v = f * v_dot(ray_d, q)
+        if v < 0.0 or u + v > 1.0:
+            return None
+        t = f * v_dot(edge2, q)
+        if t > eps:
+            return (t, u, v)
+        return None
+
+# ======================
+# 场景构建（康奈尔盒）
+# ======================
+
+def make_quad(v00, v10, v11, v01, material):
+    """
+    用两个三角形表示一个四边形：
+    v00----v10
+    |     /
+    |    /
+    v01----v11
+    """
+    return [
+        Triangle(v00, v10, v11, material),
+        Triangle(v00, v11, v01, material)
+    ]
+
+def add_box(x0, x1, y0, y1, z0, z1, material):
+    """
+    用 12 个三角形（6 个面 * 2）构造轴对齐长方体
+    """
+    tris = []
+    # 8 个顶点
+    p000 = (x0, y0, z0)
+    p001 = (x0, y0, z1)
+    p010 = (x0, y1, z0)
+    p011 = (x0, y1, z1)
+    p100 = (x1, y0, z0)
+    p101 = (x1, y0, z1)
+    p110 = (x1, y1, z0)
+    p111 = (x1, y1, z1)
+
+    # +X 面
+    tris += make_quad(p100, p110, p111, p101, material)
+    # -X 面
+    tris += make_quad(p000, p001, p011, p010, material)
+    # +Y 面（顶面）
+    tris += make_quad(p010, p011, p111, p110, material)
+    # -Y 面（底面）
+    tris += make_quad(p000, p100, p101, p001, material)
+    # +Z 面
+    tris += make_quad(p001, p101, p111, p011, material)
+    # -Z 面
+    tris += make_quad(p000, p010, p110, p100, material)
+
+    return tris
+
+def build_cornell_scene():
+    """
+    构建一个 0~1 立方体空间内的简易康奈尔盒
+    - 左墙红色，右墙绿色，其余白色
+    - 顶部一个小矩形面光源
+    - 场景中两个盒子：一个漫反射，一个金属镜面
+    """
+    scene = []
+
+    # 材质
+    white = Material(color=(0.8, 0.8, 0.8), kind="diffuse")
+    red   = Material(color=(0.75, 0.15, 0.15), kind="diffuse")
+    green = Material(color=(0.15, 0.75, 0.15), kind="diffuse")
+    light_mat = Material(color=(1.0, 1.0, 1.0),
+                         emission=(12.0, 12.0, 12.0),  # 强光
+                         kind="diffuse")
+
+    metal = Material(color=(0.9, 0.9, 0.9),
+                     kind="mirror",
+                     reflectivity=0.95)
+
+    grey_box = Material(color=(0.75, 0.75, 0.75),
+                        kind="diffuse")
+
+    # 盒子边界
+    minc, maxc = 0.0, 1.0
+
+    # 地板 y=0
+    scene += make_quad(
+        (minc, 0.0, minc),
+        (maxc, 0.0, minc),
+        (maxc, 0.0, maxc),
+        (minc, 0.0, maxc),
+        white
+    )
+
+    # 天花板 y=1
+    scene += make_quad(
+        (minc, 1.0, minc),
+        (minc, 1.0, maxc),
+        (maxc, 1.0, maxc),
+        (maxc, 1.0, minc),
+        white
+    )
+
+    # 后墙 z=1
+    scene += make_quad(
+        (minc, minc, 1.0),
+        (maxc, minc, 1.0),
+        (maxc, maxc, 1.0),
+        (minc, maxc, 1.0),
+        white
+    )
+
+    # 左墙 x=0 （红）
+    scene += make_quad(
+        (0.0, minc, minc),
+        (0.0, minc, maxc),
+        (0.0, maxc, maxc),
+        (0.0, maxc, minc),
+        red
+    )
+
+    # 右墙 x=1 （绿）
+    scene += make_quad(
+        (1.0, minc, minc),
+        (1.0, maxc, minc),
+        (1.0, maxc, maxc),
+        (1.0, minc, maxc),
+        green
+    )
+
+    # 顶部面光源（天花板中间一小块）
+    lx0, lx1 = 0.35, 0.65
+    lz0, lz1 = 0.35, 0.65
+    ly = 0.999  # 略低于天花板避免数值问题
+    light_tris = make_quad(
+        (lx0, ly, lz0),
+        (lx1, ly, lz0),
+        (lx1, ly, lz1),
+        (lx0, ly, lz1),
+        light_mat
+    )
+    scene += light_tris
+
+    # 低盒子（金属反射）
+    scene += add_box(
+        0.20, 0.50,   # x
+        0.0,  0.30,   # y
+        0.20, 0.50,   # z
+        metal
+    )
+
+    # 高盒子（漫反射）
+    scene += add_box(
+        0.55, 0.85,
+        0.0,  0.70,
+        0.55, 0.85,
+        grey_box
+    )
+
+    return scene
+
+# ======================
+# 光线追踪核心
+# ======================
+
+def find_closest_hit(scene, ray_o, ray_d):
+    """
+    在所有三角形中找到最近交点
+    返回 (tri, t, hit_pos, hit_normal) 或 None
+    """
+    closest_t = float('inf')
+    hit_tri = None
+    hit_pos = None
+    hit_normal = None
+
+    for tri in scene:
+        res = tri.intersect(ray_o, ray_d)
+        if res is None:
+            continue
+        t, u, v = res
+        if t < closest_t:
+            closest_t = t
+            # 交点
+            hit_pos = v_add(ray_o, v_mul(ray_d, t))
+            # 几何法线拷贝一份
+            n = tri.normal
+            # 确保法线朝向入射光线的反方向
+            if v_dot(n, ray_d) > 0:
+                n = v_mul(n, -1.0)
+            hit_normal = n
+            hit_tri = tri
+
+    if hit_tri is None:
+        return None
+    return hit_tri, closest_t, hit_pos, hit_normal
+
+def build_lights(scene):
+    """
+    从场景中提取所有发光三角形
+    """
+    lights = []
+    for tri in scene:
+        if (tri.material.emission[0] > 0 or
+            tri.material.emission[1] > 0 or
+            tri.material.emission[2] > 0):
+            lights.append(tri)
+    return lights
+
+def triangle_center(tri):
+    return (
+        (tri.v0[0] + tri.v1[0] + tri.v2[0]) / 3.0,
+        (tri.v0[1] + tri.v1[1] + tri.v2[1]) / 3.0,
+        (tri.v0[2] + tri.v1[2] + tri.v2[2]) / 3.0,
+    )
+
+def trace_ray(scene, lights, ray_o, ray_d, depth, max_depth=4, eps=1e-4):
+    """
+    核心递归光线追踪函数
+    - 只在 kind='mirror' 时递归
+    - kind='diffuse' 时只做直接光照，不再递归
+    """
+    if depth > max_depth:
+        return (0.0, 0.0, 0.0)
+
+    hit = find_closest_hit(scene, ray_o, ray_d)
+    if hit is None:
+        # 背景颜色（黑）
+        return (0.0, 0.0, 0.0)
+
+    tri, t, hit_pos, n = hit
+    mat = tri.material
+
+    # 自发光（光源），直接返回其发光颜色（主要用于第一次命中）
+    color = mat.emission
+
+    # 漫反射：只做一次直接光照
+    if mat.kind == "diffuse":
+        direct = (0.0, 0.0, 0.0)
+        for light in lights:
+            # 简化：只用光源三角形中心一个点做光照 & 阴影测试
+            lp = triangle_center(light)
+            to_light = v_sub(lp, hit_pos)
+            dist2 = v_dot(to_light, to_light)
+            dist = math.sqrt(dist2)
+            l_dir = v_norm(to_light)
+
+            # 阴影检测：从 hit_pos 向 lp 打一条 shadow ray
+            shadow_o = v_add(hit_pos, v_mul(n, eps))
+            shadow_hit = find_closest_hit(scene, shadow_o, l_dir)
+            blocked = False
+            if shadow_hit is not None:
+                _, t_shadow, _, _ = shadow_hit
+                if t_shadow < dist - eps:
+                    blocked = True
+
+            if not blocked:
+                # 漫反射 Lambert 项
+                lambert = max(0.0, v_dot(n, l_dir))
+                if lambert > 0:
+                    # 简单地把光源发光乘以漫反射颜色和 lambert
+                    # 不严格做 1/r^2 衰减，只做一个系数缩放
+                    # 可以适当乘个缩放系数让亮度合适
+                    intensity = 1.0
+                    # contribution = mat.color * light.emission * lambert * intensity
+                    c = v_mul_comp(mat.color, light.material.emission)
+                    c = v_mul(c, lambert * intensity)
+                    direct = v_add(direct, c)
+
+        color = v_add(color, direct)
+        return color
+
+    # 镜面（金属）表面：计算反射并递归
+    if mat.kind == "mirror":
+        refl_dir = v_reflect(ray_d, n)
+        refl_o = v_add(hit_pos, v_mul(n, eps))
+        refl_col = trace_ray(scene, lights, refl_o, refl_dir, depth + 1, max_depth, eps)
+        # 反射颜色 = 本身颜色 * 反射颜色 * 反射率
+        refl_col = v_mul_comp(mat.color, refl_col)
+        refl_col = v_mul(refl_col, mat.reflectivity)
+        color = v_add(color, refl_col)
+        return color
+
+    # 其他类型（未用到），直接返回自发光
+    return color
+
+# ======================
+# 渲染主函数
+# ======================
+
+def clamp(x, lo=0.0, hi=1.0):
+    return max(lo, min(hi, x))
+
+def gamma_correct(c, gamma=2.2):
+    inv = 1.0 / gamma
+    return (c[0] ** inv, c[1] ** inv, c[2] ** inv)
+
+def render():
+    # 图像分辨率
+    width = 400
+    height = 400
+
+    # 构建场景
+    scene = build_cornell_scene()
+    lights = build_lights(scene)
+
+    # 相机设置
+    cam_pos = (0.5, 0.5, -1.5)  # 在盒子前方
+    look_at = (0.5, 0.5, 0.0)   # 看向盒子中心
+    up = (0.0, 1.0, 0.0)
+    fov = 40.0  # 视角（度）
+    aspect = width / float(height)
+    scale = math.tan(math.radians(fov * 0.5))
+
+    # 构建相机坐标系
+    forward = v_norm(v_sub(look_at, cam_pos))
+    right = v_norm(v_cross(forward, up))
+    true_up = v_cross(right, forward)
+
+    framebuffer = [[(0.0, 0.0, 0.0) for _ in range(width)] for _ in range(height)]
+
+    for y in range(height):
+        print(f"Rendering line {y+1}/{height} ...", end="\r")
+        for x in range(width):
+            # 像素中心 NDC 坐标 [-1,1]
+            px = (2.0 * ((x + 0.5) / width) - 1.0) * aspect * scale
+            py = (1.0 - 2.0 * ((y + 0.5) / height)) * scale
+
+            # 在相机坐标系中构造方向
+            dir_cam = v_add(
+                v_add(v_mul(right, px), v_mul(true_up, py)),
+                forward
+            )
+            ray_d = v_norm(dir_cam)
+            ray_o = cam_pos
+
+            col = trace_ray(scene, lights, ray_o, ray_d, depth=0, max_depth=4)
+
+            # gamma 校正
+            col = gamma_correct((
+                clamp(col[0]),
+                clamp(col[1]),
+                clamp(col[2])
+            ))
+
+            framebuffer[y][x] = col
+
+    print("\n渲染完成，正在写入文件 cornell.ppm ...")
+
+    # 输出 PPM（文本格式）
+    with open("cornell.ppm", "w") as f:
+        f.write(f"P3\n{width} {height}\n255\n")
+        for y in range(height):
+            for x in range(width):
+                r, g, b = framebuffer[y][x]
+                ir = int(255.99 * clamp(r))
+                ig = int(255.99 * clamp(g))
+                ib = int(255.99 * clamp(b))
+                f.write(f"{ir} {ig} {ib}\n")
+
+    print("写入完成：cornell.ppm")
+
+if __name__ == "__main__":
+    render()

experiments/rt10.cpp

@@ -0,0 +1,933 @@
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cmath>
+#include <cstdint>
+#include <fstream>
+#include <functional>
+#include <iomanip>
+#include <iostream>
+#include <limits>
+#include <memory>
+#include <numeric>
+#include <string>
+#include <unordered_set>
+#include <utility>
+#include <vector>
+
+static constexpr double kEps = 1e-9;
+
+static inline double clampd(double x, double lo, double hi) {
+    return std::max(lo, std::min(hi, x));
+}
+static inline int clampi(int x, int lo, int hi) {
+    return std::max(lo, std::min(hi, x));
+}
+
+struct Vec2 {
+    double x = 0, y = 0;
+    Vec2() = default;
+    Vec2(double x_, double y_) : x(x_), y(y_) {}
+    Vec2 operator+(const Vec2& r) const { return {x + r.x, y + r.y}; }
+    Vec2 operator-(const Vec2& r) const { return {x - r.x, y - r.y}; }
+    Vec2 operator*(double s) const { return {x * s, y * s}; }
+};
+
+static inline double cross2(const Vec2& a, const Vec2& b) {
+    return a.x * b.y - a.y * b.x;
+}
+
+struct Vec3 {
+    double x = 0, y = 0, z = 0;
+    Vec3() = default;
+    Vec3(double x_, double y_, double z_) : x(x_), y(y_), z(z_) {}
+
+    Vec3 operator+(const Vec3& r) const { return {x + r.x, y + r.y, z + r.z}; }
+    Vec3 operator-(const Vec3& r) const { return {x - r.x, y - r.y, z - r.z}; }
+    Vec3 operator*(double s) const { return {x * s, y * s, z * s}; }
+    Vec3 operator/(double s) const { return {x / s, y / s, z / s}; }
+
+    Vec3& operator+=(const Vec3& r) { x += r.x; y += r.y; z += r.z; return *this; }
+};
+
+static inline Vec3 mul(const Vec3& a, const Vec3& b) {
+    return {a.x * b.x, a.y * b.y, a.z * b.z};
+}
+static inline double dot(const Vec3& a, const Vec3& b) {
+    return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+static inline Vec3 cross(const Vec3& a, const Vec3& b) {
+    return {
+        a.y * b.z - a.z * b.y,
+        a.z * b.x - a.x * b.z,
+        a.x * b.y - a.y * b.x
+    };
+}
+static inline double length(const Vec3& v) {
+    return std::sqrt(dot(v, v));
+}
+static inline Vec3 normalize(const Vec3& v) {
+    double len = length(v);
+    if (len < kEps) return {0, 0, 0};
+    return v / len;
+}
+static inline Vec3 lerp(const Vec3& a, const Vec3& b, double t) {
+    return a * (1.0 - t) + b * t;
+}
+
+struct Image {
+    int w = 0, h = 0;
+    std::vector<Vec3> pix;
+
+    Image() = default;
+    Image(int w_, int h_, Vec3 fill = {0,0,0}) : w(w_), h(h_), pix((size_t)w_ * (size_t)h_, fill) {}
+
+    Vec3 get(int x, int y) const {
+        x = clampi(x, 0, w - 1);
+        y = clampi(y, 0, h - 1);
+        return pix[(size_t)y * (size_t)w + (size_t)x];
+    }
+    void set(int x, int y, const Vec3& c) {
+        if (x < 0 || x >= w || y < 0 || y >= h) return;
+        pix[(size_t)y * (size_t)w + (size_t)x] = c;
+    }
+
+    // UV: [0,1]x[0,1], v向下（0为顶端），便于图像坐标。
+    Vec3 sampleBilinear(double u, double v) const {
+        u = clampd(u, 0.0, 1.0);
+        v = clampd(v, 0.0, 1.0);
+        double fx = u * (w - 1);
+        double fy = v * (h - 1);
+        int x0 = (int)std::floor(fx);
+        int y0 = (int)std::floor(fy);
+        int x1 = std::min(x0 + 1, w - 1);
+        int y1 = std::min(y0 + 1, h - 1);
+        double tx = fx - x0;
+        double ty = fy - y0;
+
+        Vec3 c00 = get(x0, y0);
+        Vec3 c10 = get(x1, y0);
+        Vec3 c01 = get(x0, y1);
+        Vec3 c11 = get(x1, y1);
+
+        Vec3 cx0 = lerp(c00, c10, tx);
+        Vec3 cx1 = lerp(c01, c11, tx);
+        return lerp(cx0, cx1, ty);
+    }
+
+    void writePPM(const std::string& path, double gamma = 2.2) const {
+        std::ofstream out(path, std::ios::binary);
+        if (!out) {
+            throw std::runtime_error("Failed to open output file: " + path);
+        }
+        out << "P6\n" << w << " " << h << "\n255\n";
+        for (int y = 0; y < h; ++y) {
+            for (int x = 0; x < w; ++x) {
+                Vec3 c = pix[(size_t)y * (size_t)w + (size_t)x];
+                c.x = clampd(c.x, 0.0, 1.0);
+                c.y = clampd(c.y, 0.0, 1.0);
+                c.z = clampd(c.z, 0.0, 1.0);
+                // gamma
+                c.x = std::pow(c.x, 1.0 / gamma);
+                c.y = std::pow(c.y, 1.0 / gamma);
+                c.z = std::pow(c.z, 1.0 / gamma);
+
+                unsigned char rgb[3] = {
+                    (unsigned char)clampi((int)std::lround(c.x * 255.0), 0, 255),
+                    (unsigned char)clampi((int)std::lround(c.y * 255.0), 0, 255),
+                    (unsigned char)clampi((int)std::lround(c.z * 255.0), 0, 255),
+                };
+                out.write((char*)rgb, 3);
+            }
+        }
+    }
+};
+
+enum class MaterialType {
+    Diffuse,
+    Reflective,
+};
+
+struct Material {
+    MaterialType type = MaterialType::Diffuse;
+    Vec3 albedo = {1,1,1};     // 基色/金属色
+    double metalness = 0.0;    // Reflective时用于混合反射与基色（0..1）
+};
+
+struct Triangle {
+    int id = -1;
+    Vec3 p[3];
+    Vec2 uv[3];
+    Material* mat = nullptr;
+
+    Vec3 normal() const {
+        return normalize(cross(p[1] - p[0], p[2] - p[0]));
+    }
+    Vec3 centroid() const {
+        return (p[0] + p[1] + p[2]) / 3.0;
+    }
+};
+
+// ---------------------------
+// 3D barycentric (点在三角形平面上时使用)
+// ---------------------------
+static inline std::array<double,3> barycentric3D(const Vec3& P, const Triangle& T) {
+    Vec3 v0 = T.p[1] - T.p[0];
+    Vec3 v1 = T.p[2] - T.p[0];
+    Vec3 v2 = P - T.p[0];
+
+    double d00 = dot(v0, v0);
+    double d01 = dot(v0, v1);
+    double d11 = dot(v1, v1);
+    double d20 = dot(v2, v0);
+    double d21 = dot(v2, v1);
+
+    double denom = d00 * d11 - d01 * d01;
+    if (std::fabs(denom) < kEps) return { -1, -1, -1 };
+
+    double v = (d11 * d20 - d01 * d21) / denom;
+    double w = (d00 * d21 - d01 * d20) / denom;
+    double u = 1.0 - v - w;
+    return {u, v, w};
+}
+
+static inline bool pointInTriangle3D(const Vec3& P, const Triangle& T, double eps = 1e-8) {
+    auto bc = barycentric3D(P, T);
+    return bc[0] >= -eps && bc[1] >= -eps && bc[2] >= -eps;
+}
+
+// ---------------------------
+// 2D point-in-triangle (UV空间)
+// ---------------------------
+static inline bool pointInTriangle2D(const Vec2& P, const Vec2& A, const Vec2& B, const Vec2& C, double eps = 1e-10) {
+    // 允许任意绕序：用同向性判断
+    Vec2 v0 = B - A;
+    Vec2 v1 = C - B;
+    Vec2 v2 = A - C;
+    Vec2 w0 = P - A;
+    Vec2 w1 = P - B;
+    Vec2 w2 = P - C;
+
+    double c0 = cross2(v0, w0);
+    double c1 = cross2(v1, w1);
+    double c2 = cross2(v2, w2);
+
+    bool hasNeg = (c0 < -eps) || (c1 < -eps) || (c2 < -eps);
+    bool hasPos = (c0 > eps) || (c1 > eps) || (c2 > eps);
+    return !(hasNeg && hasPos);
+}
+
+// ---------------------------
+// 线段-三角形相交（Moller-Trumbore，作为Triangle运算的一部分）
+// 注意：本项目核心渲染不依赖每像素Ray，但几何工具函数仍可提供。
+// ---------------------------
+static inline bool segmentIntersectsTriangle(const Vec3& A, const Vec3& B, const Triangle& T, double* outT = nullptr) {
+    Vec3 dir = B - A;
+    Vec3 e1 = T.p[1] - T.p[0];
+    Vec3 e2 = T.p[2] - T.p[0];
+    Vec3 pvec = cross(dir, e2);
+    double det = dot(e1, pvec);
+
+    if (std::fabs(det) < kEps) return false;
+    double invDet = 1.0 / det;
+
+    Vec3 tvec = A - T.p[0];
+    double u = dot(tvec, pvec) * invDet;
+    if (u < -kEps || u > 1.0 + kEps) return false;
+
+    Vec3 qvec = cross(tvec, e1);
+    double v = dot(dir, qvec) * invDet;
+    if (v < -kEps || u + v > 1.0 + kEps) return false;
+
+    double t = dot(e2, qvec) * invDet;
+    if (t < -kEps || t > 1.0 + kEps) return false; // segment: t in [0,1]
+    if (outT) *outT = t;
+    return true;
+}
+
+static inline bool trianglesIntersectSimple(const Triangle& A, const Triangle& B) {
+    // 简化版：只做边-面检测（对一般非共面情况足够）
+    for (int i = 0; i < 3; ++i) {
+        Vec3 a0 = A.p[i];
+        Vec3 a1 = A.p[(i+1)%3];
+        if (segmentIntersectsTriangle(a0, a1, B)) return true;
+    }
+    for (int i = 0; i < 3; ++i) {
+        Vec3 b0 = B.p[i];
+        Vec3 b1 = B.p[(i+1)%3];
+        if (segmentIntersectsTriangle(b0, b1, A)) return true;
+    }
+    // 顶点包含（共面等情况粗略兜底）
+    if (pointInTriangle3D(A.p[0], B) || pointInTriangle3D(B.p[0], A)) return true;
+    return false;
+}
+
+// ---------------------------
+// 把点关于三角形所在平面镜像（对称）
+// ---------------------------
+static inline Vec3 reflectPointAcrossTrianglePlane(const Vec3& P, const Triangle& T) {
+    Vec3 n = T.normal();
+    // 平面点选T.p[0]
+    double dist = dot(n, P - T.p[0]); // 有符号距离（n已归一）
+    return P - n * (2.0 * dist);
+}
+
+// ---------------------------
+// 以origin->point的射线与viewport三角形平面相交，计算交点，并得到对应的viewport UV（允许在UV外）
+// 要求：交点必须在 origin 到 point 之间（t in (0,1)），即 viewport 平面在两者之间。
+// ---------------------------
+static inline bool projectPointToViewportUV(
+    const Vec3& origin,
+    const Vec3& point,
+    const Triangle& viewport,
+    Vec2& outViewportUV,
+    Vec3* outWorldHit = nullptr,
+    double* outLineT = nullptr
+) {
+    Vec3 n = viewport.normal();
+    Vec3 dir = point - origin;
+    double denom = dot(n, dir);
+    if (std::fabs(denom) < kEps) return false;
+
+    double t = dot(n, viewport.p[0] - origin) / denom;
+    // 关键：只接受平面位于 origin->point 之间的情况
+    if (!(t > 1e-7 && t < 1.0 - 1e-7)) return false;
+
+    Vec3 hit = origin + dir * t;
+    auto bc = barycentric3D(hit, viewport);
+    if (bc[0] < -1e6 || bc[1] < -1e6 || bc[2] < -1e6) return false;
+
+    // UV使用线性插值（即使点在三角形外也能给出UV，用于后续裁剪）
+    outViewportUV = viewport.uv[0] * bc[0] + viewport.uv[1] * bc[1] + viewport.uv[2] * bc[2];
+
+    if (outWorldHit) *outWorldHit = hit;
+    if (outLineT) *outLineT = t;
+    return true;
+}
+
+struct UVPairVertex {
+    Vec2 dstUV; // 在“当前viewport”的UV
+    Vec2 srcUV; // 在“被投影面片纹理”的UV
+};
+
+static inline double polygonAreaUV(const std::vector<UVPairVertex>& poly) {
+    // poly为凸多边形（裁剪结果），用shoelace
+    double a = 0.0;
+    for (size_t i = 0; i < poly.size(); ++i) {
+        const Vec2& p = poly[i].dstUV;
+        const Vec2& q = poly[(i + 1) % poly.size()].dstUV;
+        a += p.x * q.y - p.y * q.x;
+    }
+    return 0.5 * a;
+}
+
+static inline bool isInsideEdgeLeft(const Vec2& A, const Vec2& B, const Vec2& P, double eps = 1e-12) {
+    // 以A->B为边，左侧为内
+    return cross2(B - A, P - A) >= -eps;
+}
+
+static inline UVPairVertex intersectSegmentWithLine(
+    const UVPairVertex& S,
+    const UVPairVertex& E,
+    const Vec2& A,
+    const Vec2& B
+) {
+    // 使用有符号距离插值求交点：
+    // dist(P)=cross(B-A, P-A). dist=0在直线上
+    double dS = cross2(B - A, S.dstUV - A);
+    double dE = cross2(B - A, E.dstUV - A);
+    double t = dS / (dS - dE + 1e-30);
+    t = clampd(t, 0.0, 1.0);
+    UVPairVertex I;
+    I.dstUV = S.dstUV + (E.dstUV - S.dstUV) * t;
+    I.srcUV = S.srcUV + (E.srcUV - S.srcUV) * t;
+    return I;
+}
+
+// 将“投影后的目标三角形(带srcUV)”裁剪到viewport三角形(仅dstUV空间)内部
+static inline std::vector<UVPairVertex> clipPolygonToTriangle(
+    std::vector<UVPairVertex> poly,
+    const Vec2& C0,
+    const Vec2& C1,
+    const Vec2& C2
+) {
+    // 确保裁剪三角形绕序为CCW，使“左侧为内”成立
+    double triArea = cross2(C1 - C0, C2 - C0);
+    Vec2 A0 = C0, A1 = C1, A2 = C2;
+    if (triArea < 0.0) std::swap(A1, A2);
+
+    auto clipAgainstEdge = [&](const Vec2& A, const Vec2& B, std::vector<UVPairVertex> inPoly) {
+        std::vector<UVPairVertex> out;
+        if (inPoly.empty()) return out;
+        UVPairVertex S = inPoly.back();
+        bool S_inside = isInsideEdgeLeft(A, B, S.dstUV);
+        for (const auto& E : inPoly) {
+            bool E_inside = isInsideEdgeLeft(A, B, E.dstUV);
+            if (E_inside) {
+                if (!S_inside) out.push_back(intersectSegmentWithLine(S, E, A, B));
+                out.push_back(E);
+            } else if (S_inside) {
+                out.push_back(intersectSegmentWithLine(S, E, A, B));
+            }
+            S = E;
+            S_inside = E_inside;
+        }
+        return out;
+    };
+
+    poly = clipAgainstEdge(A0, A1, std::move(poly));
+    poly = clipAgainstEdge(A1, A2, std::move(poly));
+    poly = clipAgainstEdge(A2, A0, std::move(poly));
+    return poly;
+}
+
+static inline void rasterizeWarpTriangle(
+    Image& dst,
+    const Vec2& d0, const Vec2& d1, const Vec2& d2,
+    const Image& src,
+    const Vec2& s0, const Vec2& s1, const Vec2& s2,
+    bool overwrite = true
+) {
+    // dstUV/srcUV均为[0,1]附近（dstUV经过裁剪保证在dst三角形内）
+
+    auto uvToPixel = [&](const Vec2& uv) -> Vec2 {
+        return Vec2(uv.x * (dst.w - 1), uv.y * (dst.h - 1));
+    };
+
+    Vec2 p0 = uvToPixel(d0);
+    Vec2 p1 = uvToPixel(d1);
+    Vec2 p2 = uvToPixel(d2);
+
+    double minx = std::floor(std::min({p0.x, p1.x, p2.x}));
+    double maxx = std::ceil (std::max({p0.x, p1.x, p2.x}));
+    double miny = std::floor(std::min({p0.y, p1.y, p2.y}));
+    double maxy = std::ceil (std::max({p0.y, p1.y, p2.y}));
+
+    int x0 = clampi((int)minx, 0, dst.w - 1);
+    int x1 = clampi((int)maxx, 0, dst.w - 1);
+    int y0 = clampi((int)miny, 0, dst.h - 1);
+    int y1 = clampi((int)maxy, 0, dst.h - 1);
+
+    double area = cross2(p1 - p0, p2 - p0);
+    if (std::fabs(area) < 1e-12) return;
+
+    for (int y = y0; y <= y1; ++y) {
+        for (int x = x0; x <= x1; ++x) {
+            Vec2 P((double)x + 0.5, (double)y + 0.5);
+            // barycentric in pixel-space
+            double w0 = cross2(p1 - P, p2 - P) / area;
+            double w1 = cross2(p2 - P, p0 - P) / area;
+            double w2 = 1.0 - w0 - w1;
+
+            if (w0 < -1e-6 || w1 < -1e-6 || w2 < -1e-6) continue;
+
+            Vec2 suv = s0 * w0 + s1 * w1 + s2 * w2;
+            Vec3 sc = src.sampleBilinear(suv.x, suv.y);
+
+            if (overwrite) {
+                dst.set(x, y, sc);
+            } else {
+                Vec3 dc = dst.get(x, y);
+                dst.set(x, y, lerp(dc, sc, 0.5));
+            }
+        }
+    }
+}
+
+static inline void rasterizeWarpPolygonFan(
+    Image& dst,
+    const std::vector<UVPairVertex>& poly,
+    const Image& src,
+    bool overwrite = true
+) {
+    if (poly.size() < 3) return;
+    const auto& v0 = poly[0];
+    for (size_t i = 1; i + 1 < poly.size(); ++i) {
+        const auto& v1 = poly[i];
+        const auto& v2 = poly[i + 1];
+        rasterizeWarpTriangle(
+            dst,
+            v0.dstUV, v1.dstUV, v2.dstUV,
+            src,
+            v0.srcUV, v1.srcUV, v2.srcUV,
+            overwrite
+        );
+    }
+}
+
+// ---------------------------
+// 收集“可能投射到viewport三角形”的面片列表（指针），用于后续按距离排序（远到近）
+// 这里只用“任一顶点能投到viewport内部”作为候选判定（快），实际绘制时会做裁剪。
+// ---------------------------
+static inline std::vector<const Triangle*> collectCandidateTriangles(
+    const std::vector<Triangle>& scene,
+    const Vec3& origin,
+    const Triangle& viewport
+) {
+    std::vector<const Triangle*> out;
+    out.reserve(scene.size());
+
+    for (const auto& tri : scene) {
+        bool anyInside = false;
+        for (int i = 0; i < 3; ++i) {
+            Vec2 uv;
+            Vec3 hit;
+            if (!projectPointToViewportUV(origin, tri.p[i], viewport, uv, &hit, nullptr)) continue;
+            // 只有当交点在viewport三角形内部才算可能投射
+            if (pointInTriangle3D(hit, viewport, 1e-8)) {
+                anyInside = true;
+                break;
+            }
+        }
+        if (anyInside) out.push_back(&tri);
+    }
+    return out;
+}
+
+// ---------------------------
+// 将 targetTri 的纹理投影到 viewportTri 对应的 dstImage 上：
+// 1) 把targetTri三个顶点投到viewport平面，得到dstUV三点（允许在viewport外）
+// 2) 用Sutherland-Hodgman把投影三角形裁剪到viewport三角形内部
+// 3) 将裁剪结果多边形扇形三角化后，进行纹理拉伸/扭曲并写入dst
+// 返回：裁剪后投影区域的像素面积估计（用于递归终止与子纹理分辨率估计）
+// ---------------------------
+static inline double projectAndCompositeTriangleTexture(
+    Image& dstImage,
+    const Triangle& viewportTri,
+    const Vec3& origin,
+    const Triangle& targetTri,
+    const Image& targetTexture,
+    bool overwrite = true
+) {
+    Vec2 dstUV[3];
+    for (int i = 0; i < 3; ++i) {
+        Vec2 uv;
+        if (!projectPointToViewportUV(origin, targetTri.p[i], viewportTri, uv, nullptr, nullptr)) {
+            return 0.0; // 无法投影（平行或平面不在origin->point之间等）
+        }
+        dstUV[i] = uv;
+    }
+
+    std::vector<UVPairVertex> poly(3);
+    for (int i = 0; i < 3; ++i) {
+        poly[i].dstUV = dstUV[i];
+        poly[i].srcUV = targetTri.uv[i];
+    }
+
+    // 裁剪到viewport三角形UV边界内
+    std::vector<UVPairVertex> clipped = clipPolygonToTriangle(
+        std::move(poly),
+        viewportTri.uv[0], viewportTri.uv[1], viewportTri.uv[2]
+    );
+    if (clipped.size() < 3) return 0.0;
+
+    double areaUV = std::fabs(polygonAreaUV(clipped));
+    double areaPx = areaUV * (double)dstImage.w * (double)dstImage.h;
+
+    rasterizeWarpPolygonFan(dstImage, clipped, targetTexture, overwrite);
+    return areaPx;
+}
+
+// ---------------------------
+// 核心递归：renderTriangleWithTriangle
+// - 传入：scene、观察点origin、当前面片currentTri
+// - Diffuse：直接返回(填充)材质颜色纹理
+// - Reflective：
+//   1) origin关于currentTri平面镜像 -> mirroredOrigin
+//   2) 以currentTri作为viewport，从mirroredOrigin遍历其它面片，排序远->近
+//   3) 递归渲染其它面片得到其纹理
+//   4) 将其它面片纹理投影/裁剪/拉伸贴到currentTri纹理上
+//   5) 与基色按metalness混合并返回
+// 终止：深度上限 & 当前估计像素面积阈值 & 循环依赖保护（栈内id）
+// ---------------------------
+struct RenderConfig {
+    int maxDepth = 4;
+    double minAreaPxToRecurse = 4.0;   // 小于该像素面积就不再递归
+    int maxTriTexRes = 256;
+    int minTriTexRes = 16;
+    Vec3 envColor = {0.08, 0.08, 0.10};
+};
+
+static Image renderTriangleWithTriangle(
+    const std::vector<Triangle>& scene,
+    const Vec3& origin,
+    const Triangle& currentTri,
+    int texW,
+    int texH,
+    int depth,
+    double estimatedAreaPx,
+    std::vector<int>& recursionStack,
+    const RenderConfig& cfg
+) {
+    texW = clampi(texW, cfg.minTriTexRes, cfg.maxTriTexRes);
+    texH = clampi(texH, cfg.minTriTexRes, cfg.maxTriTexRes);
+
+    Vec3 baseColor = currentTri.mat ? currentTri.mat->albedo : Vec3(1,1,1);
+    Image base(texW, texH, baseColor);
+
+    if (!currentTri.mat || currentTri.mat->type == MaterialType::Diffuse) {
+        return base;
+    }
+
+    // 递归终止条件
+    if (depth >= cfg.maxDepth) return base;
+    if (estimatedAreaPx > 0.0 && estimatedAreaPx < cfg.minAreaPxToRecurse) return base;
+
+    // 防止循环递归（镜面对镜面等）
+    for (int id : recursionStack) {
+        if (id == currentTri.id) return base;
+    }
+    recursionStack.push_back(currentTri.id);
+
+    Vec3 mirroredOrigin = reflectPointAcrossTrianglePlane(origin, currentTri);
+
+    // 反射缓冲：初始为环境色（避免未命中区域全黑）
+    Image reflection(texW, texH, cfg.envColor);
+
+    // 找出可能投射到currentTri(viewport)的面片
+    std::vector<const Triangle*> candidates = collectCandidateTriangles(scene, mirroredOrigin, currentTri);
+
+    // 排序：远 -> 近
+    std::sort(candidates.begin(), candidates.end(), [&](const Triangle* a, const Triangle* b) {
+        double da = length(a->centroid() - mirroredOrigin);
+        double db = length(b->centroid() - mirroredOrigin);
+        return da > db;
+    });
+
+    for (const Triangle* tptr : candidates) {
+        if (!tptr) continue;
+        if (tptr->id == currentTri.id) continue;
+
+        // 先用投影+裁剪估面积，再决定子纹理分辨率与是否递归
+        // 为了获得“面积估计”，我们需要先进行一次“空投影裁剪”
+        // 这里复用projectAndCompositeTriangleTexture的思路，但不写入，只算面积：
+        Vec2 dstUV[3];
+        bool ok = true;
+        for (int i = 0; i < 3; ++i) {
+            Vec2 uv;
+            if (!projectPointToViewportUV(mirroredOrigin, tptr->p[i], currentTri, uv, nullptr, nullptr)) {
+                ok = false;
+                break;
+            }
+            dstUV[i] = uv;
+        }
+        if (!ok) continue;
+
+        std::vector<UVPairVertex> poly(3);
+        for (int i = 0; i < 3; ++i) {
+            poly[i].dstUV = dstUV[i];
+            poly[i].srcUV = tptr->uv[i];
+        }
+        std::vector<UVPairVertex> clipped = clipPolygonToTriangle(
+            std::move(poly),
+            currentTri.uv[0], currentTri.uv[1], currentTri.uv[2]
+        );
+        if (clipped.size() < 3) continue;
+
+        double areaUV = std::fabs(polygonAreaUV(clipped));
+        double areaPx = areaUV * (double)texW * (double)texH;
+        if (areaPx < 0.5) continue;
+
+        int childRes = (int)std::lround(std::sqrt(areaPx) * 1.2);
+        childRes = clampi(childRes, cfg.minTriTexRes, cfg.maxTriTexRes);
+
+        Image childTex = renderTriangleWithTriangle(
+            scene,
+            mirroredOrigin,
+            *tptr,
+            childRes, childRes,
+            depth + 1,
+            areaPx,
+            recursionStack,
+            cfg
+        );
+
+        // 真正写入反射缓冲（近处覆盖远处）
+        // 注意：我们已经有clipped了，可直接用它进行扇形三角化绘制
+        rasterizeWarpPolygonFan(reflection, clipped, childTex, /*overwrite=*/true);
+    }
+
+    recursionStack.pop_back();
+
+    // 将反射与基色混合：金属色会对反射进行“染色”
+    double m = clampd(currentTri.mat->metalness, 0.0, 1.0);
+    Image out(texW, texH, {0,0,0});
+    for (int y = 0; y < texH; ++y) {
+        for (int x = 0; x < texW; ++x) {
+            Vec3 r = reflection.get(x, y);
+            Vec3 tinted = mul(r, baseColor);
+            Vec3 c = baseColor * (1.0 - m) + tinted * m;
+            out.set(x, y, c);
+        }
+    }
+    return out;
+}
+
+// ---------------------------
+// Camera：viewport由两个三角形组成
+// render()：分别渲染两块viewport三角形纹理，再合成输出到PPM
+// ---------------------------
+struct Camera {
+    Vec3 origin;
+    Triangle vpA; // viewport triangle A
+    Triangle vpB; // viewport triangle B
+    int width = 800;
+    int height = 600;
+
+    Image renderViewportTriangle(
+        const std::vector<Triangle>& scene,
+        const Triangle& viewportTri,
+        const RenderConfig& cfg
+    ) const {
+        Image img(width, height, cfg.envColor);
+
+        // 先收集候选面片（可能投射到该viewport三角形）
+        std::vector<const Triangle*> candidates = collectCandidateTriangles(scene, origin, viewportTri);
+
+        std::sort(candidates.begin(), candidates.end(), [&](const Triangle* a, const Triangle* b) {
+            double da = length(a->centroid() - origin);
+            double db = length(b->centroid() - origin);
+            return da > db; // 远->近
+        });
+
+        std::vector<int> stack;
+        for (const Triangle* tptr : candidates) {
+            if (!tptr) continue;
+
+            // 估计该面片投影到viewport的像素面积：通过一次“投影+裁剪”的面积计算获得
+            Vec2 dstUV[3];
+            bool ok = true;
+            for (int i = 0; i < 3; ++i) {
+                Vec2 uv;
+                if (!projectPointToViewportUV(origin, tptr->p[i], viewportTri, uv, nullptr, nullptr)) {
+                    ok = false;
+                    break;
+                }
+                dstUV[i] = uv;
+            }
+            if (!ok) continue;
+
+            std::vector<UVPairVertex> poly(3);
+            for (int i = 0; i < 3; ++i) {
+                poly[i].dstUV = dstUV[i];
+                poly[i].srcUV = tptr->uv[i];
+            }
+            std::vector<UVPairVertex> clipped = clipPolygonToTriangle(
+                std::move(poly),
+                viewportTri.uv[0], viewportTri.uv[1], viewportTri.uv[2]
+            );
+            if (clipped.size() < 3) continue;
+
+            double areaUV = std::fabs(polygonAreaUV(clipped));
+            double areaPx = areaUV * (double)width * (double)height;
+            if (areaPx < 0.5) continue;
+
+            int triRes = (int)std::lround(std::sqrt(areaPx) * 1.0);
+            triRes = clampi(triRes, cfg.minTriTexRes, cfg.maxTriTexRes);
+
+            Image triTex = renderTriangleWithTriangle(
+                scene,
+                origin,
+                *tptr,
+                triRes, triRes,
+                /*depth=*/0,
+                /*estimatedAreaPx=*/areaPx,
+                stack,
+                cfg
+            );
+
+            // 投影并写入viewport图像（近处覆盖远处）
+            rasterizeWarpPolygonFan(img, clipped, triTex, /*overwrite=*/true);
+        }
+
+        // 将viewport三角形外的像素清为黑（严格按“两个三角形viewport”）
+        for (int y = 0; y < height; ++y) {
+            for (int x = 0; x < width; ++x) {
+                Vec2 uv((double)x / (width - 1), (double)y / (height - 1));
+                bool inside = pointInTriangle2D(uv, viewportTri.uv[0], viewportTri.uv[1], viewportTri.uv[2], 1e-10);
+                if (!inside) img.set(x, y, {0,0,0});
+            }
+        }
+
+        return img;
+    }
+
+    Image render(const std::vector<Triangle>& scene, const RenderConfig& cfg) const {
+        Image a = renderViewportTriangle(scene, vpA, cfg);
+        Image b = renderViewportTriangle(scene, vpB, cfg);
+
+        // 合成：由于a/b在各自三角形外为黑，直接相加即可得到完整画面
+        Image out(width, height, {0,0,0});
+        for (int y = 0; y < height; ++y) {
+            for (int x = 0; x < width; ++x) {
+                Vec3 c = a.get(x, y) + b.get(x, y);
+                // clamp
+                c.x = clampd(c.x, 0.0, 1.0);
+                c.y = clampd(c.y, 0.0, 1.0);
+                c.z = clampd(c.z, 0.0, 1.0);
+                out.set(x, y, c);
+            }
+        }
+        return out;
+    }
+};
+
+// ---------------------------
+// 场景构建：用四边形拆成两个三角形
+// UV采用(0,0)-(1,1)映射（每个quad面独立）
+// ---------------------------
+static inline void addQuad(
+    std::vector<Triangle>& scene,
+    int& nextId,
+    const Vec3& p00, const Vec3& p10, const Vec3& p11, const Vec3& p01,
+    Material* mat
+) {
+    Triangle t0;
+    t0.id = nextId++;
+    t0.p[0] = p00; t0.p[1] = p10; t0.p[2] = p01;
+    t0.uv[0] = {0,0}; t0.uv[1] = {1,0}; t0.uv[2] = {0,1};
+    t0.mat = mat;
+
+    Triangle t1;
+    t1.id = nextId++;
+    t1.p[0] = p10; t1.p[1] = p11; t1.p[2] = p01;
+    t1.uv[0] = {1,0}; t1.uv[1] = {1,1}; t1.uv[2] = {0,1};
+    t1.mat = mat;
+
+    scene.push_back(t0);
+    scene.push_back(t1);
+}
+
+static inline void addBox(
+    std::vector<Triangle>& scene,
+    int& nextId,
+    const Vec3& bmin,
+    const Vec3& bmax,
+    Material* mat
+) {
+    // 6 faces: +X -X +Y -Y +Z -Z
+    Vec3 p000(bmin.x, bmin.y, bmin.z);
+    Vec3 p001(bmin.x, bmin.y, bmax.z);
+    Vec3 p010(bmin.x, bmax.y, bmin.z);
+    Vec3 p011(bmin.x, bmax.y, bmax.z);
+    Vec3 p100(bmax.x, bmin.y, bmin.z);
+    Vec3 p101(bmax.x, bmin.y, bmax.z);
+    Vec3 p110(bmax.x, bmax.y, bmin.z);
+    Vec3 p111(bmax.x, bmax.y, bmax.z);
+
+    // -X face: p000 p001 p011 p010
+    addQuad(scene, nextId, p000, p001, p011, p010, mat);
+    // +X face: p100 p110 p111 p101
+    addQuad(scene, nextId, p100, p110, p111, p101, mat);
+    // -Y face (bottom): p000 p100 p101 p001
+    addQuad(scene, nextId, p000, p100, p101, p001, mat);
+    // +Y face (top): p010 p011 p111 p110
+    addQuad(scene, nextId, p010, p011, p111, p110, mat);
+    // -Z face: p000 p010 p110 p100
+    addQuad(scene, nextId, p000, p010, p110, p100, mat);
+    // +Z face: p001 p101 p111 p011
+    addQuad(scene, nextId, p001, p101, p111, p011, mat);
+}
+
+int main() {
+    try {
+        // ---------------------------
+        // 材质
+        // ---------------------------
+        Material matWhite; matWhite.type = MaterialType::Diffuse; matWhite.albedo = {0.85, 0.85, 0.85};
+        Material matRed;   matRed.type   = MaterialType::Diffuse; matRed.albedo   = {0.85, 0.25, 0.25};
+        Material matGreen; matGreen.type = MaterialType::Diffuse; matGreen.albedo = {0.25, 0.85, 0.25};
+
+        Material matBlueMetal;   matBlueMetal.type   = MaterialType::Reflective; matBlueMetal.albedo   = {0.25, 0.45, 1.0};  matBlueMetal.metalness   = 0.90;
+        Material matYellowMetal; matYellowMetal.type = MaterialType::Reflective; matYellowMetal.albedo = {1.0, 0.92, 0.20}; matYellowMetal.metalness = 0.92;
+
+        // ---------------------------
+        // Cornell Box 场景（前方开口）
+        // 坐标：房间x∈[-1,1], y∈[0,2], z∈[0,2]
+        // 相机在 z<0 处朝 +z 看
+        // ---------------------------
+        std::vector<Triangle> scene;
+        int nextId = 1;
+
+        // floor y=0
+        addQuad(scene, nextId,
+            Vec3(-1,0,0), Vec3( 1,0,0), Vec3( 1,0,2), Vec3(-1,0,2),
+            &matWhite
+        );
+        // ceiling y=2
+        addQuad(scene, nextId,
+            Vec3(-1,2,0), Vec3(-1,2,2), Vec3( 1,2,2), Vec3( 1,2,0),
+            &matWhite
+        );
+        // back wall z=2
+        addQuad(scene, nextId,
+            Vec3(-1,0,2), Vec3( 1,0,2), Vec3( 1,2,2), Vec3(-1,2,2),
+            &matWhite
+        );
+        // left wall x=-1 (red)
+        addQuad(scene, nextId,
+            Vec3(-1,0,0), Vec3(-1,0,2), Vec3(-1,2,2), Vec3(-1,2,0),
+            &matRed
+        );
+        // right wall x=1 (green)
+        addQuad(scene, nextId,
+            Vec3( 1,0,0), Vec3( 1,2,0), Vec3( 1,2,2), Vec3( 1,0,2),
+            &matGreen
+        );
+
+        // ---------------------------
+        // 两个金属盒子（蓝、黄）
+        // ---------------------------
+        addBox(scene, nextId, Vec3(-0.70, 0.0, 0.80), Vec3(-0.15, 0.60, 1.30), &matBlueMetal);
+        addBox(scene, nextId, Vec3( 0.15, 0.0, 1.00), Vec3( 0.70, 1.10, 1.65), &matYellowMetal);
+
+        // ---------------------------
+        // Camera + viewport(两个三角形)
+        // viewport平面取 z = -2.0，矩形中心 y=1.0
+        // ---------------------------
+        Camera cam;
+        cam.width = 900;
+        cam.height = 650;
+        cam.origin = Vec3(0.0, 1.0, -3.0);
+
+        double vpZ = -2.0;
+        double aspect = (double)cam.width / (double)cam.height;
+        double vpH = 1.6;              // viewport世界高度
+        double vpW = vpH * aspect;     // 对应宽度
+
+        Vec3 center(0.0, 1.0, vpZ);
+        Vec3 TL(center.x - vpW * 0.5, center.y - vpH * 0.5, vpZ);
+        Vec3 TR(center.x + vpW * 0.5, center.y - vpH * 0.5, vpZ);
+        Vec3 BL(center.x - vpW * 0.5, center.y + vpH * 0.5, vpZ);
+        Vec3 BR(center.x + vpW * 0.5, center.y + vpH * 0.5, vpZ);
+
+        // viewport UV：u右 v下（0为上）
+        // 三角A：TL(0,0), TR(1,0), BL(0,1)
+        cam.vpA.id = -100;
+        cam.vpA.p[0] = TL; cam.vpA.p[1] = TR; cam.vpA.p[2] = BL;
+        cam.vpA.uv[0] = {0,0}; cam.vpA.uv[1] = {1,0}; cam.vpA.uv[2] = {0,1};
+        cam.vpA.mat = nullptr; // viewport不是场景面片，不参与材质
+
+        // 三角B：TR(1,0), BR(1,1), BL(0,1)
+        cam.vpB.id = -101;
+        cam.vpB.p[0] = TR; cam.vpB.p[1] = BR; cam.vpB.p[2] = BL;
+        cam.vpB.uv[0] = {1,0}; cam.vpB.uv[1] = {1,1}; cam.vpB.uv[2] = {0,1};
+        cam.vpB.mat = nullptr;
+
+        RenderConfig cfg;
+        cfg.maxDepth = 4;
+        cfg.minAreaPxToRecurse = 6.0;
+        cfg.maxTriTexRes = 256;
+        cfg.minTriTexRes = 16;
+        cfg.envColor = {0.06, 0.07, 0.09};
+
+        Image img = cam.render(scene, cfg);
+        img.writePPM("output_rt10.ppm");
+
+        std::cerr << "Done. Wrote output_rt10.ppm\n";
+        return 0;
+    } catch (const std::exception& e) {
+        std::cerr << "Fatal: " << e.what() << "\n";
+        return 1;
+    }
+}

experiments/rt11.cpp

@@ -0,0 +1,940 @@
+#include <iostream>
+#include <vector>
+#include <cmath>
+#include <algorithm>
+#include <fstream>
+#include <limits>
+#include <memory>
+#include <array>
+
+// ==================== 基础数学结构 ====================
+
+struct Vec3 {
+    double x, y, z;
+    
+    Vec3() : x(0), y(0), z(0) {}
+    Vec3(double x, double y, double z) : x(x), y(y), z(z) {}
+    
+    Vec3 operator+(const Vec3& v) const { return Vec3(x + v.x, y + v.y, z + v.z); }
+    Vec3 operator-(const Vec3& v) const { return Vec3(x - v.x, y - v.y, z - v.z); }
+    Vec3 operator*(double t) const { return Vec3(x * t, y * t, z * t); }
+    Vec3 operator*(const Vec3& v) const { return Vec3(x * v.x, y * v.y, z * v.z); }
+    Vec3 operator/(double t) const { return Vec3(x / t, y / t, z / t); }
+    Vec3& operator+=(const Vec3& v) { x += v.x; y += v.y; z += v.z; return *this; }
+    Vec3& operator*=(double t) { x *= t; y *= t; z *= t; return *this; }
+    
+    double dot(const Vec3& v) const { return x * v.x + y * v.y + z * v.z; }
+    Vec3 cross(const Vec3& v) const {
+        return Vec3(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x);
+    }
+    
+    double length() const { return std::sqrt(x * x + y * y + z * z); }
+    double lengthSquared() const { return x * x + y * y + z * z; }
+    Vec3 normalized() const {
+        double len = length();
+        if (len < 1e-10) return Vec3(0, 0, 0);
+        return *this / len;
+    }
+    
+    // 关于平面对称点
+    static Vec3 reflect(const Vec3& point, const Vec3& planePoint, const Vec3& planeNormal) {
+        Vec3 n = planeNormal.normalized();
+        double d = (point - planePoint).dot(n);
+        return point - n * (2 * d);
+    }
+};
+
+Vec3 operator*(double t, const Vec3& v) { return v * t; }
+
+// 颜色结构（RGB，0-1范围）
+struct Color {
+    double r, g, b;
+    
+    Color() : r(0), g(0), b(0) {}
+    Color(double r, double g, double b) : r(r), g(g), b(b) {}
+    
+    Color operator+(const Color& c) const { return Color(r + c.r, g + c.g, b + c.b); }
+    Color operator*(double t) const { return Color(r * t, g * t, b * t); }
+    Color operator*(const Color& c) const { return Color(r * c.r, g * c.g, b * c.b); }
+    Color& operator+=(const Color& c) { r += c.r; g += c.g; b += c.b; return *this; }
+    
+    Color clamped() const {
+        return Color(
+            std::max(0.0, std::min(1.0, r)),
+            std::max(0.0, std::min(1.0, g)),
+            std::max(0.0, std::min(1.0, b))
+        );
+    }
+    
+    static Color lerp(const Color& a, const Color& b, double t) {
+        return Color(a.r + (b.r - a.r) * t, a.g + (b.g - a.g) * t, a.b + (b.b - a.b) * t);
+    }
+};
+
+// ==================== 纹理类 ====================
+
+class Texture {
+public:
+    int width, height;
+    std::vector<Color> pixels;
+    
+    Texture() : width(0), height(0) {}
+    Texture(int w, int h) : width(w), height(h), pixels(w * h) {}
+    Texture(int w, int h, const Color& fillColor) : width(w), height(h), pixels(w * h, fillColor) {}
+    
+    Color getPixel(int x, int y) const {
+        if (x < 0 || x >= width || y < 0 || y >= height) return Color(0, 0, 0);
+        return pixels[y * width + x];
+    }
+    
+    void setPixel(int x, int y, const Color& c) {
+        if (x < 0 || x >= width || y < 0 || y >= height) return;
+        pixels[y * width + x] = c;
+    }
+    
+    // 双线性插值采样（UV坐标0-1）
+    Color sample(double u, double v) const {
+        if (width == 0 || height == 0) return Color(0, 0, 0);
+        
+        u = std::max(0.0, std::min(1.0, u));
+        v = std::max(0.0, std::min(1.0, v));
+        
+        double fx = u * (width - 1);
+        double fy = v * (height - 1);
+        
+        int x0 = (int)fx;
+        int y0 = (int)fy;
+        int x1 = std::min(x0 + 1, width - 1);
+        int y1 = std::min(y0 + 1, height - 1);
+        
+        double tx = fx - x0;
+        double ty = fy - y0;
+        
+        Color c00 = getPixel(x0, y0);
+        Color c10 = getPixel(x1, y0);
+        Color c01 = getPixel(x0, y1);
+        Color c11 = getPixel(x1, y1);
+        
+        Color c0 = Color::lerp(c00, c10, tx);
+        Color c1 = Color::lerp(c01, c11, tx);
+        
+        return Color::lerp(c0, c1, ty);
+    }
+    
+    // 在指定像素位置混合颜色（用于叠加）
+    void blendPixel(int x, int y, const Color& c, double alpha = 1.0) {
+        if (x < 0 || x >= width || y < 0 || y >= height) return;
+        Color existing = getPixel(x, y);
+        Color blended = Color(
+            existing.r * (1 - alpha) + c.r * alpha,
+            existing.g * (1 - alpha) + c.g * alpha,
+            existing.b * (1 - alpha) + c.b * alpha
+        );
+        setPixel(x, y, blended);
+    }
+};
+
+// ==================== 材质类型 ====================
+
+enum class MaterialType {
+    Diffuse,      // 漫反射
+    Reflective,   // 镜面反射
+    Emissive      // 发光体
+};
+
+struct Material {
+    MaterialType type;
+    Color baseColor;
+    double reflectivity;  // 0-1，反射率
+    
+    Material() : type(MaterialType::Diffuse), baseColor(0.8, 0.8, 0.8), reflectivity(0) {}
+    Material(MaterialType t, const Color& c, double refl = 0.9) 
+        : type(t), baseColor(c), reflectivity(refl) {}
+};
+
+// ==================== 三角形类 ====================
+
+class Triangle {
+public:
+    Vec3 v0, v1, v2;  // 三个顶点
+    Vec3 normal;       // 法向量
+    Material material;
+    Texture* texture;  // 可选的纹理
+    
+    // UV坐标
+    Vec3 uv0, uv1, uv2;
+    
+    Triangle() : texture(nullptr) {
+        uv0 = Vec3(0, 0, 0);
+        uv1 = Vec3(1, 0, 0);
+        uv2 = Vec3(0, 1, 0);
+    }
+    
+    Triangle(const Vec3& a, const Vec3& b, const Vec3& c, const Material& mat = Material())
+        : v0(a), v1(b), v2(c), material(mat), texture(nullptr) {
+        normal = (v1 - v0).cross(v2 - v0).normalized();
+        uv0 = Vec3(0, 0, 0);
+        uv1 = Vec3(1, 0, 0);
+        uv2 = Vec3(0, 1, 0);
+    }
+    
+    void setUV(const Vec3& u0, const Vec3& u1, const Vec3& u2) {
+        uv0 = u0; uv1 = u1; uv2 = u2;
+    }
+    
+    // 获取三角形中心
+    Vec3 center() const {
+        return (v0 + v1 + v2) / 3.0;
+    }
+    
+    // 获取三角形面积
+    double area() const {
+        return (v1 - v0).cross(v2 - v0).length() * 0.5;
+    }
+    
+    // 计算重心坐标
+    bool barycentricCoords(const Vec3& p, double& u, double& v, double& w) const {
+        Vec3 v0v1 = v1 - v0;
+        Vec3 v0v2 = v2 - v0;
+        Vec3 v0p = p - v0;
+        
+        double d00 = v0v1.dot(v0v1);
+        double d01 = v0v1.dot(v0v2);
+        double d11 = v0v2.dot(v0v2);
+        double d20 = v0p.dot(v0v1);
+        double d21 = v0p.dot(v0v2);
+        
+        double denom = d00 * d11 - d01 * d01;
+        if (std::abs(denom) < 1e-10) return false;
+        
+        v = (d11 * d20 - d01 * d21) / denom;
+        w = (d00 * d21 - d01 * d20) / denom;
+        u = 1.0 - v - w;
+        
+        return true;
+    }
+    
+    // 从重心坐标获取UV
+    Vec3 getUVFromBarycentric(double u, double v, double w) const {
+        return Vec3(
+            u * uv0.x + v * uv1.x + w * uv2.x,
+            u * uv0.y + v * uv1.y + w * uv2.y,
+            0
+        );
+    }
+    
+    // 射线与三角形相交测试（Möller–Trumbore算法）
+    bool rayIntersect(const Vec3& origin, const Vec3& dir, double& t, double& u, double& v) const {
+        const double EPSILON = 1e-8;
+        Vec3 edge1 = v1 - v0;
+        Vec3 edge2 = v2 - v0;
+        Vec3 h = dir.cross(edge2);
+        double a = edge1.dot(h);
+        
+        if (std::abs(a) < EPSILON) return false;
+        
+        double f = 1.0 / a;
+        Vec3 s = origin - v0;
+        u = f * s.dot(h);
+        
+        if (u < 0.0 || u > 1.0) return false;
+        
+        Vec3 q = s.cross(edge1);
+        v = f * dir.dot(q);
+        
+        if (v < 0.0 || u + v > 1.0) return false;
+        
+        t = f * edge2.dot(q);
+        
+        return t > EPSILON;
+    }
+    
+    // 获取指定UV处的颜色
+    Color getColorAtUV(double u, double v) const {
+        if (texture != nullptr) {
+            return texture->sample(u, v);
+        }
+        return material.baseColor;
+    }
+};
+
+// ==================== 视锥体类（由原点和三角形viewport组成） ====================
+
+class Frustum {
+public:
+    Vec3 apex;           // 视锥体顶点（相机原点）
+    Triangle viewport;   // 底面三角形
+    
+    // 四个平面（侧面3个 + 底面1个）
+    // 每个平面由法向量和平面上的一点定义
+    std::array<Vec3, 4> planeNormals;
+    std::array<Vec3, 4> planePoints;
+    
+    Frustum() {}
+    
+    Frustum(const Vec3& origin, const Triangle& vp) : apex(origin), viewport(vp) {
+        buildPlanes();
+    }
+    
+    void buildPlanes() {
+        // 三个侧面
+        Vec3 edge0 = viewport.v1 - viewport.v0;
+        Vec3 edge1 = viewport.v2 - viewport.v1;
+        Vec3 edge2 = viewport.v0 - viewport.v2;
+        
+        Vec3 toApex0 = apex - viewport.v0;
+        Vec3 toApex1 = apex - viewport.v1;
+        Vec3 toApex2 = apex - viewport.v2;
+        
+        // 侧面0: v0-v1-apex
+        planeNormals[0] = edge0.cross(toApex0).normalized();
+        planePoints[0] = viewport.v0;
+        
+        // 侧面1: v1-v2-apex
+        planeNormals[1] = edge1.cross(toApex1).normalized();
+        planePoints[1] = viewport.v1;
+        
+        // 侧面2: v2-v0-apex
+        planeNormals[2] = edge2.cross(toApex2).normalized();
+        planePoints[2] = viewport.v2;
+        
+        // 底面（viewport平面）
+        planeNormals[3] = viewport.normal;
+        planePoints[3] = viewport.v0;
+        
+        // 确保法向量朝向视锥体内部
+        Vec3 center = (viewport.v0 + viewport.v1 + viewport.v2) / 3.0;
+        Vec3 frustumCenter = (center + apex) / 2.0;
+        
+        for (int i = 0; i < 3; ++i) {
+            Vec3 toCenter = frustumCenter - planePoints[i];
+            if (planeNormals[i].dot(toCenter) < 0) {
+                planeNormals[i] = planeNormals[i] * (-1);
+            }
+        }
+        
+        // 底面法向量应该指向apex方向
+        Vec3 toApex = apex - planePoints[3];
+        if (planeNormals[3].dot(toApex) < 0) {
+            planeNormals[3] = planeNormals[3] * (-1);
+        }
+    }
+    
+    // 检测点是否在视锥体内
+    bool containsPoint(const Vec3& p) const {
+        for (int i = 0; i < 4; ++i) {
+            Vec3 toPoint = p - planePoints[i];
+            if (planeNormals[i].dot(toPoint) < -1e-6) {
+                return false;
+            }
+        }
+        return true;
+    }
+    
+    // 检测三角形是否与视锥体相交或被包含
+    bool intersectsTriangle(const Triangle& tri) const {
+        // 简化检测：检查三角形的任意顶点是否在视锥体内，
+        // 或者视锥体的任意边是否与三角形相交
+        
+        // 检查三角形顶点
+        if (containsPoint(tri.v0) || containsPoint(tri.v1) || containsPoint(tri.v2)) {
+            return true;
+        }
+        
+        // 检查视锥体边与三角形的相交
+        std::vector<std::pair<Vec3, Vec3>> frustumEdges = {
+            {apex, viewport.v0},
+            {apex, viewport.v1},
+            {apex, viewport.v2},
+            {viewport.v0, viewport.v1},
+            {viewport.v1, viewport.v2},
+            {viewport.v2, viewport.v0}
+        };
+        
+        for (const auto& edge : frustumEdges) {
+            Vec3 dir = edge.second - edge.first;
+            double t, u, v;
+            if (tri.rayIntersect(edge.first, dir.normalized(), t, u, v)) {
+                if (t >= 0 && t <= dir.length()) {
+                    return true;
+                }
+            }
+        }
+        
+        // 检查三角形边与视锥体平面的相交
+        std::vector<std::pair<Vec3, Vec3>> triEdges = {
+            {tri.v0, tri.v1},
+            {tri.v1, tri.v2},
+            {tri.v2, tri.v0}
+        };
+        
+        for (const auto& edge : triEdges) {
+            Vec3 dir = edge.second - edge.first;
+            double t, u, v;
+            if (viewport.rayIntersect(edge.first, dir.normalized(), t, u, v)) {
+                if (t >= 0 && t <= dir.length()) {
+                    return true;
+                }
+            }
+        }
+        
+        return false;
+    }
+};
+
+// ==================== 前向声明 ====================
+
+class Scene;
+Texture renderTriangleWithTriangle(
+    const std::vector<Triangle*>& triangles,
+    const Vec3& cameraOrigin,
+    const Triangle& currentTriangle,
+    int estimatedWidth,
+    int estimatedHeight,
+    int depth,
+    int maxDepth,
+    const Scene& scene
+);
+
+// ==================== 场景类 ====================
+
+class Scene {
+public:
+    std::vector<Triangle> triangles;
+    Color ambientLight;
+    Vec3 lightPosition;
+    Color lightColor;
+    
+    Scene() : ambientLight(0.1, 0.1, 0.1), lightPosition(0, 1.9, 0), lightColor(1, 1, 1) {}
+    
+    void addTriangle(const Triangle& tri) {
+        triangles.push_back(tri);
+    }
+    
+    // 添加四边形（分解为两个三角形）
+    void addQuad(const Vec3& v0, const Vec3& v1, const Vec3& v2, const Vec3& v3, const Material& mat) {
+        Triangle t1(v0, v1, v2, mat);
+        Triangle t2(v0, v2, v3, mat);
+        
+        // 设置UV坐标
+        t1.setUV(Vec3(0, 0, 0), Vec3(1, 0, 0), Vec3(1, 1, 0));
+        t2.setUV(Vec3(0, 0, 0), Vec3(1, 1, 0), Vec3(0, 1, 0));
+        
+        triangles.push_back(t1);
+        triangles.push_back(t2);
+    }
+    
+    // 添加盒子
+    void addBox(const Vec3& minCorner, const Vec3& maxCorner, const Material& mat) {
+        Vec3 v000 = minCorner;
+        Vec3 v111 = maxCorner;
+        Vec3 v100 = Vec3(maxCorner.x, minCorner.y, minCorner.z);
+        Vec3 v010 = Vec3(minCorner.x, maxCorner.y, minCorner.z);
+        Vec3 v001 = Vec3(minCorner.x, minCorner.y, maxCorner.z);
+        Vec3 v110 = Vec3(maxCorner.x, maxCorner.y, minCorner.z);
+        Vec3 v101 = Vec3(maxCorner.x, minCorner.y, maxCorner.z);
+        Vec3 v011 = Vec3(minCorner.x, maxCorner.y, maxCorner.z);
+        
+        // 前面 (z = max)
+        addQuad(v001, v101, v111, v011, mat);
+        // 后面 (z = min)
+        addQuad(v100, v000, v010, v110, mat);
+        // 左面 (x = min)
+        addQuad(v000, v001, v011, v010, mat);
+        // 右面 (x = max)
+        addQuad(v101, v100, v110, v111, mat);
+        // 顶面 (y = max)
+        addQuad(v010, v011, v111, v110, mat);
+        // 底面 (y = min)
+        addQuad(v000, v100, v101, v001, mat);
+    }
+    
+    std::vector<Triangle*> getTrianglePointers() {
+        std::vector<Triangle*> ptrs;
+        for (auto& tri : triangles) {
+            ptrs.push_back(&tri);
+        }
+        return ptrs;
+    }
+};
+
+// ==================== 工具函数 ====================
+
+// 将点从相机原点投影到目标平面上
+Vec3 projectPointToPlane(const Vec3& origin, const Vec3& point, const Vec3& planePoint, const Vec3& planeNormal) {
+    Vec3 dir = (point - origin).normalized();
+    double denom = dir.dot(planeNormal);
+    if (std::abs(denom) < 1e-10) return point; // 平行
+    
+    double t = (planePoint - origin).dot(planeNormal) / denom;
+    return origin + dir * t;
+}
+
+// 将三角形的纹理变换并绘制到目标纹理上
+void drawTransformedTriangle(
+    Texture& destTexture,
+    const Triangle& destTriangle,  // 目标三角形（viewport）
+    const Triangle& srcTriangle,   // 源三角形
+    const Texture& srcTexture,     // 源纹理
+    const Vec3& cameraOrigin       // 相机原点
+) {
+    // 计算源三角形三个顶点投影到目标三角形平面上的位置
+    Vec3 proj0 = projectPointToPlane(cameraOrigin, srcTriangle.v0, destTriangle.v0, destTriangle.normal);
+    Vec3 proj1 = projectPointToPlane(cameraOrigin, srcTriangle.v1, destTriangle.v0, destTriangle.normal);
+    Vec3 proj2 = projectPointToPlane(cameraOrigin, srcTriangle.v2, destTriangle.v0, destTriangle.normal);
+    
+    // 将投影点转换为目标三角形的重心坐标
+    double u0, v0, w0, u1, v1, w1, u2, v2, w2;
+    destTriangle.barycentricCoords(proj0, u0, v0, w0);
+    destTriangle.barycentricCoords(proj1, u1, v1, w1);
+    destTriangle.barycentricCoords(proj2, u2, v2, w2);
+    
+    // 转换为纹理坐标
+    Vec3 texCoord0 = destTriangle.getUVFromBarycentric(u0, v0, w0);
+    Vec3 texCoord1 = destTriangle.getUVFromBarycentric(u1, v1, w1);
+    Vec3 texCoord2 = destTriangle.getUVFromBarycentric(u2, v2, w2);
+    
+    // 在目标纹理上栅格化源三角形
+    // 计算边界框
+    double minU = std::min({texCoord0.x, texCoord1.x, texCoord2.x});
+    double maxU = std::max({texCoord0.x, texCoord1.x, texCoord2.x});
+    double minV = std::min({texCoord0.y, texCoord1.y, texCoord2.y});
+    double maxV = std::max({texCoord0.y, texCoord1.y, texCoord2.y});
+    
+    int startX = std::max(0, (int)(minU * destTexture.width) - 1);
+    int endX = std::min(destTexture.width - 1, (int)(maxU * destTexture.width) + 1);
+    int startY = std::max(0, (int)(minV * destTexture.height) - 1);
+    int endY = std::min(destTexture.height - 1, (int)(maxV * destTexture.height) + 1);
+    
+    // 使用重心坐标进行纹理映射
+    for (int py = startY; py <= endY; ++py) {
+        for (int px = startX; px <= endX; ++px) {
+            double u = (px + 0.5) / destTexture.width;
+            double v = (py + 0.5) / destTexture.height;
+            
+            // 检查点是否在投影三角形内（使用2D重心坐标）
+            Vec3 p(u, v, 0);
+            Vec3 a(texCoord0.x, texCoord0.y, 0);
+            Vec3 b(texCoord1.x, texCoord1.y, 0);
+            Vec3 c(texCoord2.x, texCoord2.y, 0);
+            
+            Vec3 v0v = b - a;
+            Vec3 v1v = c - a;
+            Vec3 v2v = p - a;
+            
+            double d00 = v0v.x * v0v.x + v0v.y * v0v.y;
+            double d01 = v0v.x * v1v.x + v0v.y * v1v.y;
+            double d11 = v1v.x * v1v.x + v1v.y * v1v.y;
+            double d20 = v2v.x * v0v.x + v2v.y * v0v.y;
+            double d21 = v2v.x * v1v.x + v2v.y * v1v.y;
+            
+            double denom = d00 * d11 - d01 * d01;
+            if (std::abs(denom) < 1e-10) continue;
+            
+            double baryV = (d11 * d20 - d01 * d21) / denom;
+            double baryW = (d00 * d21 - d01 * d20) / denom;
+            double baryU = 1.0 - baryV - baryW;
+            
+            // 检查是否在三角形内
+            if (baryU >= -0.001 && baryV >= -0.001 && baryW >= -0.001) {
+                // 计算源纹理的UV坐标
+                double srcU = baryU * srcTriangle.uv0.x + baryV * srcTriangle.uv1.x + baryW * srcTriangle.uv2.x;
+                double srcV = baryU * srcTriangle.uv0.y + baryV * srcTriangle.uv1.y + baryW * srcTriangle.uv2.y;
+                
+                Color srcColor = srcTexture.sample(srcU, srcV);
+                destTexture.setPixel(px, py, srcColor);
+            }
+        }
+    }
+}
+
+// 计算三角形投影到viewport上的近似像素面积
+double estimateProjectedArea(const Triangle& tri, const Vec3& cameraOrigin, const Triangle& viewport, int viewportWidth, int viewportHeight) {
+    Vec3 proj0 = projectPointToPlane(cameraOrigin, tri.v0, viewport.v0, viewport.normal);
+    Vec3 proj1 = projectPointToPlane(cameraOrigin, tri.v1, viewport.v0, viewport.normal);
+    Vec3 proj2 = projectPointToPlane(cameraOrigin, tri.v2, viewport.v0, viewport.normal);
+    
+    double u0, v0, w0, u1, v1, w1, u2, v2, w2;
+    viewport.barycentricCoords(proj0, u0, v0, w0);
+    viewport.barycentricCoords(proj1, u1, v1, w1);
+    viewport.barycentricCoords(proj2, u2, v2, w2);
+    
+    Vec3 tc0 = viewport.getUVFromBarycentric(u0, v0, w0);
+    Vec3 tc1 = viewport.getUVFromBarycentric(u1, v1, w1);
+    Vec3 tc2 = viewport.getUVFromBarycentric(u2, v2, w2);
+    
+    // 计算2D三角形面积
+    double area = 0.5 * std::abs(
+        (tc1.x - tc0.x) * (tc2.y - tc0.y) - (tc2.x - tc0.x) * (tc1.y - tc0.y)
+    );
+    
+    return area * viewportWidth * viewportHeight;
+}
+
+// ==================== 核心渲染函数 ====================
+
+Texture renderTriangleWithTriangle(
+    const std::vector<Triangle*>& triangles,
+    const Vec3& cameraOrigin,
+    const Triangle& currentTriangle,
+    int estimatedWidth,
+    int estimatedHeight,
+    int depth,
+    int maxDepth,
+    const Scene& scene
+) {
+    // 检查终止条件
+    if (depth >= maxDepth || estimatedWidth < 2 || estimatedHeight < 2) {
+        // 返回基础颜色纹理
+        Texture result(std::max(1, estimatedWidth), std::max(1, estimatedHeight), currentTriangle.material.baseColor);
+        return result;
+    }
+    
+    // 如果是漫反射材质，直接返回基础颜色
+    if (currentTriangle.material.type == MaterialType::Diffuse) {
+        Texture result(estimatedWidth, estimatedHeight, currentTriangle.material.baseColor);
+        
+        // 添加简单的光照计算
+        Vec3 toLight = (scene.lightPosition - currentTriangle.center()).normalized();
+        double diffuse = std::max(0.0, currentTriangle.normal.dot(toLight));
+        
+        Color litColor = currentTriangle.material.baseColor * (0.3 + 0.7 * diffuse);
+        for (int y = 0; y < estimatedHeight; ++y) {
+            for (int x = 0; x < estimatedWidth; ++x) {
+                result.setPixel(x, y, litColor);
+            }
+        }
+        
+        return result;
+    }
+    
+    // 如果是发光材质，返回发光颜色
+    if (currentTriangle.material.type == MaterialType::Emissive) {
+        Texture result(estimatedWidth, estimatedHeight, currentTriangle.material.baseColor);
+        return result;
+    }
+    
+    // 镜面反射材质
+    // 初始化当前面片的纹理（使用基础颜色）
+    Texture currentTexture(estimatedWidth, estimatedHeight, currentTriangle.material.baseColor * 0.1);
+    
+    // 计算反射后的相机原点（关于当前面片对称）
+    Vec3 reflectedOrigin = Vec3::reflect(cameraOrigin, currentTriangle.center(), currentTriangle.normal);
+    
+    // 构建视锥体
+    Frustum frustum(reflectedOrigin, currentTriangle);
+    
+    // 收集与视锥体相交的三角形
+    struct TriangleDistance {
+        Triangle* tri;
+        double distance;
+        
+        bool operator<(const TriangleDistance& other) const {
+            return distance > other.distance; // 由远到近
+        }
+    };
+    
+    std::vector<TriangleDistance> intersectedTriangles;
+    
+    for (Triangle* tri : triangles) {
+        // 跳过当前三角形
+        if (tri->v0.x == currentTriangle.v0.x && tri->v0.y == currentTriangle.v0.y && tri->v0.z == currentTriangle.v0.z &&
+            tri->v1.x == currentTriangle.v1.x && tri->v1.y == currentTriangle.v1.y && tri->v1.z == currentTriangle.v1.z &&
+            tri->v2.x == currentTriangle.v2.x && tri->v2.y == currentTriangle.v2.y && tri->v2.z == currentTriangle.v2.z) {
+            continue;
+        }
+        
+        // 检查三角形是否在视锥体的"前方"（从反射原点看去）
+        Vec3 toTriCenter = tri->center() - reflectedOrigin;
+        Vec3 viewDir = (currentTriangle.center() - reflectedOrigin).normalized();
+        
+        if (toTriCenter.dot(viewDir) <= 0) {
+            continue; // 三角形在视锥体后方
+        }
+        
+        if (frustum.intersectsTriangle(*tri)) {
+            double dist = (tri->center() - reflectedOrigin).length();
+            intersectedTriangles.push_back({tri, dist});
+        }
+    }
+    
+    // 按距离排序（由远到近）
+    std::sort(intersectedTriangles.begin(), intersectedTriangles.end());
+    
+    // 遍历并渲染每个相交的三角形
+    for (const auto& td : intersectedTriangles) {
+        Triangle* tri = td.tri;
+        
+        // 估计该三角形投影到当前面片上的像素大小
+        double projectedArea = estimateProjectedArea(*tri, reflectedOrigin, currentTriangle, estimatedWidth, estimatedHeight);
+        int subWidth = std::max(2, (int)std::sqrt(projectedArea));
+        int subHeight = subWidth;
+        
+        // 递归获取该三角形的纹理
+        Texture subTexture = renderTriangleWithTriangle(
+            triangles, reflectedOrigin, *tri, subWidth, subHeight, depth + 1, maxDepth, scene
+        );
+        
+        // 创建临时三角形用于绘制（带有获取的纹理）
+        Triangle tempTri = *tri;
+        tempTri.texture = &subTexture;
+        
+        // 将该三角形的纹理变换并绘制到当前纹理上
+        drawTransformedTriangle(currentTexture, currentTriangle, *tri, subTexture, reflectedOrigin);
+    }
+    
+    // 混合基础颜色和反射结果
+    double refl = currentTriangle.material.reflectivity;
+    for (int y = 0; y < estimatedHeight; ++y) {
+        for (int x = 0; x < estimatedWidth; ++x) {
+            Color reflected = currentTexture.getPixel(x, y);
+            Color base = currentTriangle.material.baseColor * 0.1;
+            Color mixed = Color(
+                base.r * (1 - refl) + reflected.r * refl,
+                base.g * (1 - refl) + reflected.g * refl,
+                base.b * (1 - refl) + reflected.b * refl
+            );
+            currentTexture.setPixel(x, y, mixed);
+        }
+    }
+    
+    return currentTexture;
+}
+
+// ==================== 相机类 ====================
+
+class Camera {
+public:
+    Vec3 position;
+    Vec3 lookAt;
+    Vec3 up;
+    double fov;
+    int width, height;
+    
+    // Viewport三角形
+    Triangle viewportTri1, viewportTri2;
+    
+    Camera(const Vec3& pos, const Vec3& look, const Vec3& upDir, double fieldOfView, int w, int h)
+        : position(pos), lookAt(look), up(upDir), fov(fieldOfView), width(w), height(h) {
+        setupViewport();
+    }
+    
+    void setupViewport() {
+        Vec3 forward = (lookAt - position).normalized();
+        Vec3 right = forward.cross(up).normalized();
+        Vec3 upVec = right.cross(forward).normalized();
+        
+        double aspectRatio = (double)width / height;
+        double halfHeight = std::tan(fov * 0.5 * M_PI / 180.0);
+        double halfWidth = aspectRatio * halfHeight;
+        
+        // Viewport在相机前方单位距离处
+        Vec3 center = position + forward;
+        
+        Vec3 bottomLeft = center - right * halfWidth - upVec * halfHeight;
+        Vec3 bottomRight = center + right * halfWidth - upVec * halfHeight;
+        Vec3 topLeft = center - right * halfWidth + upVec * halfHeight;
+        Vec3 topRight = center + right * halfWidth + upVec * halfHeight;
+        
+        // 创建两个三角形组成viewport
+        Material viewportMat(MaterialType::Diffuse, Color(0, 0, 0));
+        viewportTri1 = Triangle(bottomLeft, bottomRight, topRight, viewportMat);
+        viewportTri2 = Triangle(bottomLeft, topRight, topLeft, viewportMat);
+        
+        // 设置UV坐标（用于纹理映射到最终图像）
+        viewportTri1.setUV(Vec3(0, 1, 0), Vec3(1, 1, 0), Vec3(1, 0, 0));  // 注意Y轴翻转
+        viewportTri2.setUV(Vec3(0, 1, 0), Vec3(1, 0, 0), Vec3(0, 0, 0));
+    }
+    
+    void render(Scene& scene, const std::string& filename) {
+        std::vector<Triangle*> triPtrs = scene.getTrianglePointers();
+        int maxDepth = 4;
+        
+        std::cout << "Rendering viewport triangle 1..." << std::endl;
+        Texture tex1 = renderTriangleWithTriangle(triPtrs, position, viewportTri1, width, height, 0, maxDepth, scene);
+        
+        std::cout << "Rendering viewport triangle 2..." << std::endl;
+        Texture tex2 = renderTriangleWithTriangle(triPtrs, position, viewportTri2, width, height, 0, maxDepth, scene);
+        
+        // 合并两个三角形的纹理到最终图像
+        Texture finalImage(width, height);
+        
+        for (int y = 0; y < height; ++y) {
+            for (int x = 0; x < width; ++x) {
+                double u = (x + 0.5) / width;
+                double v = (y + 0.5) / height;
+                
+                // 计算在viewport平面上的3D位置
+                Vec3 forward = (lookAt - position).normalized();
+                Vec3 right = forward.cross(up).normalized();
+                Vec3 upVec = right.cross(forward).normalized();
+                
+                double aspectRatio = (double)width / height;
+                double halfHeight = std::tan(fov * 0.5 * M_PI / 180.0);
+                double halfWidth = aspectRatio * halfHeight;
+                
+                Vec3 center = position + forward;
+                Vec3 point = center + right * (u * 2 - 1) * halfWidth + upVec * (1 - v * 2) * halfHeight;
+                
+                // 检查点在哪个三角形内
+                double bu, bv, bw;
+                if (viewportTri1.barycentricCoords(point, bu, bv, bw) && bu >= 0 && bv >= 0 && bw >= 0) {
+                    Vec3 uv = viewportTri1.getUVFromBarycentric(bu, bv, bw);
+                    finalImage.setPixel(x, y, tex1.sample(uv.x, uv.y));
+                } else if (viewportTri2.barycentricCoords(point, bu, bv, bw) && bu >= 0 && bv >= 0 && bw >= 0) {
+                    Vec3 uv = viewportTri2.getUVFromBarycentric(bu, bv, bw);
+                    finalImage.setPixel(x, y, tex2.sample(uv.x, uv.y));
+                }
+            }
+        }
+        
+        // 写入PPM文件
+        writePPM(filename, finalImage);
+        std::cout << "Image saved to " << filename << std::endl;
+    }
+    
+    void writePPM(const std::string& filename, const Texture& image) {
+        std::ofstream file(filename);
+        file << "P3\n" << image.width << " " << image.height << "\n255\n";
+        
+        for (int y = 0; y < image.height; ++y) {
+            for (int x = 0; x < image.width; ++x) {
+                Color c = image.getPixel(x, y).clamped();
+                int r = (int)(c.r * 255);
+                int g = (int)(c.g * 255);
+                int b = (int)(c.b * 255);
+                file << r << " " << g << " " << b << "\n";
+            }
+        }
+        
+        file.close();
+    }
+};
+
+// ==================== 构建Cornell Box场景 ====================
+
+void buildCornellBox(Scene& scene) {
+    // Cornell Box尺寸：大约 [-1, 1] x [0, 2] x [-1, 1]
+    double boxSize = 1.0;
+    
+    // 材质定义
+    Material whiteDiffuse(MaterialType::Diffuse, Color(0.75, 0.75, 0.75));
+    Material redDiffuse(MaterialType::Diffuse, Color(0.75, 0.15, 0.15));
+    Material greenDiffuse(MaterialType::Diffuse, Color(0.15, 0.75, 0.15));
+    Material blueReflective(MaterialType::Reflective, Color(0.2, 0.4, 0.8), 0.85);
+    Material yellowReflective(MaterialType::Reflective, Color(0.8, 0.7, 0.2), 0.85);
+    Material lightEmissive(MaterialType::Emissive, Color(1.0, 0.95, 0.9));
+    
+    // 地板（白色）
+    scene.addQuad(
+        Vec3(-boxSize, 0, -boxSize),
+        Vec3(boxSize, 0, -boxSize),
+        Vec3(boxSize, 0, boxSize),
+        Vec3(-boxSize, 0, boxSize),
+        whiteDiffuse
+    );
+    
+    // 天花板（白色）
+    scene.addQuad(
+        Vec3(-boxSize, 2 * boxSize, boxSize),
+        Vec3(boxSize, 2 * boxSize, boxSize),
+        Vec3(boxSize, 2 * boxSize, -boxSize),
+        Vec3(-boxSize, 2 * boxSize, -boxSize),
+        whiteDiffuse
+    );
+    
+    // 后墙（白色）
+    scene.addQuad(
+        Vec3(-boxSize, 0, -boxSize),
+        Vec3(-boxSize, 2 * boxSize, -boxSize),
+        Vec3(boxSize, 2 * boxSize, -boxSize),
+        Vec3(boxSize, 0, -boxSize),
+        whiteDiffuse
+    );
+    
+    // 左墙（红色）
+    scene.addQuad(
+        Vec3(-boxSize, 0, boxSize),
+        Vec3(-boxSize, 2 * boxSize, boxSize),
+        Vec3(-boxSize, 2 * boxSize, -boxSize),
+        Vec3(-boxSize, 0, -boxSize),
+        redDiffuse
+    );
+    
+    // 右墙（绿色）
+    scene.addQuad(
+        Vec3(boxSize, 0, -boxSize),
+        Vec3(boxSize, 2 * boxSize, -boxSize),
+        Vec3(boxSize, 2 * boxSize, boxSize),
+        Vec3(boxSize, 0, boxSize),
+        greenDiffuse
+    );
+    
+    // 顶部灯光（发光面板）
+    scene.addQuad(
+        Vec3(-0.25, 1.99, -0.25),
+        Vec3(0.25, 1.99, -0.25),
+        Vec3(0.25, 1.99, 0.25),
+        Vec3(-0.25, 1.99, 0.25),
+        lightEmissive
+    );
+    
+    // 蓝色金属盒子（左侧，稍微旋转）
+    double boxHeight1 = 0.6;
+    double boxWidth1 = 0.35;
+    Vec3 box1Center(-0.4, boxHeight1 / 2, -0.2);
+    
+    // 简化：使用轴对齐的盒子
+    scene.addBox(
+        Vec3(box1Center.x - boxWidth1/2, 0, box1Center.z - boxWidth1/2),
+        Vec3(box1Center.x + boxWidth1/2, boxHeight1, box1Center.z + boxWidth1/2),
+        blueReflective
+    );
+    
+    // 黄色金属盒子（右侧，更高一些）
+    double boxHeight2 = 0.9;
+    double boxWidth2 = 0.35;
+    Vec3 box2Center(0.35, boxHeight2 / 2, 0.15);
+    
+    scene.addBox(
+        Vec3(box2Center.x - boxWidth2/2, 0, box2Center.z - boxWidth2/2),
+        Vec3(box2Center.x + boxWidth2/2, boxHeight2, box2Center.z + boxWidth2/2),
+        yellowReflective
+    );
+    
+    // 设置光源
+    scene.lightPosition = Vec3(0, 1.95, 0);
+    scene.lightColor = Color(1, 1, 1);
+    scene.ambientLight = Color(0.05, 0.05, 0.05);
+}
+
+// ==================== 主函数 ====================
+
+int main() {
+    std::cout << "=== Panel-based Cornell Box Renderer ===" << std::endl;
+    std::cout << "Building scene..." << std::endl;
+    
+    Scene scene;
+    buildCornellBox(scene);
+    
+    std::cout << "Scene contains " << scene.triangles.size() << " triangles." << std::endl;
+    
+    // 设置相机
+    Vec3 cameraPos(0, 1, 2.5);
+    Vec3 lookAt(0, 1, 0);
+    Vec3 up(0, 1, 0);
+    
+    int imageWidth = 400;
+    int imageHeight = 400;
+    double fov = 50.0;
+    
+    Camera camera(cameraPos, lookAt, up, fov, imageWidth, imageHeight);
+    
+    std::cout << "Starting render at " << imageWidth << "x" << imageHeight << "..." << std::endl;
+    
+    camera.render(scene, "cornell_box.ppm");
+    
+    std::cout << "Render complete!" << std::endl;
+    
+    return 0;
+}

experiments/rt12.cpp

@@ -0,0 +1,620 @@
+/*
+ * Cornell Box Renderer based on Recursive Viewport Texture Transformation
+ * Compilation: g++ -O3 -std=c++17 main.cpp -o renderer
+ */
+
+#include <iostream>
+#include <vector>
+#include <cmath>
+#include <algorithm>
+#include <limits>
+#include <memory>
+#include <iomanip>
+
+// --- Constants & Configuration ---
+const int IMAGE_WIDTH = 800;
+const int IMAGE_HEIGHT = 600;
+const int MAX_DEPTH = 5;
+const float AREA_THRESHOLD = 4.0f; // Stop recursion if projected area is less than 4 pixels
+const float EPSILON = 1e-4f;
+
+// --- Basic Math Structures ---
+struct Vec3 {
+    float x, y, z;
+
+    Vec3() : x(0), y(0), z(0) {}
+    Vec3(float x, float y, float z) : x(x), y(y), z(z) {}
+
+    Vec3 operator+(const Vec3& v) const { return Vec3(x + v.x, y + v.y, z + v.z); }
+    Vec3 operator-(const Vec3& v) const { return Vec3(x - v.x, y - v.y, z - v.z); }
+    Vec3 operator*(float t) const { return Vec3(x * t, y * t, z * t); }
+    Vec3 operator/(float t) const { return Vec3(x / t, y / t, z / t); }
+    float dot(const Vec3& v) const { return x * v.x + y * v.y + z * v.z; }
+    Vec3 cross(const Vec3& v) const { return Vec3(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x); }
+    float length() const { return std::sqrt(x * x + y * y + z * z); }
+    Vec3 normalize() const { float l = length(); if (l > 0) return *this / l; return *this; }
+    
+    // Component-wise min/max for bounding box
+    Vec3 min(const Vec3& v) const { return Vec3(std::min(x, v.x), std::min(y, v.y), std::min(z, v.z)); }
+    Vec3 max(const Vec3& v) const { return Vec3(std::max(x, v.x), std::max(y, v.y), std::max(z, v.z)); }
+};
+
+struct Color {
+    unsigned char r, g, b;
+    Color() : r(0), g(0), b(0) {}
+    Color(float fr, float fg, float fb) {
+        r = static_cast<unsigned char>(std::min(255.0f, std::max(0.0f, fr * 255.0f)));
+        g = static_cast<unsigned char>(std::min(255.0f, std::max(0.0f, fg * 255.0f)));
+        b = static_cast<unsigned char>(std::min(255.0f, std::max(0.0f, fb * 255.0f)));
+    }
+    Color(unsigned char r, unsigned char g, unsigned char b) : r(r), g(g), b(b) {}
+    
+    Color operator*(float t) const {
+        return Color(r * t, g * t, b * t);
+    }
+    // Alpha blending helper
+    Color blendOver(const Color& background, float alpha) const {
+        float invAlpha = 1.0f - alpha;
+        return Color(
+            r * alpha + background.r * invAlpha,
+            g * alpha + background.g * invAlpha,
+            b * alpha + background.b * invAlpha
+        );
+    }
+};
+
+// --- Texture Class (2D Image Buffer) ---
+class Texture {
+public:
+    int width, height;
+    std::vector<Color> data;
+
+    Texture() : width(0), height(0) {}
+    Texture(int w, int h) : width(w), height(h), data(w * h, Color(0.0f, 0.0f, 0.0f)) {}
+
+    void setPixel(int x, int y, const Color& c) {
+        if (x >= 0 && x < width && y >= 0 && y < height) {
+            data[y * width + x] = c;
+        }
+    }
+
+    Color getPixel(float u, float v) const {
+        // Clamp or wrap? Let's clamp for UV mapping safety
+        u = std::max(0.0f, std::min(1.0f, u));
+        v = std::max(0.0f, std::min(1.0f, v));
+        
+        int x = static_cast<int>(u * (width - 1));
+        int y = static_cast<int>(v * (height - 1));
+        return data[y * width + x];
+    }
+    
+    // Resampling (Bilinear-ish approximation for texture mapping)
+    Color sample(float u, float v) const {
+        return getPixel(u, v);
+    }
+};
+
+// --- Geometry & Math Helpers ---
+
+// Plane defined by normal N and point P
+float planeDist(const Vec3& N, const Vec3& P, const Vec3& X) {
+    return (X - P).dot(N);
+}
+
+// Ray-Triangle Intersection (Möller–Trumbore for culling visibility checks)
+// Returns distance, -1 if no hit
+float rayTriangleIntersect(const Vec3& orig, const Vec3& dir, const Vec3& v0, const Vec3& v1, const Vec3& v2) {
+    Vec3 edge1 = v1 - v0;
+    Vec3 edge2 = v2 - v0;
+    Vec3 h = dir.cross(edge2);
+    float a = edge1.dot(h);
+    if (std::abs(a) < EPSILON) return -1; // Parallel
+    float f = 1.0 / a;
+    Vec3 s = orig - v0;
+    float u = f * s.dot(h);
+    if (u < 0.0 || u > 1.0) return -1;
+    Vec3 q = s.cross(edge1);
+    float v = f * dir.dot(q);
+    if (v < 0.0 || u + v > 1.0) return -1;
+    float t = f * edge2.dot(q);
+    if (t > EPSILON) return t;
+    return -1;
+}
+
+// Project 3D point P onto Plane defined by N and point P_plane
+Vec3 projectOnPlane(const Vec3& P, const Vec3& N, const Vec3& P_plane) {
+    float d = (P - P_plane).dot(N);
+    return P - N * d;
+}
+
+// Barycentric coordinates
+Vec3 barycentric(const Vec3& P, const Vec3& A, const Vec3& B, const Vec3& C) {
+    Vec3 v0 = B - A, v1 = C - A, v2 = P - A;
+    float d00 = v0.dot(v0);
+    float d01 = v0.dot(v1);
+    float d11 = v1.dot(v1);
+    float d20 = v2.dot(v0);
+    float d21 = v2.dot(v1);
+    float denom = d00 * d11 - d01 * d01;
+    float v = (d11 * d20 - d01 * d21) / denom;
+    float w = (d00 * d21 - d01 * d20) / denom;
+    float u = 1.0f - v - w;
+    return Vec3(u, v, w);
+}
+
+// --- Triangle Class ---
+enum MaterialType { DIFFUSE, REFLECTIVE };
+
+struct Triangle {
+    Vec3 v0, v1, v2;
+    Vec3 normal;
+    Vec3 color; // Base color for Diffuse
+    MaterialType matType;
+    float reflectivity; // 0.0 to 1.0
+    Texture* texture; // Cached rendered texture if any (optional usage)
+    
+    // Cached bounding box for optimization
+    Vec3 boundsMin, boundsMax;
+
+    Triangle(Vec3 v0, Vec3 v1, Vec3 v2, Vec3 col, MaterialType mt = DIFFUSE, float refl = 0.0) 
+        : v0(v0), v1(v1), v2(v2), color(col), matType(mt), reflectivity(refl), texture(nullptr) {
+        
+        Vec3 e1 = v1 - v0;
+        Vec3 e2 = v2 - v0;
+        normal = e1.cross(e2).normalize();
+        
+        boundsMin = v0.min(v1).min(v2);
+        boundsMax = v0.max(v1).max(v2);
+    }
+    
+    float area() const {
+        return (v1 - v0).cross(v2 - v0).length() * 0.5f;
+    }
+};
+
+// --- Forward Declarations ---
+class Camera;
+Texture renderTriangleWithTriangle(const std::vector<Triangle*>& scene, const Vec3& origin, Triangle* viewportTri, int depth, float estArea);
+
+// --- Camera Class ---
+class Camera {
+public:
+    Vec3 origin;
+    Triangle* viewportLeft;
+    Triangle* viewportRight;
+    int width, height;
+
+    Camera(Vec3 o, Triangle* left, Triangle* right, int w, int h) 
+        : origin(o), viewportLeft(left), viewportRight(right), width(w), height(h) {}
+
+    void render(const std::vector<Triangle*>& scene, const std::string& filename) {
+        // Render the two triangles representing the image plane
+        // We need to map these triangles to the full image pixels. 
+        // However, the algorithm asks to render the triangles. 
+        // Since the viewport is exactly the image plane, the texture of these triangles IS the image.
+        // We pass the full resolution as the estimated area/resolution for the root call.
+        
+        std::cout << "Rendering Viewport Left..." << std::endl;
+        Texture texLeft = renderTriangleWithTriangle(scene, origin, viewportLeft, 0, width * height);
+        
+        std::cout << "Rendering Viewport Right..." << std::endl;
+        Texture texRight = renderTriangleWithTriangle(scene, origin, viewportRight, 0, width * height);
+
+        // Combine into PPM. 
+        // The Left and Right triangles might overlap or split the screen. 
+        // Assuming they split the screen vertically or form a quad.
+        // Let's assume they form a Quad: Left (Left half), Right (Right half).
+        
+        std::ofstream file(filename);
+        file << "P3\n" << width << " " << height << "\n255\n";
+        
+        // Naive combination: scan pixels.
+        // Since this is a "viewport based" renderer, mapping the triangle texture back to screen pixels 
+        // is technically a reverse lookup. But since the camera viewport triangles ARE the projection surface,
+        // the texture generated for `viewportLeft` covers exactly the region of the screen that triangle projects to.
+        // If we constructed the camera with two triangles covering the whole screen, 
+        // we can just iterate pixels and ask "Which triangle am I in?".
+        // Simplification: We assume the user constructs the viewport such that we can just dump the textures 
+        // or we map the UV of the triangles.
+        
+        // Let's implement a simple rasterizer to combine the two triangles onto the screen buffer.
+        // This is "Post-processing" the triangle textures to the image.
+        
+        std::vector<Vec3> screenBuffer(width * height, Vec3(0,0,0));
+        
+        // Helper to write texture to screen buffer based on projection
+        auto blitTriangle = [&](Triangle* tri, const Texture& tex) {
+            // Bounding box of triangle on screen
+            // We need to project triangle vertices to screen space? 
+            // No, the triangles ARE the viewport. They are defined in 3D at some distance Z.
+            // We need to project them to the screen plane (Z=0 or near plane).
+            // Actually, simpler: Use Barycentric in 2D on the XY plane if camera looks along Z.
+            // Let's assume standard Cornell Box orientation: Camera looks +Z.
+            // Viewport is at Z=1 (example). Screen is at Z=0.
+            // We project the 3D viewport triangle to 2D (x,y).
+            
+            float fov_dist = (tri->v0.z - origin.z); // Distance to viewport plane
+            float scale = 1.0f; // Adjust based on aspect ratio/FOV setup
+            
+            // Map World X,Y to Screen X,Y
+            // Assume orthographic scaling for simplicity of this specific mapping step
+            // or perspective divide.
+            
+            for(int y = 0; y < height; ++y) {
+                for(int x = 0; x < width; ++x) {
+                    // Convert pixel to world coord at viewport plane
+                    float u = (float)x / width;
+                    float v = (float)y / height; // Flip Y?
+                    
+                    // This logic is getting coupled to how we constructed the camera.
+                    // Alternative: The Texture returned by renderTriangleWithTriangle is already "rasterized" 
+                    // in its own UV space.
+                    // We need to know UV coordinates for the viewport triangles to index the texture.
+                    // Since we didn't store UVs in Triangle class explicitly, let's add a rasterizer 
+                    // that draws the triangle pixels.
+                    
+                    // Perspective Projection mapping:
+                    // Screen Pixel (x,y) -> Ray -> Intersect Viewport Plane -> UV
+                }
+            }
+        };
+
+        // To keep it robust and simple without a full rasterizer in main:
+        // We will just create a Texture for the Whole Screen, and renderTriangleWithTriangle
+        // will effectively draw onto the screen buffer if we pass the screen buffer.
+        // BUT, the requirement says: "Camera... calls render function twice and dumps texture to PPM".
+        // This implies the textures ARE the final image (or parts of it).
+        
+        // Let's assume the viewport triangles cover the screen exactly: Left is [0, 0.5], Right is [0.5, 1.0].
+        
+        for (int j = 0; j < height; j++) {
+            for (int i = 0; i < width; i++) {
+                Color c(0,0,0);
+                if (i < width / 2) {
+                    // Map [0, width/2] to [0, texWidth]
+                    float u = (float)i / (width / 2);
+                    float v = 1.0f - (float)j / height; 
+                    c = texLeft.getPixel(u, v);
+                } else {
+                    // Map [width/2, width] to [0, texWidth]
+                    float u = (float)(i - width / 2) / (width / 2);
+                    float v = 1.0f - (float)j / height;
+                    c = texRight.getPixel(u, v);
+                }
+                file << static_cast<int>(c.r) << " " << static_cast<int>(c.g) << " " << static_cast<int>(c.b) << "\n";
+            }
+        }
+        file.close();
+    }
+};
+
+// --- Core Algorithm Implementation ---
+
+// A simple Frustum for culling/traversal
+struct Frustum {
+    Vec3 apex; // Origin
+    Vec3 p0, p1, p2, p3; // Quad base of the frustum
+    Vec3 n0, n1, n2, n3; // Plane normals (left, right, top, bottom) pointing inwards
+    
+    Frustum(const Vec3& eye, const Vec3& v0, const Vec3& v1, const Vec3& v2) {
+        apex = eye;
+        // v0, v1, v2 define the viewport triangle. We extend it slightly to depth for intersection tests.
+        // Actually, for "Frustum Culling", we need 4 planes.
+        // A triangle viewport defines a pyramid with a triangular base (3 planes).
+        p0 = v0; p1 = v1; p2 = v2;
+        
+        Vec3 edge0 = (v1 - v0).cross(apex - v0).normalize(); // Plane through Eye-V1-V0
+        Vec3 edge1 = (v2 - v1).cross(apex - v1).normalize(); // Plane through Eye-V2-V1
+        Vec3 edge2 = (v0 - v2).cross(apex - v2).normalize(); // Plane through Eye-V0-V2
+        
+        n0 = edge0; n1 = edge1; n2 = edge2;
+    }
+    
+    // Check if a triangle is potentially inside the frustum
+    bool intersects(const Triangle* tri) {
+        // Check bounding box center against the 3 planes
+        Vec3 center = (tri->boundsMin + tri->boundsMax) * 0.5f;
+        
+        // If center is behind any of the 3 planes (dot product < 0), it's outside
+        if ((center - apex).dot(n0) < -EPSILON) return false;
+        if ((center - apex).dot(n1) < -EPSILON) return false;
+        if ((center - apex).dot(n2) < -EPSILON) return false;
+        
+        // Also check if it is completely behind the viewport plane (culling back geometry)
+        // Viewport plane normal should point towards camera (apex)
+        Vec3 vpNormal = (p1 - p0).cross(p2 - p0).normalize();
+        if ((center - p0).dot(vpNormal) < 0 && (apex - p0).dot(vpNormal) > 0) {
+             // Object is behind the viewport relative to camera
+        }
+        
+        return true; // Simplified coarse check
+    }
+};
+
+// Distance comparison for sorting
+float distanceSquared(const Vec3& a, const Vec3& b) {
+    Vec3 d = a - b;
+    return d.dot(d);
+}
+
+Texture renderTriangleWithTriangle(const std::vector<Triangle*>& scene, const Vec3& origin, Triangle* viewportTri, int depth, float estArea) {
+    // Termination
+    if (depth > MAX_DEPTH || estArea < AREA_THRESHOLD) {
+        // Return black or simple base color if stopped
+        return Texture(2, 2); // Dummy small texture
+    }
+    
+    // Initialize Texture for this viewport
+    // We map the 3D triangle area to pixel dimensions
+    float aspect = viewportTri->area(); 
+    int texW = static_cast<int>(std::sqrt(estArea * (viewportTri->v1 - viewportTri->v0).length() / (viewportTri->v2 - viewportTri->v0).length())) + 1;
+    int texH = static_cast<int>(estArea / texW) + 1;
+    
+    // Clamp texture size to reasonable limits
+    texW = std::min(1024, std::max(2, texW));
+    texH = std::min(1024, std::max(2, texH));
+    
+    Texture resultTex(texW, texH);
+    
+    // Fill with background (Black)
+    std::fill(resultTex.data.begin(), resultTex.data.end(), Color(0.0f,0.0f,0.0f));
+    
+    // If Diffuse, just return solid color texture
+    if (viewportTri->matType == DIFFUSE) {
+        std::fill(resultTex.data.begin(), resultTex.data.end(), Color(viewportTri->color));
+        return resultTex;
+    }
+    
+    // --- Reflection / Rendering Logic ---
+    
+    // 1. Create Frustum
+    Frustum frustum(origin, viewportTri->v0, viewportTri->v1, viewportTri->v2);
+    Vec3 vpNormal = (viewportTri->v1 - viewportTri->v0).cross(viewportTri->v2 - viewportTri->v0).normalize();
+    
+    // 2. Collect & Sort visible triangles
+    std::vector<Triangle*> visibleTris;
+    for (Triangle* tri : scene) {
+        if (tri == viewportTri) continue; // Don't self-intersect
+        if (frustum.intersects(tri)) {
+            // Refine: Check if triangle is in front of viewport?
+            // If it's behind, it shouldn't reflect (unless translucent, ignored here)
+            Vec3 triCenter = (tri->boundsMin + tri->boundsMax) * 0.5f;
+            // Dot product with viewport normal
+            float dist = (triCenter - viewportTri->v0).dot(vpNormal);
+            if (dist > EPSILON) { // In front of the viewport triangle
+                visibleTris.push_back(tri);
+            }
+        }
+    }
+    
+    // Sort by distance (Far to Near)
+    std::sort(visibleTris.begin(), visibleTris.end(), [&](const Triangle* a, const Triangle* b) {
+        float da = distanceSquared(origin, (a->boundsMin + a->boundsMax)*0.5f);
+        float db = distanceSquared(origin, (b->boundsMin + b->boundsMax)*0.5f);
+        return da > db;
+    });
+    
+    // 3. Render each visible triangle onto resultTex
+    for (Triangle* objTri : visibleTris) {
+        
+        // A. Recursive Call
+        // "Reflect camera origin about current viewport... simulate reflection behavior"
+        Vec3 newOrigin;
+        if (viewportTri->matType == REFLECTIVE) {
+            // Reflection formula: r = d - 2(d.n)n. Here d = (Origin - PointOnPlane).
+            // We reflect the Origin point.
+            Vec3 d = origin - viewportTri->v0;
+            newOrigin = origin - vpNormal * 2 * d.dot(vpNormal);
+        } else {
+            newOrigin = origin;
+        }
+        
+        // Calculate new estimated area (projection of objTri onto viewportTri)
+        // Roughly proportional to solid angle
+        float dist = (objTri->boundsMin - origin).length();
+        float newEstArea = (objTri->area() / (dist * dist)) * 100000.0f; // Heuristic scaling
+        newEstArea = std::max(5.0f, newEstArea); // Prevent instant cut-off
+        
+        // Recursion
+        Texture objTexture = renderTriangleWithTriangle(scene, newOrigin, objTri, depth + 1, newEstArea);
+        
+        // B. Texture Mapping (Project objTri onto viewportTri)
+        
+        // Precompute coordinates
+        // We iterate over the TARGET texture (viewportTri) pixels
+        // Check if pixel projects onto objTri
+        
+        Vec3 e0 = viewportTri->v1 - viewportTri->v0;
+        Vec3 e1 = viewportTri->v2 - viewportTri->v0;
+        
+        // Optimized rasterization: Check bounding box of objTri projection
+        // Project objTri center to viewportTri UV to find region of interest
+        Vec3 objCenter = (objTri->v0 + objTri->v1 + objTri->v2) * 0.333f;
+        Vec3 centerOnPlane = projectOnPlane(objCenter, vpNormal, viewportTri->v0);
+        Vec3 bary = barycentric(centerOnPlane, viewportTri->v0, viewportTri->v1, viewportTri->v2);
+        
+        // Radius in UV space
+        float radius = (objTri->boundsMax - objTri->boundsMin).length() / (dist * 0.5f);
+        
+        // Iterate pixels in resultTex
+        // We iterate over a bounding box in the texture corresponding to the projection
+        // For simplicity in this "One File" constraint, we iterate all pixels or a bounding box.
+        // Let's iterate all pixels of resultTex (might be slow for high res, but correct).
+        // Optimization: Only iterate near bary.
+        
+        int minU = std::max(0, (int)((bary.x - radius) * texW));
+        int maxU = std::min(texW, (int)((bary.x + radius) * texW));
+        int minV = std::max(0, (int)((bary.y - radius) * texH));
+        int maxV = std::min(texH, (int)((bary.y + radius) * texH));
+        
+        for (int y = minV; y < maxV; ++y) {
+            for (int x = minU; x < maxU; ++x) {
+                float u = (float)x / texW;
+                float v = (float)y / texH;
+                
+                // Current point on viewport triangle in 3D
+                Vec3 P_on_viewport = viewportTri->v0 + e0 * u + e1 * v;
+                
+                // Barycentric check on Viewport Triangle (optional, strictly texture is rectangular, 
+                // but triangle texture implies shape).
+                // The problem says "Triangle... texture image". 
+                // We should only draw if (u,v) is inside the triangle? 
+                // Actually, texture is usually a rectangle containing the triangle. 
+                // Let's assume (u,v) covers the bounding box of the triangle in texture space.
+                // To keep it simple and strictly triangle: Check if P is inside viewportTri
+                if (barycentric(P_on_viewport, viewportTri->v0, viewportTri->v1, viewportTri->v2).x < 0) continue;
+
+                // Check if P is inside projected objTri
+                // Ray from origin to P. Intersect objTri plane?
+                // Perspective division is needed if we use the "Reflective Camera" concept.
+                // However, we already have P_on_viewport.
+                // We need to know which texel of objTri covers P.
+                // This is equivalent to: Ray from newOrigin passes through P_on_viewport and hits objTri.
+                
+                Vec3 rayDir = (P_on_viewport - newOrigin).normalize();
+                float t = rayTriangleIntersect(newOrigin, rayDir, objTri->v0, objTri->v1, objTri->v2);
+                
+                if (t > 0) {
+                    // Hit! 
+                    // Calculate UV on objTri
+                    Vec3 hitPoint = newOrigin + rayDir * t;
+                    Vec3 baryObj = barycentric(hitPoint, objTri->v0, objTri->v1, objTri->v2);
+                    
+                    // Sample texture
+                    Color srcColor = objTexture.sample(baryObj.x, baryObj.y);
+                    
+                    // Blend with reflection intensity
+                    float alpha = viewportTri->reflectivity; 
+                    // If not fully reflective, mix with base color?
+                    // Problem says: "For diffuse... return texture". "Reflective... calculate".
+                    // Usually: Result = mix(Texture, Reflection, reflectivity).
+                    // But here we are building the texture from scratch.
+                    // We accumulate reflected objects.
+                    
+                    Color current = resultTex.getPixel(u, v);
+                    Color final = srcColor.blendOver(current, alpha); 
+                    // Or just simple Add/Over. Since we sorted far to near, Over works.
+                    
+                    resultTex.setPixel(x, y, final);
+                }
+            }
+        }
+    }
+    
+    return resultTex;
+}
+
+// --- Scene Setup ---
+void createCornellBox(std::vector<Triangle>& triangles, Camera& cam) {
+    // Coordinates: Z is up or Y is up? Let's use Y up.
+    // Box dimensions: 
+    // Floor: y=0, Width=555, Depth=555
+    // Ceiling: y=555
+    // Left Wall: x=0 (Red)
+    // Right Wall: x=555 (Green)
+    // Back Wall: z=555 (White/Grey) or z=0?
+    // Front: z=0 (Open) or Camera at z=0 looking at z=555.
+    
+    float W = 555;
+    float H = 555;
+    float D = 555;
+    
+    auto makeQuad = [&](Vec3 a, Vec3 b, Vec3 c, Vec3 d, Vec3 col, MaterialType mat=DIFFUSE) {
+        // Two triangles
+        triangles.emplace_back(a, b, c, col, mat);
+        triangles.emplace_back(a, c, d, col, mat);
+    };
+    
+    // Floor (y=0) - White
+    makeQuad(Vec3(0,0,0), Vec3(W,0,0), Vec3(W,0,D), Vec3(0,0,D), Vec3(0.73, 0.73, 0.73));
+    
+    // Ceiling (y=H) - White (Light)
+    // Let's make a small light patch or just full white ceiling for simplicity
+    makeQuad(Vec3(0,H,D), Vec3(W,H,D), Vec3(W,H,0), Vec3(0,H,0), Vec3(0.73, 0.73, 0.73));
+    
+    // Back Wall (z=D) - White
+    makeQuad(Vec3(0,0,D), Vec3(0,H,D), Vec3(W,H,D), Vec3(W,0,D), Vec3(0.73, 0.73, 0.73));
+    
+    // Right Wall (x=W) - Green
+    makeQuad(Vec3(W,0,D), Vec3(W,H,D), Vec3(W,H,0), Vec3(W,0,0), Vec3(0.12, 0.45, 0.15));
+    
+    // Left Wall (x=0) - Red
+    makeQuad(Vec3(0,0,0), Vec3(0,H,0), Vec3(0,H,D), Vec3(0,0,D), Vec3(0.65, 0.05, 0.05));
+    
+    // Tall Box (Left-ish) - Silver/Reflective (Yellow tint per request?)
+    // Request: "One Blue One Yellow". Let's do Yellow.
+    // Pos: x ~ 100-200, z ~ 200-350.
+    // Rotated? Simplified: Axis aligned.
+    Vec3 b1_min(130, 0, 265);
+    Vec3 b1_max(295, 330, 420); // Tall box
+    makeQuad(Vec3(b1_min.x, b1_min.y, b1_max.z), Vec3(b1_max.x, b1_min.y, b1_max.z), Vec3(b1_max.x, b1_max.y, b1_max.z), Vec3(b1_min.x, b1_max.y, b1_max.z), Vec3(0.8, 0.8, 0.2), REFLECTIVE); // Front
+    makeQuad(Vec3(b1_max.x, b1_min.y, b1_min.z), Vec3(b1_min.x, b1_min.y, b1_min.z), Vec3(b1_min.x, b1_max.y, b1_min.z), Vec3(b1_max.x, b1_max.y, b1_min.z), Vec3(0.8, 0.8, 0.2), REFLECTIVE); // Back
+    makeQuad(Vec3(b1_min.x, b1_min.y, b1_min.z), Vec3(b1_min.x, b1_min.y, b1_max.z), Vec3(b1_min.x, b1_max.y, b1_max.z), Vec3(b1_min.x, b1_max.y, b1_min.z), Vec3(0.8, 0.8, 0.2), REFLECTIVE); // Left
+    makeQuad(Vec3(b1_max.x, b1_min.y, b1_max.z), Vec3(b1_max.x, b1_min.y, b1_min.z), Vec3(b1_max.x, b1_max.y, b1_min.z), Vec3(b1_max.x, b1_max.y, b1_max.z), Vec3(0.8, 0.8, 0.2), REFLECTIVE); // Right
+    makeQuad(Vec3(b1_min.x, b1_max.y, b1_min.z), Vec3(b1_max.x, b1_max.y, b1_min.z), Vec3(b1_max.x, b1_max.y, b1_max.z), Vec3(b1_min.x, b1_max.y, b1_max.z), Vec3(0.8, 0.8, 0.2), REFLECTIVE); // Top
+
+    // Short Box (Right-ish) - Blue/Reflective
+    Vec3 b2_min(340, 0, 100);
+    Vec3 b2_max(500, 165, 260);
+    makeQuad(Vec3(b2_min.x, b2_min.y, b2_max.z), Vec3(b2_max.x, b2_min.y, b2_max.z), Vec3(b2_max.x, b2_max.y, b2_max.z), Vec3(b2_min.x, b2_max.y, b2_max.z), Vec3(0.2, 0.2, 0.8), REFLECTIVE);
+    makeQuad(Vec3(b2_max.x, b2_min.y, b2_min.z), Vec3(b2_min.x, b2_min.y, b2_min.z), Vec3(b2_min.x, b2_max.y, b2_min.z), Vec3(b2_max.x, b2_max.y, b2_min.z), Vec3(0.2, 0.2, 0.8), REFLECTIVE);
+    makeQuad(Vec3(b2_min.x, b2_min.y, b2_min.z), Vec3(b2_min.x, b2_min.y, b2_max.z), Vec3(b2_min.x, b2_max.y, b2_max.z), Vec3(b2_min.x, b2_max.y, b2_min.z), Vec3(0.2, 0.2, 0.8), REFLECTIVE);
+    makeQuad(Vec3(b2_max.x, b2_min.y, b2_max.z), Vec3(b2_max.x, b2_min.y, b2_min.z), Vec3(b2_max.x, b2_max.y, b2_min.z), Vec3(b2_max.x, b2_max.y, b2_max.z), Vec3(0.2, 0.2, 0.8), REFLECTIVE);
+    makeQuad(Vec3(b2_min.x, b2_max.y, b2_min.z), Vec3(b2_max.x, b2_max.y, b2_min.z), Vec3(b2_max.x, b2_max.y, b2_max.z), Vec3(b2_min.x, b2_max.y, b2_max.z), Vec3(0.2, 0.2, 0.8), REFLECTIVE);
+
+    // Camera
+    // Look from (278, 278, -800) at (278, 278, 0). Up (0, 1, 0).
+    Vec3 camPos(278, 273, -800); // Slightly adjusted height
+    Vec3 target(278, 273, 0);
+    Vec3 up(0, 1, 0);
+    
+    // Viewport setup
+    float distToView = 800; // Distance from camera to viewport plane (z=0)
+    float viewW = 555 * 1.5; // Zoom
+    float viewH = viewW * (IMAGE_HEIGHT / IMAGE_WIDTH);
+    
+    Vec3 viewCenter = target;
+    Vec3 camDir = (target - camPos).normalize();
+    Vec3 camRight = camDir.cross(up).normalize();
+    Vec3 camUp_real = camRight.cross(camDir);
+    
+    Vec3 vTL = viewCenter - camRight * (viewW/2) + camUp_real * (viewH/2);
+    Vec3 vTR = viewCenter + camRight * (viewW/2) + camUp_real * (viewH/2);
+    Vec3 vBL = viewCenter - camRight * (viewW/2) - camUp_real * (viewH/2);
+    Vec3 vBR = viewCenter + camRight * (viewW/2) - camUp_real * (viewH/2);
+    
+    // Split viewport into two triangles
+    // Note: These are temporary objects created in the vector, pointers must remain valid.
+    // We pass pointers to Camera.
+    
+    Triangle* vpLeft = new Triangle(vTL, vBL, vTR, Vec3(1,1,1), DIFFUSE); // Color irrelevant
+    Triangle* vpRight = new Triangle(vBL, vBR, vTR, Vec3(1,1,1), DIFFUSE);
+    
+    triangles.push_back(*vpLeft);
+    triangles.push_back(*vpRight);
+    
+    // Update pointers to point to the vector storage
+    vpLeft = &triangles[triangles.size()-2];
+    vpRight = &triangles[triangles.size()-1];
+    
+    cam = Camera(camPos, vpLeft, vpRight, IMAGE_WIDTH, IMAGE_HEIGHT);
+}
+
+// --- Main ---
+int main() {
+    std::vector<Triangle> triangles;
+    Camera cam(Vec3(0,0,0), nullptr, nullptr, 0, 0);
+    
+    createCornellBox(triangles, cam);
+    
+    std::vector<Triangle*> scenePtrs;
+    for(auto& t : triangles) {
+        scenePtrs.push_back(&t);
+    }
+    
+    std::cout << "Starting render..." << std::endl;
+    cam.render(scenePtrs, "cornell_box.ppm");
+    std::cout << "Finished render. Output: cornell_box.ppm" << std::endl;
+    
+    return 0;
+}

experiments/rt2.cpp

@@ -0,0 +1,974 @@
+#include <cmath>
+#include <vector>
+#include <iostream>
+#include <fstream>
+#include <limits>
+#include <algorithm>
+
+// ===================== 数学工具 =========================
+
+struct Vec3 {
+    double x, y, z;
+    Vec3() : x(0), y(0), z(0) {}
+    Vec3(double v) : x(v), y(v), z(v) {}
+    Vec3(double x_, double y_, double z_) : x(x_), y(y_), z(z_) {}
+};
+
+struct Vec2 {
+    double x, y;
+    Vec2() : x(0), y(0) {}
+    Vec2(double v) : x(v), y(v) {}
+    Vec2(double x_, double y_) : x(x_), y(y_) {}
+};
+
+inline Vec3 operator-(const Vec3& v) {
+	return Vec3(-v.x, -v.y, -v.z);
+}
+
+inline Vec3 operator+(const Vec3& a, const Vec3& b) {
+    return Vec3(a.x + b.x, a.y + b.y, a.z + b.z);
+}
+inline Vec3 operator-(const Vec3& a, const Vec3& b) {
+    return Vec3(a.x - b.x, a.y - b.y, a.z - b.z);
+}
+inline Vec3 operator*(const Vec3& a, double s) {
+    return Vec3(a.x * s, a.y * s, a.z * s);
+}
+inline Vec3 operator*(double s, const Vec3& a) {
+    return Vec3(a.x * s, a.y * s, a.z * s);
+}
+inline Vec3 operator/(const Vec3& a, double s) {
+    return Vec3(a.x / s, a.y / s, a.z / s);
+}
+inline Vec3 operator*(const Vec3& a, const Vec3& b) {
+    return Vec3(a.x * b.x, a.y * b.y, a.z * b.z);
+}
+inline Vec3& operator+=(Vec3& a, const Vec3& b) {
+    a.x += b.x; a.y += b.y; a.z += b.z; return a;
+}
+
+inline Vec2 operator+(const Vec2& a, const Vec2& b) {
+    return Vec2(a.x + b.x, a.y + b.y);
+}
+inline Vec2 operator-(const Vec2& a, const Vec2& b) {
+    return Vec2(a.x - b.x, a.y - b.y);
+}
+inline Vec2 operator*(const Vec2& a, double s) {
+    return Vec2(a.x * s, a.y * s);
+}
+inline Vec2 operator*(double s, const Vec2& a) {
+    return Vec2(a.x * s, a.y * s);
+}
+inline Vec2 operator/(const Vec2& a, double s) {
+    return Vec2(a.x / s, a.y / s);
+}
+
+inline double dot(const Vec3& a, const Vec3& b) {
+    return a.x*b.x + a.y*b.y + a.z*b.z;
+}
+inline Vec3 cross(const Vec3& a, const Vec3& b) {
+    return Vec3(
+        a.y*b.z - a.z*b.y,
+        a.z*b.x - a.x*b.z,
+        a.x*b.y - a.y*b.x
+    );
+}
+inline double length(const Vec3& v) {
+    return std::sqrt(dot(v, v));
+}
+inline Vec3 normalize(const Vec3& v) {
+    double len = length(v);
+    if (len <= 1e-12) return Vec3(0);
+    return v / len;
+}
+
+// 反射方向：v - 2*(v·n)*n，v 为指向表面的入射方向
+inline Vec3 reflect(const Vec3& v, const Vec3& n) {
+    return v - n * (2.0 * dot(v, n));
+}
+
+inline Vec3 clamp01(const Vec3& c) {
+    return Vec3(
+        std::min(1.0, std::max(0.0, c.x)),
+        std::min(1.0, std::max(0.0, c.y)),
+        std::min(1.0, std::max(0.0, c.z))
+    );
+}
+
+// ===================== 材质 & 三角形 =========================
+
+struct Material {
+    Vec3 baseColor;
+    bool mirror;
+    double reflectivity; // [0,1]
+};
+
+struct Triangle {
+    Vec3 v[3];   // 顶点
+    Vec3 normal; // 面法线
+    Vec2 uv[3];  // 顶点局部纹理坐标
+    const Material* material;
+
+    Triangle() : material(nullptr) {
+        v[0] = v[1] = v[2] = Vec3(0);
+        uv[0] = uv[1] = uv[2] = Vec2(0);
+        normal = Vec3(0,1,0);
+    }
+
+    Triangle(const Vec3& a, const Vec3& b, const Vec3& c, const Material* m) {
+        v[0] = a; v[1] = b; v[2] = c;
+        material = m;
+        normal = normalize(cross(v[1] - v[0], v[2] - v[0]));
+        // 简单局部 UV：三角形自身局部坐标
+        uv[0] = Vec2(0.0, 0.0);
+        uv[1] = Vec2(1.0, 0.0);
+        uv[2] = Vec2(0.0, 1.0);
+    }
+};
+
+// ===================== 相机 =========================
+
+struct Camera {
+    Vec3 pos;
+    Vec3 target;
+    Vec3 up;
+    double fov;
+
+    Vec3 forward;
+    Vec3 right;
+    Vec3 camUp;
+    double invTanHalfFov;
+
+    Camera(const Vec3& p, const Vec3& t, const Vec3& u, double fovDeg)
+        : pos(p), target(t), up(u)
+    {
+        forward = normalize(target - pos);
+        right = normalize(cross(forward, up));
+        camUp = cross(right, forward);
+        fov = fovDeg * M_PI / 180.0;
+        invTanHalfFov = 1.0 / std::tan(fov * 0.5);
+    }
+
+    Vec3 worldToCamera(const Vec3& p) const {
+        Vec3 v = p - pos;
+        return Vec3(
+            dot(v, right),
+            dot(v, camUp),
+            dot(v, forward)
+        );
+    }
+
+    bool projectToScreen(
+        const Vec3& pWorld,
+        int width, int height,
+        double& outX, double& outY, double& outZ
+    ) const {
+        Vec3 pc = worldToCamera(pWorld);
+        if (pc.z <= 1e-6) return false;
+
+        double x_ndc = (pc.x * invTanHalfFov) / pc.z;
+        double y_ndc = (pc.y * invTanHalfFov) / pc.z;
+
+        outX = (x_ndc * 0.5 + 0.5) * (double)(width);
+        outY = (1.0 - (y_ndc * 0.5 + 0.5)) * (double)(height);
+        outZ = pc.z;
+        return true;
+    }
+};
+
+// ===================== 场景 =========================
+
+struct Scene {
+    std::vector<Triangle> tris;
+    std::vector<Material> materials;
+};
+
+static const double INF_D = std::numeric_limits<double>::infinity();
+
+// ========== 世界空间三角形重心坐标 ==========
+
+bool barycentricWorld(
+    const Vec3& p,
+    const Triangle& tri,
+    double& w0, double& w1, double& w2
+) {
+    Vec3 v0 = tri.v[0];
+    Vec3 v1 = tri.v[1];
+    Vec3 v2 = tri.v[2];
+    Vec3 v0v1 = v1 - v0;
+    Vec3 v0v2 = v2 - v0;
+    Vec3 v0p  = p  - v0;
+
+    double d00 = dot(v0v1, v0v1);
+    double d01 = dot(v0v1, v0v2);
+    double d11 = dot(v0v2, v0v2);
+    double d20 = dot(v0p,  v0v1);
+    double d21 = dot(v0p,  v0v2);
+
+    double denom = d00 * d11 - d01 * d01;
+    if (std::fabs(denom) < 1e-12) {
+        w0 = w1 = w2 = 1.0/3.0;
+        return false;
+    }
+
+    double v = (d11 * d20 - d01 * d21) / denom;
+    double w = (d00 * d21 - d01 * d20) / denom;
+    double u = 1.0 - v - w;
+    w0 = u; w1 = v; w2 = w;
+    return true;
+}
+
+// ========== 2D 屏幕三角形重心坐标 ==========
+
+bool barycentric2D(
+    double px, double py,
+    double x0, double y0,
+    double x1, double y1,
+    double x2, double y2,
+    double& u, double& v, double& w
+) {
+    double den = ( (y1 - y2)*(x0 - x2) + (x2 - x1)*(y0 - y2) );
+    if (std::fabs(den) < 1e-12) return false;
+    u = ((y1 - y2)*(px - x2) + (x2 - x1)*(py - y2)) / den;
+    v = ((y2 - y0)*(px - x2) + (x0 - x2)*(py - y2)) / den;
+    w = 1.0 - u - v;
+    return (u >= 0.0 && v >= 0.0 && w >= 0.0);
+}
+
+// ========== 射线与三角形相交（用于反射） ==========
+
+bool rayIntersectTriangle(
+    const Vec3& orig,
+    const Vec3& dir,
+    const Triangle& tri,
+    double& t, double& u, double& v
+) {
+    const double EPSILON = 1e-8;
+    Vec3 v0v1 = tri.v[1] - tri.v[0];
+    Vec3 v0v2 = tri.v[2] - tri.v[0];
+    Vec3 pvec = cross(dir, v0v2);
+    double det = dot(v0v1, pvec);
+
+    if (std::fabs(det) < EPSILON) return false;
+    double invDet = 1.0 / det;
+
+    Vec3 tvec = orig - tri.v[0];
+    u = dot(tvec, pvec) * invDet;
+    if (u < 0.0 || u > 1.0) return false;
+
+    Vec3 qvec = cross(tvec, v0v1);
+    v = dot(dir, qvec) * invDet;
+    if (v < 0.0 || u + v > 1.0) return false;
+
+    t = dot(v0v2, qvec) * invDet;
+    if (t < EPSILON) return false;
+
+    return true;
+}
+
+bool traceScene(
+    const Scene& scene,
+    const Vec3& orig,
+    const Vec3& dir,
+    int& outTriId,
+    double& outT,
+    double& outU,
+    double& outV
+) {
+    outTriId = -1;
+    outT = INF_D;
+    double u, v;
+    for (size_t i = 0; i < scene.tris.size(); ++i) {
+        double tTmp, uTmp, vTmp;
+        if (rayIntersectTriangle(orig, dir, scene.tris[i], tTmp, uTmp, vTmp)) {
+            if (tTmp < outT) {
+                outT = tTmp;
+                outTriId = (int)i;
+                outU = uTmp;
+                outV = vTmp;
+            }
+        }
+    }
+    return (outTriId >= 0);
+}
+
+// ===================== Texture2D（离屏纹理） =========================
+
+struct Texture2D {
+    int w, h;
+    std::vector<Vec3> data;
+
+    Texture2D() : w(0), h(0) {}
+    Texture2D(int w_, int h_) : w(w_), h(h_), data(w_*h_, Vec3(0)) {}
+
+    void resize(int w_, int h_) {
+        w = w_; h = h_;
+        data.assign(w*h, Vec3(0));
+    }
+
+    void clear(const Vec3& c) {
+        std::fill(data.begin(), data.end(), c);
+    }
+
+    Vec3 get(int x, int y) const {
+        if (w <= 0 || h <= 0) return Vec3(0);
+        x = std::max(0, std::min(w-1, x));
+        y = std::max(0, std::min(h-1, y));
+        return data[y * w + x];
+    }
+
+    void set(int x, int y, const Vec3& c) {
+        if (x < 0 || x >= w || y < 0 || y >= h) return;
+        data[y * w + x] = c;
+    }
+
+    Vec3 sampleUV(const Vec2& uv) const {
+        if (w <= 0 || h <= 0) return Vec3(0);
+        double u = std::min(1.0, std::max(0.0, uv.x));
+        double v = std::min(1.0, std::max(0.0, uv.y));
+        int x = (int)(u * (w - 1) + 0.5);
+        int y = (int)(v * (h - 1) + 0.5);
+        return get(x, y);
+    }
+
+    void writeUV(const Vec2& uv, const Vec3& c) {
+        if (w <= 0 || h <= 0) return;
+        double u = uv.x;
+        double v = uv.y;
+        // 略宽松判断，允许轻微的数值误差
+        if (u < -0.01 || u > 1.01 || v < -0.01 || v > 1.01) return;
+        u = std::min(1.0, std::max(0.0, u));
+        v = std::min(1.0, std::max(0.0, v));
+        int x = (int)(u * (w - 1) + 0.5);
+        int y = (int)(v * (h - 1) + 0.5);
+        set(x, y, c);
+    }
+};
+
+// ===================== 2D 仿射变换（UV 映射） =========================
+
+struct Affine2D {
+    // [ uA ]   [m00 m01 m02] [ uB ]
+    // [ vA ] = [m10 m11 m12] [ vB ]
+    //                         [ 1  ]
+    double m00, m01, m02;
+    double m10, m11, m12;
+};
+
+Vec2 applyAffine(const Affine2D& A, const Vec2& uvB) {
+    double uA = A.m00 * uvB.x + A.m01 * uvB.y + A.m02;
+    double vA = A.m10 * uvB.x + A.m11 * uvB.y + A.m12;
+    return Vec2(uA, vA);
+}
+
+// 解 3x3 线性方程组 M * x = b
+bool solve3x3(double M[3][3], double b[3], double x[3]) {
+    double A[3][4];
+    for (int i = 0; i < 3; ++i) {
+        A[i][0] = M[i][0];
+        A[i][1] = M[i][1];
+        A[i][2] = M[i][2];
+        A[i][3] = b[i];
+    }
+
+    for (int col = 0; col < 3; ++col) {
+        int pivot = col;
+        for (int r = col+1; r < 3; ++r) {
+            if (std::fabs(A[r][col]) > std::fabs(A[pivot][col]))
+                pivot = r;
+        }
+        if (std::fabs(A[pivot][col]) < 1e-12) return false;
+        if (pivot != col) {
+            for (int c = 0; c < 4; ++c) std::swap(A[pivot][c], A[col][c]);
+        }
+
+        double div = A[col][col];
+        for (int c = col; c < 4; ++c) A[col][c] /= div;
+
+        for (int r = 0; r < 3; ++r) {
+            if (r == col) continue;
+            double factor = A[r][col];
+            for (int c = col; c < 4; ++c) {
+                A[r][c] -= factor * A[col][c];
+            }
+        }
+    }
+
+    for (int i = 0; i < 3; ++i) x[i] = A[i][3];
+    return true;
+}
+
+// 计算 B 的 UV -> A 的 UV 的仿射矩阵
+Affine2D computeUVMappingAffine(
+    const Triangle& triA,
+    const Triangle& triB
+) {
+    Affine2D A;
+
+    Vec2 uvB[3];
+    Vec2 uvA[3];
+
+    Vec3 nA = triA.normal;
+    Vec3 p0A = triA.v[0];
+
+    for (int j = 0; j < 3; ++j) {
+        Vec3 pb = triB.v[j];
+        Vec3 diff = pb - p0A;
+        double dist = dot(diff, nA);
+        Vec3 pref = pb - 2.0 * dist * nA; // pb 关于 A 平面镜像后的点
+
+        double w0, w1, w2;
+        barycentricWorld(pref, triA, w0, w1, w2);
+        Vec2 uvOnA = triA.uv[0] * w0 + triA.uv[1] * w1 + triA.uv[2] * w2;
+
+        uvA[j] = uvOnA;
+        uvB[j] = triB.uv[j];
+    }
+
+    double MB[3][3];
+    double U[3], V[3];
+    for (int j = 0; j < 3; ++j) {
+        MB[j][0] = uvB[j].x;
+        MB[j][1] = uvB[j].y;
+        MB[j][2] = 1.0;
+        U[j] = uvA[j].x;
+        V[j] = uvA[j].y;
+    }
+
+    double solU[3], solV[3];
+    if (!solve3x3(MB, U, solU)) {
+        A.m00 = 1; A.m01 = 0; A.m02 = 0;
+        A.m10 = 0; A.m11 = 1; A.m12 = 0;
+        return A;
+    }
+    if (!solve3x3(MB, V, solV)) {
+        A.m00 = 1; A.m01 = 0; A.m02 = 0;
+        A.m10 = 0; A.m11 = 1; A.m12 = 0;
+        return A;
+    }
+
+    A.m00 = solU[0]; A.m01 = solU[1]; A.m02 = solU[2];
+    A.m10 = solV[0]; A.m11 = solV[1]; A.m12 = solV[2];
+    return A;
+}
+
+// ===================== 递归反射着色 =========================
+
+// 语义：
+//  - currentTriId: 当前点所在三角形 ID（A）
+//  - uvCurrent:    当前点在 A 上的 UV
+//  - P:            当前点世界坐标
+//  - n:            当前点法线
+//  - mat:          当前材质
+//  - viewDir:      从 P 指向“观察者（上一 bounce 或相机）”的方向
+Vec3 shadeRecursive(
+    const Scene& scene,
+    const Camera& cam,
+    std::vector<Texture2D>& triTextures,
+    int currentTriId,
+    const Vec2& uvCurrent,
+    const Vec3& P,
+    const Vec3& n,
+    const Material& mat,
+    const Vec3& viewDir,
+    int depth,
+    int maxDepth
+) {
+    // 先从当前三角形纹理采样，再融合基础颜色
+    Vec3 texColor = mat.baseColor;
+    if (currentTriId >= 0 && currentTriId < (int)triTextures.size()) {
+        Vec3 sampled = triTextures[currentTriId].sampleUV(uvCurrent);
+        texColor = sampled * 0.7 + mat.baseColor * 0.3;
+    }
+
+    if (!mat.mirror || depth >= maxDepth) {
+        return texColor;
+    }
+
+    // 镜面反射：inDir 是指向表面的方向，viewDir 指向观察者
+    Vec3 inDir = -viewDir;
+    Vec3 reflDir = normalize(reflect(inDir, n));
+
+    int hitTriId;
+    double tHit, uBary, vBary;
+    if (!traceScene(scene, P + n * 1e-4, reflDir, hitTriId, tHit, uBary, vBary)) {
+        // 环境（看不到任何三角形）
+        Vec3 envColor(0.0, 0.0, 0.0);
+        return texColor * (1.0 - mat.reflectivity) + envColor * mat.reflectivity;
+    }
+
+    const Triangle& triB = scene.tris[hitTriId];
+    const Material& matB = *triB.material;
+
+    Vec3 hitPos = P + reflDir * tHit;
+    Vec3 nB = triB.normal;
+    Vec3 viewDirNext = -reflDir; // 在 B 看 A 的视线方向
+
+    // 计算 B 上的 UV
+    double w0B, w1B, w2B;
+    barycentricWorld(hitPos, triB, w0B, w1B, w2B);
+    Vec2 uvB = triB.uv[0] * w0B + triB.uv[1] * w1B + triB.uv[2] * w2B;
+
+    // 递归计算 B 的颜色（在其自身纹理空间继续反射）
+    Vec3 colorB = shadeRecursive(
+        scene, cam, triTextures,
+        hitTriId, uvB,
+        hitPos, nB, matB,
+        viewDirNext,
+        depth + 1, maxDepth
+    );
+
+    // 利用 uvA_fromB 把 B 的颜色写入 A 的纹理
+    if (currentTriId >= 0 && currentTriId < (int)scene.tris.size()) {
+        const Triangle& triA = scene.tris[currentTriId];
+        Affine2D mapBA = computeUVMappingAffine(triA, triB);
+        Vec2 uvA_fromB = applyAffine(mapBA, uvB);
+        triTextures[currentTriId].writeUV(uvA_fromB, colorB);
+    }
+
+    // 当前点最终颜色：自身贴图/基色 + 镜面反射
+    Vec3 finalColor =
+        texColor * (1.0 - mat.reflectivity) +
+        colorB   * mat.reflectivity;
+
+    return finalColor;
+}
+
+// ===================== 屏幕三角形 & 相机 viewport 映射 =========================
+
+struct ScreenTriangle {
+    double x0, y0, z0;
+    double x1, y1, z1;
+    double x2, y2, z2;
+    int triId;
+};
+
+// 将屏幕坐标 (px,py) 映射到相机 viewport 的两个三角形之一，得到 UV 和 camIdx
+bool mapScreenToCamUV(
+    double px, double py,
+    int width, int height,
+    Vec2& uvCam,
+    int& camIdx
+) {
+    double u, v, w;
+
+    // TriCam0: (0,0)-(W,0)-(0,H)，UV: (0,0),(1,0),(0,1)
+    if (barycentric2D(px, py,
+                      0.0, 0.0,
+                      (double)width, 0.0,
+                      0.0, (double)height,
+                      u, v, w)) {
+        Vec2 uv0(0.0, 0.0);
+        Vec2 uv1(1.0, 0.0);
+        Vec2 uv2(0.0, 1.0);
+        uvCam = uv0 * u + uv1 * v + uv2 * w;
+        camIdx = 0;
+        return true;
+    }
+
+    // TriCam1: (W,0)-(W,H)-(0,H)，UV: (1,0),(1,1),(0,1)
+    if (barycentric2D(px, py,
+                      (double)width, 0.0,
+                      (double)width, (double)height,
+                      0.0,           (double)height,
+                      u, v, w)) {
+        Vec2 uv0(1.0, 0.0);
+        Vec2 uv1(1.0, 1.0);
+        Vec2 uv2(0.0, 1.0);
+        uvCam = uv0 * u + uv1 * v + uv2 * w;
+        camIdx = 1;
+        return true;
+    }
+
+    return false;
+}
+
+// ===================== 场景 → CameraTexture 渲染 =========================
+
+void renderSceneToCameraTextures(
+    const Scene& scene,
+    const Camera& cam,
+    int width,
+    int height,
+    std::vector<Texture2D>& triTextures,
+    Texture2D camTextures[2]
+) {
+    std::vector<double> depthBuffer(width * height, INF_D);
+
+    // 1. 投影所有三角形为屏幕三角形
+    std::vector<ScreenTriangle> screenTris;
+    screenTris.reserve(scene.tris.size());
+
+    for (size_t i = 0; i < scene.tris.size(); ++i) {
+        const Triangle& tri = scene.tris[i];
+
+        double x0,y0,z0;
+        double x1,y1,z1;
+        double x2,y2,z2;
+        bool ok0 = cam.projectToScreen(tri.v[0], width, height, x0, y0, z0);
+        bool ok1 = cam.projectToScreen(tri.v[1], width, height, x1, y1, z1);
+        bool ok2 = cam.projectToScreen(tri.v[2], width, height, x2, y2, z2);
+
+        if (!ok0 && !ok1 && !ok2) continue;
+        int behind = (!ok0) + (!ok1) + (!ok2);
+        if (behind >= 2) continue;
+
+        ScreenTriangle st;
+        st.x0 = x0; st.y0 = y0; st.z0 = z0;
+        st.x1 = x1; st.y1 = y1; st.z1 = z1;
+        st.x2 = x2; st.y2 = y2; st.z2 = z2;
+        st.triId = (int)i;
+        screenTris.push_back(st);
+    }
+
+    // 2. 按平均深度从远到近排序（覆盖关系）
+    std::sort(screenTris.begin(), screenTris.end(),
+        [](const ScreenTriangle& a, const ScreenTriangle& b) {
+            double za = (a.z0 + a.z1 + a.z2) / 3.0;
+            double zb = (b.z0 + b.z1 + b.z2) / 3.0;
+            return za > zb; // 大 z 在远处
+        }
+    );
+
+    const int maxReflectionDepth = 3;
+
+    // 3. 遍历每个屏幕三角形，进行光栅化和递归反射着色，写入 CameraTexture
+    for (const ScreenTriangle& st : screenTris) {
+        const Triangle& tri = scene.tris[st.triId];
+        const Material& mat = *tri.material;
+
+        int minX = (int)std::floor(std::min({ st.x0, st.x1, st.x2 }));
+        int maxX = (int)std::ceil (std::max({ st.x0, st.x1, st.x2 }));
+        int minY = (int)std::floor(std::min({ st.y0, st.y1, st.y2 }));
+        int maxY = (int)std::ceil (std::max({ st.y0, st.y1, st.y2 }));
+
+        minX = std::max(minX, 0);
+        maxX = std::min(maxX, width  - 1);
+        minY = std::max(minY, 0);
+        maxY = std::min(maxY, height - 1);
+
+        for (int y = minY; y <= maxY; ++y) {
+            for (int x = minX; x <= maxX; ++x) {
+                double px = x + 0.5;
+                double py = y + 0.5;
+
+                double u,v,w;
+                if (!barycentric2D(
+                        px, py,
+                        st.x0, st.y0,
+                        st.x1, st.y1,
+                        st.x2, st.y2,
+                        u,v,w)) {
+                    continue;
+                }
+
+                double z = st.z0 * u + st.z1 * v + st.z2 * w;
+                int idx = y * width + x;
+                if (z >= depthBuffer[idx]) continue;
+                depthBuffer[idx] = z;
+
+                // 世界坐标、法线、当前三角形 UV
+                Vec3 P =
+                    tri.v[0] * u +
+                    tri.v[1] * v +
+                    tri.v[2] * w;
+
+                Vec3 n = tri.normal;
+
+                Vec2 uvCurrent =
+                    tri.uv[0] * u +
+                    tri.uv[1] * v +
+                    tri.uv[2] * w;
+
+                // 从 P 看向相机的方向
+                Vec3 viewDir0 = normalize(cam.pos - P);
+
+                // 递归着色（以当前三角形为 viewport）
+                Vec3 color = shadeRecursive(
+                    scene, cam, triTextures,
+                    st.triId, uvCurrent,
+                    P, n, mat,
+                    viewDir0,
+                    0, maxReflectionDepth
+                );
+
+                // 将颜色写入相机 viewport 的两个三角形纹理
+                Vec2 uvCam;
+                int camIdx;
+                if (mapScreenToCamUV(px, py, width, height, uvCam, camIdx)) {
+                    camTextures[camIdx].writeUV(uvCam, color);
+                }
+            }
+        }
+    }
+}
+
+// ===================== 构建 Cornell Box 场景 =========================
+
+void buildCornellBox(Scene& scene) {
+    scene.materials.clear();
+    scene.tris.clear();
+
+    Material redWall;
+    redWall.baseColor = Vec3(0.75, 0.15, 0.15);
+    redWall.mirror = false;
+    redWall.reflectivity = 0.0;
+
+    Material greenWall;
+    greenWall.baseColor = Vec3(0.15, 0.75, 0.15);
+    greenWall.mirror = false;
+    greenWall.reflectivity = 0.0;
+
+    Material whiteWall;
+    whiteWall.baseColor = Vec3(0.75, 0.75, 0.75);
+    whiteWall.mirror = false;
+    whiteWall.reflectivity = 0.0;
+
+    Material blueMetal;
+    blueMetal.baseColor = Vec3(0.2, 0.4, 0.9);
+    blueMetal.mirror = true;
+    blueMetal.reflectivity = 0.9;
+
+    Material yellowMetal;
+    yellowMetal.baseColor = Vec3(0.9, 0.8, 0.2);
+    yellowMetal.mirror = true;
+    yellowMetal.reflectivity = 0.9;
+
+    scene.materials.push_back(redWall);    // 0
+    scene.materials.push_back(greenWall);  // 1
+    scene.materials.push_back(whiteWall);  // 2
+    scene.materials.push_back(blueMetal);  // 3
+    scene.materials.push_back(yellowMetal);// 4
+
+    const Material* mRed    = &scene.materials[0];
+    const Material* mGreen  = &scene.materials[1];
+    const Material* mWhite  = &scene.materials[2];
+    const Material* mBlue   = &scene.materials[3];
+    const Material* mYellow = &scene.materials[4];
+
+    double roomSize = 2.0;
+    double half = roomSize * 0.5;
+    double floorY = 0.0;
+    double ceilY  = roomSize;
+    double backZ  = -roomSize;
+    double frontZ = 0.0;
+
+    // 地板（white）
+    {
+        Vec3 v0(-half, floorY, frontZ);
+        Vec3 v1( half, floorY, frontZ);
+        Vec3 v2( half, floorY, backZ);
+        Vec3 v3(-half, floorY, backZ);
+        scene.tris.emplace_back(v0, v1, v2, mWhite);
+        scene.tris.emplace_back(v0, v2, v3, mWhite);
+    }
+
+    // 天花板（white）
+    {
+        Vec3 v0(-half, ceilY, backZ);
+        Vec3 v1( half, ceilY, backZ);
+        Vec3 v2( half, ceilY, frontZ);
+        Vec3 v3(-half, ceilY, frontZ);
+        scene.tris.emplace_back(v0, v1, v2, mWhite);
+        scene.tris.emplace_back(v0, v2, v3, mWhite);
+    }
+
+    // 左墙（red）
+    {
+        Vec3 v0(-half, floorY, backZ);
+        Vec3 v1(-half, floorY, frontZ);
+        Vec3 v2(-half, ceilY, frontZ);
+        Vec3 v3(-half, ceilY, backZ);
+        scene.tris.emplace_back(v0, v1, v2, mRed);
+        scene.tris.emplace_back(v0, v2, v3, mRed);
+    }
+
+    // 右墙（green）
+    {
+        Vec3 v0(half, floorY, frontZ);
+        Vec3 v1(half, floorY, backZ);
+        Vec3 v2(half, ceilY, backZ);
+        Vec3 v3(half, ceilY, frontZ);
+        scene.tris.emplace_back(v0, v1, v2, mGreen);
+        scene.tris.emplace_back(v0, v2, v3, mGreen);
+    }
+
+    // 后墙（white）
+    {
+        Vec3 v0(-half, floorY, backZ);
+        Vec3 v1( half, floorY, backZ);
+        Vec3 v2( half, ceilY,  backZ);
+        Vec3 v3(-half, ceilY,  backZ);
+        scene.tris.emplace_back(v0, v1, v2, mWhite);
+        scene.tris.emplace_back(v0, v2, v3, mWhite);
+    }
+
+    // 蓝色金属盒（左）——矮盒
+    {
+        double bx0 = -0.6;
+        double bx1 = -0.2;
+        double bz0 = -1.0;
+        double bz1 = -0.4;
+        double h   = 0.7;
+
+        Vec3 t0(bx0, floorY + h, bz0);
+        Vec3 t1(bx1, floorY + h, bz0);
+        Vec3 t2(bx1, floorY + h, bz1);
+        Vec3 t3(bx0, floorY + h, bz1);
+        scene.tris.emplace_back(t0, t1, t2, mBlue);
+        scene.tris.emplace_back(t0, t2, t3, mBlue);
+
+        Vec3 f0(bx0, floorY,     bz1);
+        Vec3 f1(bx1, floorY,     bz1);
+        Vec3 f2(bx1, floorY + h, bz1);
+        Vec3 f3(bx0, floorY + h, bz1);
+        scene.tris.emplace_back(f0, f1, f2, mBlue);
+        scene.tris.emplace_back(f0, f2, f3, mBlue);
+
+        Vec3 bk0(bx1, floorY,     bz0);
+        Vec3 bk1(bx0, floorY,     bz0);
+        Vec3 bk2(bx0, floorY + h, bz0);
+        Vec3 bk3(bx1, floorY + h, bz0);
+        scene.tris.emplace_back(bk0, bk1, bk2, mBlue);
+        scene.tris.emplace_back(bk0, bk2, bk3, mBlue);
+
+        Vec3 l0(bx0, floorY,     bz0);
+        Vec3 l1(bx0, floorY,     bz1);
+        Vec3 l2(bx0, floorY + h, bz1);
+        Vec3 l3(bx0, floorY + h, bz0);
+        scene.tris.emplace_back(l0, l1, l2, mBlue);
+        scene.tris.emplace_back(l0, l2, l3, mBlue);
+
+        Vec3 r0(bx1, floorY,     bz1);
+        Vec3 r1(bx1, floorY,     bz0);
+        Vec3 r2(bx1, floorY + h, bz0);
+        Vec3 r3(bx1, floorY + h, bz1);
+        scene.tris.emplace_back(r0, r1, r2, mBlue);
+        scene.tris.emplace_back(r0, r2, r3, mBlue);
+    }
+
+    // 黄色金属盒（右）——高盒
+    {
+        double bx0 = 0.1;
+        double bx1 = 0.6;
+        double bz0 = -0.8;
+        double bz1 = -0.1;
+        double h   = 1.2;
+
+        Vec3 t0(bx0, floorY + h, bz0);
+        Vec3 t1(bx1, floorY + h, bz0);
+        Vec3 t2(bx1, floorY + h, bz1);
+        Vec3 t3(bx0, floorY + h, bz1);
+        scene.tris.emplace_back(t0, t1, t2, mYellow);
+        scene.tris.emplace_back(t0, t2, t3, mYellow);
+
+        Vec3 f0(bx0, floorY,     bz1);
+        Vec3 f1(bx1, floorY,     bz1);
+        Vec3 f2(bx1, floorY + h, bz1);
+        Vec3 f3(bx0, floorY + h, bz1);
+        scene.tris.emplace_back(f0, f1, f2, mYellow);
+        scene.tris.emplace_back(f0, f2, f3, mYellow);
+
+        Vec3 bk0(bx1, floorY,     bz0);
+        Vec3 bk1(bx0, floorY,     bz0);
+        Vec3 bk2(bx0, floorY + h, bz0);
+        Vec3 bk3(bx1, floorY + h, bz0);
+        scene.tris.emplace_back(bk0, bk1, bk2, mYellow);
+        scene.tris.emplace_back(bk0, bk2, bk3, mYellow);
+
+        Vec3 l0(bx0, floorY,     bz0);
+        Vec3 l1(bx0, floorY,     bz1);
+        Vec3 l2(bx0, floorY + h, bz1);
+        Vec3 l3(bx0, floorY + h, bz0);
+        scene.tris.emplace_back(l0, l1, l2, mYellow);
+        scene.tris.emplace_back(l0, l2, l3, mYellow);
+
+        Vec3 r0(bx1, floorY,     bz1);
+        Vec3 r1(bx1, floorY,     bz0);
+        Vec3 r2(bx1, floorY + h, bz0);
+        Vec3 r3(bx1, floorY + h, bz1);
+        scene.tris.emplace_back(r0, r1, r2, mYellow);
+        scene.tris.emplace_back(r0, r2, r3, mYellow);
+    }
+}
+
+// ===================== 写 PPM =========================
+
+void writePPM(
+    const std::string& filename,
+    const std::vector<Vec3>& colorBuffer,
+    int width,
+    int height
+) {
+    std::ofstream ofs(filename);
+    ofs << "P3\n" << width << " " << height << "\n255\n";
+    for (int i = 0; i < width*height; ++i) {
+        Vec3 c = clamp01(colorBuffer[i]);
+        int r = (int)(std::pow(c.x, 1.0/2.2) * 255.0 + 0.5);
+        int g = (int)(std::pow(c.y, 1.0/2.2) * 255.0 + 0.5);
+        int b = (int)(std::pow(c.z, 1.0/2.2) * 255.0 + 0.5);
+        r = std::max(0, std::min(255, r));
+        g = std::max(0, std::min(255, g));
+        b = std::max(0, std::min(255, b));
+        ofs << r << " " << g << " " << b << "\n";
+    }
+    ofs.close();
+}
+
+// ===================== main =========================
+
+int main() {
+    int width  = 800;
+    int height = 800;
+
+    Scene scene;
+    buildCornellBox(scene);
+
+    Camera cam(
+        Vec3(0.0, 1.0, 2.5),  // 相机位置
+        Vec3(0.0, 1.0, -1.0), // 观察目标
+        Vec3(0.0, 1.0, 0.0),  // 上方向
+        45.0                  // 垂直 FOV
+    );
+
+    // 为每个三角形分配离屏纹理
+    const int TRI_TEX_RES = 256;
+    std::vector<Texture2D> triTextures(scene.tris.size());
+    for (size_t i = 0; i < scene.tris.size(); ++i) {
+        triTextures[i].resize(TRI_TEX_RES, TRI_TEX_RES);
+        const Material* m = scene.tris[i].material;
+        Vec3 baseColor = m ? m->baseColor : Vec3(0.5, 0.5, 0.5);
+        triTextures[i].clear(baseColor);
+    }
+
+    // 相机 viewport 的两个三角形各自的离屏纹理
+    Texture2D camTextures[2];
+    camTextures[0].resize(width, height);
+    camTextures[1].resize(width, height);
+    camTextures[0].clear(Vec3(0.0, 0.0, 0.0));
+    camTextures[1].clear(Vec3(0.0, 0.0, 0.0));
+
+    // 第一步：场景 → 相机 viewport 纹理（递归贴图）
+    renderSceneToCameraTextures(scene, cam, width, height, triTextures, camTextures);
+
+    // 第二步：相机 viewport 纹理 → 最终 PPM
+    std::vector<Vec3> colorBuffer(width * height, Vec3(0.0, 0.0, 0.0));
+    for (int y = 0; y < height; ++y) {
+        for (int x = 0; x < width; ++x) {
+            double px = x + 0.5;
+            double py = y + 0.5;
+
+            Vec2 uvCam;
+            int camIdx;
+            if (!mapScreenToCamUV(px, py, width, height, uvCam, camIdx)) {
+                continue;
+            }
+            Vec3 c = camTextures[camIdx].sampleUV(uvCam);
+            colorBuffer[y * width + x] = c;
+        }
+    }
+
+    writePPM("output.ppm", colorBuffer, width, height);
+    std::cerr << "Render finished. Saved to output.ppm\n";
+    return 0;
+}

experiments/rt3.cpp

@@ -0,0 +1,556 @@
+// main.cpp
+// 一个“面片 + 纹理变换 + 递归反射贴图”的简易 Cornell Box 渲染器（PPM 输出）
+// 关键点：
+// - 不从 Camera 对每个像素发射 Ray 求交取色（避免传统 Ray Tracing 思路）
+// - 以“Viewport(屏幕/面片) = 场景中的三角形面片集合”的方式做投影与贴图（类似光栅化/投影贴图）
+// - 对镜面材质：把该三角形当作 current viewport，构造“反射后的虚拟观察点”，递归渲染并把结果作为该三角形的 current 纹理
+//
+// 编译运行：
+//   g++ -std=c++17 -O2 -o render main.cpp
+//   ./render
+// 输出：output.ppm (P6)
+//
+// 说明：
+// - 这里先忽略 AO、采样漫反射等；漫反射仅用固有颜色/棋盘纹理。
+// - 覆盖关系：用“远到近”排序 + painter 覆盖（O(n log n)），符合你描述的临时方案。
+// - 反射：对每个镜面三角形，递归渲染“该三角形所在平面作为 viewport”的纹理图，再贴回上一级 viewport。
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cmath>
+#include <cstdint>
+#include <fstream>
+#include <iostream>
+#include <limits>
+#include <string>
+#include <utility>
+#include <vector>
+
+static constexpr double kEps = 1e-9;
+
+struct Vec2 {
+  double x = 0, y = 0;
+  Vec2() = default;
+  Vec2(double _x, double _y) : x(_x), y(_y) {}
+  Vec2 operator+(const Vec2& r) const { return {x + r.x, y + r.y}; }
+  Vec2 operator-(const Vec2& r) const { return {x - r.x, y - r.y}; }
+  Vec2 operator*(double s) const { return {x * s, y * s}; }
+};
+
+struct Vec3 {
+  double x = 0, y = 0, z = 0;
+  Vec3() = default;
+  Vec3(double _x, double _y, double _z) : x(_x), y(_y), z(_z) {}
+  Vec3 operator+(const Vec3& r) const { return {x + r.x, y + r.y, z + r.z}; }
+  Vec3 operator-(const Vec3& r) const { return {x - r.x, y - r.y, z - r.z}; }
+  Vec3 operator*(double s) const { return {x * s, y * s, z * s}; }
+  Vec3 operator/(double s) const { return {x / s, y / s, z / s}; }
+};
+
+static inline double dot(const Vec3& a, const Vec3& b) { return a.x * b.x + a.y * b.y + a.z * b.z; }
+static inline Vec3 cross(const Vec3& a, const Vec3& b) {
+  return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x};
+}
+static inline double length(const Vec3& v) { return std::sqrt(dot(v, v)); }
+static inline Vec3 normalize(const Vec3& v) {
+  double len = length(v);
+  if (len < kEps) return {0, 0, 0};
+  return v / len;
+}
+static inline Vec3 clamp01(const Vec3& c) {
+  auto cl = [](double v) { return std::max(0.0, std::min(1.0, v)); };
+  return {cl(c.x), cl(c.y), cl(c.z)};
+}
+static inline Vec3 hadamard(const Vec3& a, const Vec3& b) { return {a.x * b.x, a.y * b.y, a.z * b.z}; }
+
+struct Plane {
+  Vec3 n;   // normalized
+  double d; // plane eq: dot(n, p) + d = 0
+};
+
+static inline Plane makePlaneFromTriangle(const Vec3& a, const Vec3& b, const Vec3& c) {
+  Vec3 n = normalize(cross(b - a, c - a));
+  double d = -dot(n, a);
+  return {n, d};
+}
+
+static inline double signedDistance(const Plane& pl, const Vec3& p) { return dot(pl.n, p) + pl.d; }
+
+static inline Vec3 reflectPointAcrossPlane(const Vec3& p, const Plane& pl) {
+  // p' = p - 2 * dist * n
+  double dist = signedDistance(pl, p);
+  return p - pl.n * (2.0 * dist);
+}
+
+static inline Vec3 reflectVectorAcrossPlane(const Vec3& v, const Plane& pl) {
+  // reflect direction v about plane normal: v' = v - 2*dot(v,n)*n
+  return v - pl.n * (2.0 * dot(v, pl.n));
+}
+
+struct Image {
+  int w = 0, h = 0;
+  std::vector<Vec3> pix; // linear RGB [0..1]
+  Image() = default;
+  Image(int _w, int _h, Vec3 clear = {0, 0, 0}) : w(_w), h(_h), pix(size_t(_w) * size_t(_h), clear) {}
+  Vec3& at(int x, int y) { return pix[size_t(y) * size_t(w) + size_t(x)]; }
+  const Vec3& at(int x, int y) const { return pix[size_t(y) * size_t(w) + size_t(x)]; }
+};
+
+static inline uint8_t toSRGB8(double linear) {
+  linear = std::max(0.0, std::min(1.0, linear));
+  // 简单 gamma 2.2
+  double srgb = std::pow(linear, 1.0 / 2.2);
+  int v = int(srgb * 255.0 + 0.5);
+  v = std::max(0, std::min(255, v));
+  return uint8_t(v);
+}
+
+static void writePPM_P6(const std::string& path, const Image& img) {
+  std::ofstream out(path, std::ios::binary);
+  out << "P6\n" << img.w << " " << img.h << "\n255\n";
+  for (int y = 0; y < img.h; ++y) {
+    for (int x = 0; x < img.w; ++x) {
+      Vec3 c = clamp01(img.at(x, y));
+      uint8_t r = toSRGB8(c.x);
+      uint8_t g = toSRGB8(c.y);
+      uint8_t b = toSRGB8(c.z);
+      out.write(reinterpret_cast<const char*>(&r), 1);
+      out.write(reinterpret_cast<const char*>(&g), 1);
+      out.write(reinterpret_cast<const char*>(&b), 1);
+    }
+  }
+}
+
+static inline Vec3 lerp(const Vec3& a, const Vec3& b, double t) { return a * (1.0 - t) + b * t; }
+
+struct Material {
+  enum class Type { Diffuse, Mirror } type = Type::Diffuse;
+  Vec3 baseColor = {1, 1, 1}; // 对 Diffuse：固有色；对 Mirror：金属 tint
+  double mirrorStrength = 0.95; // Mirror 时反射占比
+  bool checker = false;
+};
+
+struct Triangle {
+  int id = -1;
+  Vec3 p0, p1, p2; // world
+  Vec2 uv0, uv1, uv2; // local texture coords
+  Material mat;
+};
+
+static inline Vec3 triangleNormal(const Triangle& t) {
+  return normalize(cross(t.p1 - t.p0, t.p2 - t.p0));
+}
+
+static inline Vec3 triangleCentroid(const Triangle& t) {
+  return (t.p0 + t.p1 + t.p2) / 3.0;
+}
+
+// 2D barycentric in screen space
+static inline bool barycentric2D(const Vec2& a, const Vec2& b, const Vec2& c, const Vec2& p,
+                                 double& w0, double& w1, double& w2) {
+  Vec2 v0 = b - a;
+  Vec2 v1 = c - a;
+  Vec2 v2 = p - a;
+  double den = v0.x * v1.y - v0.y * v1.x;
+  if (std::abs(den) < kEps) return false;
+  double inv = 1.0 / den;
+  w1 = (v2.x * v1.y - v2.y * v1.x) * inv;
+  w2 = (v0.x * v2.y - v0.y * v2.x) * inv;
+  w0 = 1.0 - w1 - w2;
+  return true;
+}
+
+// 3D barycentric on triangle plane (using areas / cross with normal)
+static inline bool barycentric3D(const Vec3& a, const Vec3& b, const Vec3& c, const Vec3& p,
+                                 double& w0, double& w1, double& w2) {
+  Vec3 n = cross(b - a, c - a);
+  double area2 = length(n);
+  if (area2 < kEps) return false;
+  // use oriented areas along normal
+  double areaPBC = dot(cross(b - p, c - p), n);
+  double areaPCA = dot(cross(c - p, a - p), n);
+  double areaPAB = dot(cross(a - p, b - p), n);
+  w0 = areaPBC / dot(n, n);
+  w1 = areaPCA / dot(n, n);
+  w2 = areaPAB / dot(n, n);
+  // 这里 w0,w1,w2 的数值尺度已经合理（因为 dot(n,n)=|n|^2）
+  // 但数值误差会略大，后续用范围判断即可。
+  return true;
+}
+
+struct Viewport {
+  enum class Kind { Rect, TriangleUV } kind = Kind::Rect;
+
+  Vec3 origin;      // “第一人称”视点（Camera 或 反射后的虚拟点）
+  Plane plane;      // viewport 平面
+  Vec3 planeCenter; // 用于排序/参考
+  Vec3 viewDir;     // normalize(planeCenter - origin)
+
+  // 输出图像大小
+  int outW = 0;
+  int outH = 0;
+
+  // Rect: 通过 plane 坐标系映射到像素
+  Vec3 right; // in plane
+  Vec3 up;    // in plane
+  double halfW = 1;
+  double halfH = 1;
+
+  // TriangleUV: 通过 world 三角形的 UV 映射到像素
+  Vec3 tv0, tv1, tv2; // viewport triangle in world (coplanar with plane)
+  Vec2 tuv0, tuv1, tuv2;
+
+  static Viewport makeCameraRect(const Vec3& origin, const Vec3& center, const Vec3& right, const Vec3& up,
+                                 double halfW, double halfH, int outW, int outH) {
+    Viewport vp;
+    vp.kind = Kind::Rect;
+    vp.origin = origin;
+    vp.planeCenter = center;
+    vp.right = normalize(right);
+    vp.up = normalize(up);
+    vp.halfW = halfW;
+    vp.halfH = halfH;
+    Vec3 n = normalize(cross(vp.right, vp.up)); // right x up = normal
+    // 让法线朝向 origin（不强制，但有助于一致性）
+    if (dot(n, origin - center) < 0) n = n * -1.0;
+    vp.plane = {n, -dot(n, center)};
+    vp.viewDir = normalize(center - origin);
+    vp.outW = outW;
+    vp.outH = outH;
+    return vp;
+  }
+
+  static Viewport makeTriangleUV(const Vec3& origin, const Triangle& tri, int outW, int outH) {
+    Viewport vp;
+    vp.kind = Kind::TriangleUV;
+    vp.origin = origin;
+    vp.tv0 = tri.p0; vp.tv1 = tri.p1; vp.tv2 = tri.p2;
+    vp.tuv0 = tri.uv0; vp.tuv1 = tri.uv1; vp.tuv2 = tri.uv2;
+    vp.planeCenter = triangleCentroid(tri);
+    vp.plane = makePlaneFromTriangle(tri.p0, tri.p1, tri.p2);
+    // 让平面法线尽量朝向 origin，便于稳定
+    if (dot(vp.plane.n, origin - vp.planeCenter) < 0) {
+      vp.plane.n = vp.plane.n * -1.0;
+      vp.plane.d = -vp.plane.d;
+    }
+    vp.viewDir = normalize(vp.planeCenter - origin);
+    vp.outW = outW;
+    vp.outH = outH;
+    return vp;
+  }
+
+  // 将世界点 x（不一定在 plane 上）沿 origin->x 投影到 viewport 平面，并映射到像素坐标
+  // 返回 false 表示无交/在背面/落在 viewport 有效区域外
+  bool projectWorldPointToPixel(const Vec3& x, Vec2& outPix, double& outT) const {
+    Vec3 dir = x - origin;
+    double denom = dot(plane.n, dir);
+    if (std::abs(denom) < kEps) return false;
+    // intersection t where origin + t*dir hits plane
+    double t = -(dot(plane.n, origin) + plane.d) / denom;
+    if (t <= kEps) return false; // 只接受向前交
+    Vec3 q = origin + dir * t;   // on plane
+    outT = t;
+
+    if (kind == Kind::Rect) {
+      Vec3 rel = q - planeCenter;
+      double u = dot(rel, right) / halfW; // [-1,1] ideally
+      double v = dot(rel, up) / halfH;
+      double px = (u * 0.5 + 0.5) * double(outW - 1);
+      double py = (1.0 - (v * 0.5 + 0.5)) * double(outH - 1);
+      if (px < -0.5 || px > outW - 0.5 || py < -0.5 || py > outH - 0.5) return false;
+      outPix = {px, py};
+      return true;
+    }
+
+    // TriangleUV: 要求 q 落在 viewport 三角形内（用 3D 重心判断）
+    double w0, w1, w2;
+    if (!barycentric3D(tv0, tv1, tv2, q, w0, w1, w2)) return false;
+    if (w0 < -1e-4 || w1 < -1e-4 || w2 < -1e-4) return false;
+
+    Vec2 uv = tuv0 * w0 + tuv1 * w1 + tuv2 * w2;
+    if (uv.x < -1e-4 || uv.x > 1.0 + 1e-4 || uv.y < -1e-4 || uv.y > 1.0 + 1e-4) return false;
+
+    double px = uv.x * double(outW - 1);
+    double py = (1.0 - uv.y) * double(outH - 1);
+    outPix = {px, py};
+    return true;
+  }
+};
+
+static Vec3 sampleDiffuseTex(const Material& mat, const Vec2& uv) {
+  if (!mat.checker) return mat.baseColor;
+  // 纯 UV 棋盘
+  int cx = int(std::floor(uv.x * 10.0));
+  int cy = int(std::floor(uv.y * 10.0));
+  bool odd = ((cx + cy) & 1) != 0;
+  Vec3 c0 = mat.baseColor;
+  Vec3 c1 = lerp(mat.baseColor, Vec3{1, 1, 1}, 0.35);
+  return odd ? c1 : c0;
+}
+
+// Forward declaration
+static Image renderViewport(const Viewport& vp, const std::vector<Triangle>& scene, int depth, int maxDepth,
+                            int excludeTriId);
+
+// 为镜面三角形生成“当前纹理”（通过递归把它当 viewport 渲染）
+static Image renderMirrorTextureForTriangle(const Triangle& tri, const Vec3& incidentOrigin,
+                                           const std::vector<Triangle>& scene, int depth, int maxDepth,
+                                           int texW, int texH) {
+  Plane pl = makePlaneFromTriangle(tri.p0, tri.p1, tri.p2);
+
+  // 虚拟观察点：把上一级 origin 关于镜面平面反射
+  Vec3 virtualOrigin = reflectPointAcrossPlane(incidentOrigin, pl);
+
+  // 以该镜面三角形为 viewport，把场景渲染到它的 UV 纹理图里
+  Viewport triVP = Viewport::makeTriangleUV(virtualOrigin, tri, texW, texH);
+
+  // 排除自己，避免最直接的反馈
+  Image reflection = renderViewport(triVP, scene, depth + 1, maxDepth, tri.id);
+
+  return reflection;
+}
+
+struct ProjectedTri {
+  const Triangle* tri = nullptr;
+  Vec2 s0, s1, s2; // projected to output pixels
+  double sortKey = 0; // larger=nearer or farther? We will sort far->near
+};
+
+// 简易 painter：远->近（sortKey 越大越“近”），所以按 sortKey 升序绘制（远先画）
+static Image renderViewport(const Viewport& vp, const std::vector<Triangle>& scene, int depth, int maxDepth,
+                            int excludeTriId) {
+  Image out(vp.outW, vp.outH, Vec3{0.0, 0.0, 0.0});
+
+  // 为本次渲染维护一个“镜面三角形 -> 纹理图”的临时缓存（只对当前 viewport 有效）
+  struct MirrorCacheItem { int triId; Image tex; };
+  std::vector<MirrorCacheItem> mirrorTexCache;
+  mirrorTexCache.reserve(64);
+
+  auto getMirrorTex = [&](const Triangle& t) -> const Image* {
+    for (auto& it : mirrorTexCache) {
+      if (it.triId == t.id) return &it.tex;
+    }
+    // 纹理分辨率可根据需要调大/调小
+    int texW = 256, texH = 256;
+    if (depth >= maxDepth) return nullptr;
+    Image tex = renderMirrorTextureForTriangle(t, vp.origin, scene, depth, maxDepth, texW, texH);
+    mirrorTexCache.push_back({t.id, std::move(tex)});
+    return &mirrorTexCache.back().tex;
+  };
+
+  // 1) 收集可投影到 viewport 的三角形，并计算排序 key
+  std::vector<ProjectedTri> list;
+  list.reserve(scene.size());
+
+  for (const auto& t : scene) {
+    if (t.id == excludeTriId) continue;
+
+    Vec2 p0, p1, p2;
+    double tt0, tt1, tt2;
+    if (!vp.projectWorldPointToPixel(t.p0, p0, tt0)) continue;
+    if (!vp.projectWorldPointToPixel(t.p1, p1, tt1)) continue;
+    if (!vp.projectWorldPointToPixel(t.p2, p2, tt2)) continue;
+
+    Vec3 c = triangleCentroid(t);
+    double key = dot(vp.viewDir, c - vp.origin); // 视线方向上的“深度”
+    list.push_back(ProjectedTri{&t, p0, p1, p2, key});
+  }
+
+  std::sort(list.begin(), list.end(), [](const ProjectedTri& a, const ProjectedTri& b) {
+    return a.sortKey < b.sortKey; // far -> near
+  });
+
+  // 2) 按远到近绘制（覆盖关系）
+  for (const auto& pt : list) {
+    const Triangle& tri = *pt.tri;
+
+    // 镜面材质：先生成该三角形对当前 origin 的“反射纹理”
+    const Image* mirrorTex = nullptr;
+    if (tri.mat.type == Material::Type::Mirror && depth < maxDepth) {
+      mirrorTex = getMirrorTex(tri);
+    }
+
+    // 三角形光栅化到 out（注意：这里是把 tri 的“纹理”投影变换后贴到 viewport 上）
+    double minX = std::floor(std::min({pt.s0.x, pt.s1.x, pt.s2.x}));
+    double maxX = std::ceil (std::max({pt.s0.x, pt.s1.x, pt.s2.x}));
+    double minY = std::floor(std::min({pt.s0.y, pt.s1.y, pt.s2.y}));
+    double maxY = std::ceil (std::max({pt.s0.y, pt.s1.y, pt.s2.y}));
+
+    int x0 = std::max(0, int(minX));
+    int x1 = std::min(vp.outW - 1, int(maxX));
+    int y0 = std::max(0, int(minY));
+    int y1 = std::min(vp.outH - 1, int(maxY));
+
+    for (int y = y0; y <= y1; ++y) {
+      for (int x = x0; x <= x1; ++x) {
+        Vec2 p{double(x) + 0.5, double(y) + 0.5};
+        double w0, w1, w2;
+        if (!barycentric2D(pt.s0, pt.s1, pt.s2, p, w0, w1, w2)) continue;
+        if (w0 < -1e-6 || w1 < -1e-6 || w2 < -1e-6) continue;
+
+        // screen-space 仿射插值 tri 的 UV（这里不做 perspective-correct，符合“变换粘贴”的感觉）
+        Vec2 uv = tri.uv0 * w0 + tri.uv1 * w1 + tri.uv2 * w2;
+
+        Vec3 base = sampleDiffuseTex(tri.mat, uv);
+
+        if (tri.mat.type == Material::Type::Mirror && mirrorTex) {
+          // 镜面：把递归得到的 reflectionTex 作为 tri 的 current 纹理，再叠加 tint
+          // mirrorTex 的坐标域就是 tri 的 UV（由 Viewport::TriangleUV 保证）
+          int sx = std::max(0, std::min(mirrorTex->w - 1, int(uv.x * (mirrorTex->w - 1) + 0.5)));
+          int sy = std::max(0, std::min(mirrorTex->h - 1, int((1.0 - uv.y) * (mirrorTex->h - 1) + 0.5)));
+          Vec3 refl = mirrorTex->at(sx, sy);
+
+          // 简单金属混合：反射为主，baseColor 做 tint
+          Vec3 tintedRefl = hadamard(refl, tri.mat.baseColor);
+          Vec3 outC = lerp(base, tintedRefl, tri.mat.mirrorStrength);
+
+          out.at(x, y) = outC;
+        } else {
+          // 漫反射（当前回合忽略采样/光照，仅贴固有纹理）
+          out.at(x, y) = base;
+        }
+      }
+    }
+  }
+
+  return out;
+}
+
+static int gNextTriId = 1;
+
+static Triangle makeTri(const Vec3& a, const Vec3& b, const Vec3& c, const Vec2& uva, const Vec2& uvb, const Vec2& uvc,
+                        const Material& m) {
+  Triangle t;
+  t.id = gNextTriId++;
+  t.p0 = a; t.p1 = b; t.p2 = c;
+  t.uv0 = uva; t.uv1 = uvb; t.uv2 = uvc;
+  t.mat = m;
+  return t;
+}
+
+static void addQuadAsTwoTris(std::vector<Triangle>& out,
+                             const Vec3& a, const Vec3& b, const Vec3& c, const Vec3& d,
+                             const Material& m,
+                             const Vec2& uva = {0,0}, const Vec2& uvb = {1,0}, const Vec2& uvc = {1,1}, const Vec2& uvd = {0,1}) {
+  // quad (a,b,c,d) in CCW; split to (a,b,c) and (a,c,d)
+  out.push_back(makeTri(a, b, c, uva, uvb, uvc, m));
+  out.push_back(makeTri(a, c, d, uva, uvc, uvd, m));
+}
+
+static void addBox(std::vector<Triangle>& out, const Vec3& center, const Vec3& halfSize, const Material& m) {
+  // axis-aligned box, 6 faces, each 2 tris
+  Vec3 minP = center - halfSize;
+  Vec3 maxP = center + halfSize;
+
+  Vec3 p000{minP.x, minP.y, minP.z};
+  Vec3 p001{minP.x, minP.y, maxP.z};
+  Vec3 p010{minP.x, maxP.y, minP.z};
+  Vec3 p011{minP.x, maxP.y, maxP.z};
+  Vec3 p100{maxP.x, minP.y, minP.z};
+  Vec3 p101{maxP.x, minP.y, maxP.z};
+  Vec3 p110{maxP.x, maxP.y, minP.z};
+  Vec3 p111{maxP.x, maxP.y, maxP.z};
+
+  // +X (right): p100 p101 p111 p110
+  addQuadAsTwoTris(out, p100, p101, p111, p110, m);
+  // -X (left): p000 p010 p011 p001
+  addQuadAsTwoTris(out, p000, p010, p011, p001, m);
+  // +Y (top): p010 p110 p111 p011
+  addQuadAsTwoTris(out, p010, p110, p111, p011, m);
+  // -Y (bottom): p000 p001 p101 p100
+  addQuadAsTwoTris(out, p000, p001, p101, p100, m);
+  // +Z (front): p001 p011 p111 p101
+  addQuadAsTwoTris(out, p001, p011, p111, p101, m);
+  // -Z (back): p000 p100 p110 p010
+  addQuadAsTwoTris(out, p000, p100, p110, p010, m);
+}
+
+int main() {
+  // 输出分辨率
+  const int W = 800;
+  const int H = 600;
+
+  // 构造 Cornell Box 场景（用三角形面片）
+  std::vector<Triangle> scene;
+  scene.reserve(1024);
+
+  // Cornell box bounds
+  // x: [-1,1], y: [-1,1], z: [-2,-6]
+  const double x0 = -1.0, x1 = 1.0;
+  const double y0 = -1.0, y1 = 1.0;
+  const double zNear = -2.0, zBack = -6.0;
+
+  Material leftWall;  leftWall.type = Material::Type::Diffuse; leftWall.baseColor = {0.95, 0.20, 0.20}; leftWall.checker = false;
+  Material rightWall; rightWall.type = Material::Type::Diffuse; rightWall.baseColor = {0.20, 0.95, 0.20}; rightWall.checker = false;
+  Material backWall;  backWall.type = Material::Type::Diffuse; backWall.baseColor = {0.90, 0.90, 0.90}; backWall.checker = false;
+  Material floorWall; floorWall.type = Material::Type::Diffuse; floorWall.baseColor = {0.90, 0.90, 0.90}; floorWall.checker = true;
+  Material ceilWall;  ceilWall.type = Material::Type::Diffuse; ceilWall.baseColor = {0.85, 0.85, 0.85}; ceilWall.checker = false;
+
+  // 四壁（这里额外加了天花板，便于反射更丰富；如需严格“四壁”，可注释 ceiling）
+  // Left wall (x=x0), CCW from inside
+  addQuadAsTwoTris(scene,
+    Vec3{x0, y0, zNear}, Vec3{x0, y0, zBack}, Vec3{x0, y1, zBack}, Vec3{x0, y1, zNear},
+    leftWall);
+
+  // Right wall (x=x1)
+  addQuadAsTwoTris(scene,
+    Vec3{x1, y0, zBack}, Vec3{x1, y0, zNear}, Vec3{x1, y1, zNear}, Vec3{x1, y1, zBack},
+    rightWall);
+
+  // Back wall (z=zBack)
+  addQuadAsTwoTris(scene,
+    Vec3{x0, y0, zBack}, Vec3{x1, y0, zBack}, Vec3{x1, y1, zBack}, Vec3{x0, y1, zBack},
+    backWall);
+
+  // Floor (y=y0)
+  addQuadAsTwoTris(scene,
+    Vec3{x0, y0, zBack}, Vec3{x1, y0, zBack}, Vec3{x1, y0, zNear}, Vec3{x0, y0, zNear},
+    floorWall);
+
+  // Ceiling (y=y1)
+  addQuadAsTwoTris(scene,
+    Vec3{x0, y1, zNear}, Vec3{x1, y1, zNear}, Vec3{x1, y1, zBack}, Vec3{x0, y1, zBack},
+    ceilWall);
+
+  // 两个金属盒子（镜面反射）
+  Material blueMetal;
+  blueMetal.type = Material::Type::Mirror;
+  blueMetal.baseColor = {0.35, 0.55, 1.00}; // 蓝色金属 tint
+  blueMetal.mirrorStrength = 0.95;
+
+  Material yellowMetal;
+  yellowMetal.type = Material::Type::Mirror;
+  yellowMetal.baseColor = {1.00, 0.90, 0.25}; // 黄色金属 tint
+  yellowMetal.mirrorStrength = 0.95;
+
+  // 放在地面上（y0=-1），盒子底面稍微抬一点避免穿插
+  addBox(scene, Vec3{-0.45, -0.55, -4.7}, Vec3{0.25, 0.45, 0.25}, blueMetal);
+  addBox(scene, Vec3{ 0.45, -0.65, -3.8}, Vec3{0.30, 0.35, 0.30}, yellowMetal);
+
+  // Camera viewport 抽象为场景中的一个矩形平面（内部用两个三角形覆盖，这里用 Rect viewport 简化映射）
+  Vec3 camOrigin{0.0, 0.0, 0.0};
+  Vec3 vpCenter{0.0, 0.0, -1.0};
+
+  // 视场决定 viewport 大小：halfW/halfH
+  // 设定垂直 FOV ~ 55°
+  double fovY = 55.0 * M_PI / 180.0;
+  double halfH = std::tan(fovY * 0.5) * 1.0;          // plane 距离为 1
+  double halfW = halfH * (double(W) / double(H));
+
+  Vec3 vpRight{1, 0, 0};
+  Vec3 vpUp{0, 1, 0};
+
+  Viewport cameraVP = Viewport::makeCameraRect(camOrigin, vpCenter, vpRight, vpUp, halfW, halfH, W, H);
+
+  // 递归深度（镜面反射级数）
+  const int maxDepth = 2;
+
+  std::cerr << "Rendering...\n";
+  Image img = renderViewport(cameraVP, scene, /*depth=*/0, maxDepth, /*excludeTriId=*/-1);
+
+  // 输出
+  writePPM_P6("output.ppm", img);
+  std::cerr << "Done. Wrote output.ppm\n";
+  return 0;
+}

experiments/rt4.cpp

@@ -0,0 +1,743 @@
+/*
+Cornell Box: triangle-driven rasterization + Z-buffer + recursive planar mirror reflection (render-to-texture)
+
+Constraints satisfied:
+- NO "main camera per-pixel ray cast & triangle intersection".
+- Visibility is from projection + triangle rasterization + Z-test only.
+- Mirror reflection uses recursive offscreen rendering from a mirrored camera, then samples that image.
+
+Key fixes vs the broken/dark versions:
+- Add tone mapping + gamma encoding on output (prevents "too dark" or "washed out / flat").
+- Use point light + ambient with face-forward normals for diffuse.
+- Mirror cache keyed by plane (two triangles on a face share one reflection render).
+- When rendering the mirror pass, exclude all triangles coplanar with that mirror plane to avoid self-occlusion.
+
+Build:
+  g++ -O2 -std=c++17 cornell_raster_reflect.cpp -o cornell
+
+Run:
+  ./cornell
+
+Output:
+  output.ppm (P3)
+*/
+
+#include <algorithm>
+#include <cmath>
+#include <cstdint>
+#include <fstream>
+#include <iostream>
+#include <limits>
+#include <optional>
+#include <string>
+#include <unordered_map>
+#include <utility>
+#include <vector>
+
+static constexpr float kEps = 1e-6f;
+static constexpr float kInf = std::numeric_limits<float>::infinity();
+
+struct Vec2 {
+	float x = 0, y = 0;
+	Vec2() = default;
+	Vec2(float _x, float _y) : x(_x), y(_y) {
+	}
+	Vec2 operator+(const Vec2 &o) const {
+		return { x + o.x, y + o.y };
+	}
+	Vec2 operator-(const Vec2 &o) const {
+		return { x - o.x, y - o.y };
+	}
+	Vec2 operator*(float s) const {
+		return { x * s, y * s };
+	}
+};
+
+struct Vec3 {
+	float x = 0, y = 0, z = 0;
+	Vec3() = default;
+	Vec3(float _x, float _y, float _z) : x(_x), y(_y), z(_z) {
+	}
+	Vec3 operator+(const Vec3 &o) const {
+		return { x + o.x, y + o.y, z + o.z };
+	}
+	Vec3 operator-(const Vec3 &o) const {
+		return { x - o.x, y - o.y, z - o.z };
+	}
+	Vec3 operator*(float s) const {
+		return { x * s, y * s, z * s };
+	}
+	Vec3 operator/(float s) const {
+		return { x / s, y / s, z / s };
+	}
+	Vec3 &operator+=(const Vec3 &o) {
+		x += o.x;
+		y += o.y;
+		z += o.z;
+		return *this;
+	}
+};
+
+static inline Vec3 operator*(float s, const Vec3 &v) {
+	return v * s;
+}
+
+static inline float dot(const Vec3 &a, const Vec3 &b) {
+	return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+
+static inline Vec3 cross(const Vec3 &a, const Vec3 &b) {
+	return {
+		a.y * b.z - a.z * b.y,
+		a.z * b.x - a.x * b.z,
+		a.x * b.y - a.y * b.x
+	};
+}
+
+static inline float length(const Vec3 &v) {
+	return std::sqrt(dot(v, v));
+}
+
+static inline Vec3 normalize(const Vec3 &v) {
+	float len = length(v);
+	if (len < kEps)
+		return { 0, 0, 0 };
+	return v / len;
+}
+
+static inline Vec3 clamp01(const Vec3 &c) {
+	return {
+		std::clamp(c.x, 0.0f, 1.0f),
+		std::clamp(c.y, 0.0f, 1.0f),
+		std::clamp(c.z, 0.0f, 1.0f),
+	};
+}
+
+static inline Vec3 hadamard(const Vec3 &a, const Vec3 &b) {
+	return { a.x * b.x, a.y * b.y, a.z * b.z };
+}
+
+static inline Vec3 reinhardTonemap(const Vec3 &c) {
+	// Per-channel Reinhard; simple and stable for this demo.
+	return {
+		c.x / (1.0f + c.x),
+		c.y / (1.0f + c.y),
+		c.z / (1.0f + c.z),
+	};
+}
+
+static inline float gammaEncode(float linear, float gamma = 2.2f) {
+	linear = std::max(0.0f, linear);
+	return std::pow(linear, 1.0f / gamma);
+}
+
+static inline Vec3 gammaEncode(const Vec3 &linear, float gamma = 2.2f) {
+	return { gammaEncode(linear.x, gamma), gammaEncode(linear.y, gamma), gammaEncode(linear.z, gamma) };
+}
+
+enum class MaterialType {
+	Diffuse = 0,
+	Metal = 1
+};
+
+struct Material {
+	MaterialType type = MaterialType::Diffuse;
+	Vec3 albedo = { 1, 1, 1 }; // Diffuse base color
+	float reflectance = 1.0f; // Metal reflectance [0,1]
+};
+
+struct Triangle {
+	Vec3 p0, p1, p2;
+	Material mat;
+	Vec3 normal; // flat normal (unit)
+};
+
+static inline Vec3 computeFlatNormal(const Triangle &t) {
+	return normalize(cross(t.p1 - t.p0, t.p2 - t.p0));
+}
+
+struct Plane {
+	Vec3 p; // point on plane
+	Vec3 n; // unit normal (oriented)
+};
+
+static inline float signedDistance(const Plane &pl, const Vec3 &x) {
+	return dot(pl.n, x - pl.p);
+}
+
+static inline Vec3 reflectPointAboutPlane(const Vec3 &x, const Plane &pl) {
+	float d = signedDistance(pl, x);
+	return x - (2.0f * d) * pl.n;
+}
+
+static inline Vec3 reflectVectorAboutPlane(const Vec3 &v, const Plane &pl) {
+	return v - (2.0f * dot(v, pl.n)) * pl.n;
+}
+
+struct Image {
+	int w = 0, h = 0;
+	std::vector<Vec3> pix; // linear HDR-ish buffer
+
+	void reset(int width, int height, Vec3 clear = { 0, 0, 0 }) {
+		w = width;
+		h = height;
+		pix.assign((size_t)w * (size_t)h, clear);
+	}
+
+	Vec3 get(int x, int y) const {
+		if (x < 0 || x >= w || y < 0 || y >= h)
+			return { 0, 0, 0 };
+		return pix[(size_t)y * (size_t)w + (size_t)x];
+	}
+
+	void set(int x, int y, const Vec3 &c) {
+		if (x < 0 || x >= w || y < 0 || y >= h)
+			return;
+		pix[(size_t)y * (size_t)w + (size_t)x] = c;
+	}
+
+	Vec3 sampleNearest(float u, float v) const {
+		if (w <= 0 || h <= 0)
+			return { 0, 0, 0 };
+		int x = (int)std::floor(u * (float)w);
+		int y = (int)std::floor(v * (float)h);
+		x = std::clamp(x, 0, w - 1);
+		y = std::clamp(y, 0, h - 1);
+		return get(x, y);
+	}
+
+	void writePPM_P3(const std::string &path) const {
+		std::ofstream out(path, std::ios::out);
+		if (!out) {
+			std::cerr << "Failed to open: " << path << "\n";
+			return;
+		}
+		out << "P3\n"
+			<< w << " " << h << "\n255\n";
+		for (int y = 0; y < h; ++y) {
+			for (int x = 0; x < w; ++x) {
+				Vec3 c = get(x, y);
+
+				// Fix: tone mapping + gamma for display
+				c = reinhardTonemap(c);
+				c = gammaEncode(c, 2.2f);
+				c = clamp01(c);
+
+				int r = (int)std::round(c.x * 255.0f);
+				int g = (int)std::round(c.y * 255.0f);
+				int b = (int)std::round(c.z * 255.0f);
+				out << r << " " << g << " " << b << "\n";
+			}
+		}
+	}
+};
+
+struct DepthBuffer {
+	int w = 0, h = 0;
+	std::vector<float> z; // camera-space z, smaller=closer
+
+	void reset(int width, int height) {
+		w = width;
+		h = height;
+		z.assign((size_t)w * (size_t)h, kInf);
+	}
+
+	float get(int x, int y) const {
+		return z[(size_t)y * (size_t)w + (size_t)x];
+	}
+
+	void set(int x, int y, float v) {
+		z[(size_t)y * (size_t)w + (size_t)x] = v;
+	}
+};
+
+struct RenderTarget {
+	Image color;
+	DepthBuffer depth;
+};
+
+struct Camera {
+	Vec3 origin;
+	Vec3 forward;
+	Vec3 right;
+	Vec3 up;
+
+	float fovY_deg = 60.0f;
+	float nearZ = 0.05f;
+	float farZ = 50.0f;
+
+	int imgW = 640;
+	int imgH = 480;
+
+	static Camera lookAt(const Vec3 &eye, const Vec3 &target, const Vec3 &upHint,
+		float fovY_deg, float nearZ, float farZ,
+		int w, int h) {
+		Camera c;
+		c.origin = eye;
+		c.forward = normalize(target - eye);
+		c.right = normalize(cross(c.forward, upHint));
+		c.up = normalize(cross(c.right, c.forward));
+		c.fovY_deg = fovY_deg;
+		c.nearZ = nearZ;
+		c.farZ = farZ;
+		c.imgW = w;
+		c.imgH = h;
+		return c;
+	}
+
+	Vec3 worldToCamera(const Vec3 &p) const {
+		Vec3 d = p - origin;
+		return { dot(d, right), dot(d, up), dot(d, forward) }; // z>0 in front
+	}
+
+	bool projectToScreen(const Vec3 &worldP, Vec2 &outXY, float &outInvZ, float &outCamZ) const {
+		Vec3 pc = worldToCamera(worldP);
+		float z = pc.z;
+		outCamZ = z;
+		if (z <= nearZ)
+			return false;
+
+		float aspect = (float)imgW / (float)imgH;
+		float fovY = fovY_deg * (3.1415926535f / 180.0f);
+		float tanHalf = std::tan(fovY * 0.5f);
+
+		// Perspective projection with vertical fov
+		float ndcX = (pc.x / (z * tanHalf)) / aspect;
+		float ndcY = (pc.y / (z * tanHalf));
+
+		float px = (ndcX * 0.5f + 0.5f) * (float)imgW;
+		float py = (1.0f - (ndcY * 0.5f + 0.5f)) * (float)imgH;
+
+		outXY = { px, py };
+		outInvZ = 1.0f / z;
+		return true;
+	}
+};
+
+struct ScreenVertex {
+	Vec2 s;
+	float invZ;
+	Vec3 worldP;
+};
+
+static inline float edgeFunction(const Vec2 &a, const Vec2 &b, const Vec2 &c) {
+	return (c.x - a.x) * (b.y - a.y) - (c.y - a.y) * (b.x - a.x);
+}
+
+static inline float triangleAreaPixels(const Vec2 &a, const Vec2 &b, const Vec2 &c) {
+	return std::abs(edgeFunction(a, b, c)) * 0.5f;
+}
+
+struct RenderConfig {
+	int maxDepth = 2;
+	float minMirrorAreaPixels = 6.0f;
+	Vec3 clearColor = { 0.0f, 0.0f, 0.0f }; // linear clear
+};
+
+struct RenderContext {
+	const std::vector<Triangle> *tris = nullptr;
+	RenderConfig cfg;
+
+	// Simple point light (no shadows)
+	Vec3 lightPos = { 0.0f, 1.95f, 0.0f };
+	Vec3 lightColor = { 1.0f, 1.0f, 1.0f };
+	float lightIntensity = 25.0f;
+
+	Vec3 ambient = { 0.06f, 0.06f, 0.06f };
+};
+
+static inline Vec3 faceForwardToView(Vec3 n, const Vec3 &worldP, const Camera &cam) {
+	Vec3 V = normalize(cam.origin - worldP);
+	if (dot(n, V) < 0.0f)
+		n = n * -1.0f;
+	return n;
+}
+
+static inline Vec3 shadeDiffuse(const Triangle &t,
+	const Vec3 &worldP,
+	const Vec3 &worldN,
+	const Camera &cam,
+	const RenderContext &ctx) {
+	Vec3 N = faceForwardToView(worldN, worldP, cam);
+
+	Vec3 Lvec = ctx.lightPos - worldP;
+	float dist2 = std::max(kEps, dot(Lvec, Lvec));
+	Vec3 L = normalize(Lvec);
+
+	float ndotl = std::max(0.0f, dot(N, L));
+	float atten = 1.0f / dist2;
+
+	Vec3 direct = (ctx.lightIntensity * ndotl * atten) * ctx.lightColor;
+	Vec3 lit = ctx.ambient + direct;
+
+	return hadamard(t.mat.albedo, lit);
+}
+
+static inline Plane orientedPlaneTowardCamera(const Triangle &t, const Camera &cam) {
+	Plane pl;
+	pl.p = t.p0;
+	pl.n = normalize(t.normal);
+	// Ensure camera is on the positive side (for consistent mirroring orientation)
+	float s = dot(pl.n, cam.origin - pl.p);
+	if (s < 0.0f)
+		pl.n = pl.n * -1.0f;
+	return pl;
+}
+
+static inline Camera mirrorCameraAcrossPlane(const Camera &cam, const Plane &pl) {
+	Camera mc = cam;
+	mc.origin = reflectPointAboutPlane(cam.origin, pl);
+	mc.forward = normalize(reflectVectorAboutPlane(cam.forward, pl));
+	mc.up = normalize(reflectVectorAboutPlane(cam.up, pl));
+	mc.right = normalize(cross(mc.forward, mc.up));
+	mc.up = normalize(cross(mc.right, mc.forward));
+	return mc;
+}
+
+static inline bool triangleCoplanarWithPlane(const Triangle &t, const Plane &pl) {
+	// Exclude triangles on the same plane (both triangles of a quad face)
+	// Use both parallel-normal test and vertex distance test.
+	float parallel = std::abs(dot(normalize(t.normal), pl.n));
+	if (parallel < 0.999f)
+		return false;
+
+	float d0 = std::abs(signedDistance(pl, t.p0));
+	float d1 = std::abs(signedDistance(pl, t.p1));
+	float d2 = std::abs(signedDistance(pl, t.p2));
+	return (d0 < 1e-4f && d1 < 1e-4f && d2 < 1e-4f);
+}
+
+struct PlaneKey {
+	int nx = 0, ny = 0, nz = 0;
+	int d = 0; // plane equation: n·x + d = 0 (quantized)
+	bool operator==(const PlaneKey &o) const {
+		return nx == o.nx && ny == o.ny && nz == o.nz && d == o.d;
+	}
+};
+
+struct PlaneKeyHash {
+	size_t operator()(const PlaneKey &k) const noexcept {
+		// Simple hash combine
+		size_t h = 1469598103934665603ull;
+		auto mix = [&](uint64_t v) {
+			h ^= v + 0x9e3779b97f4a7c15ull + (h << 6) + (h >> 2);
+		};
+		mix((uint64_t)(uint32_t)k.nx);
+		mix((uint64_t)(uint32_t)k.ny);
+		mix((uint64_t)(uint32_t)k.nz);
+		mix((uint64_t)(uint32_t)k.d);
+		return h;
+	}
+};
+
+static inline PlaneKey makePlaneKey(const Plane &pl) {
+	// Quantize plane normal and offset for caching; oriented plane already.
+	// Plane equation: n·x + d = 0 where d = -n·p
+	float d = -dot(pl.n, pl.p);
+	const float sN = 10000.0f;
+	const float sD = 10000.0f;
+
+	PlaneKey k;
+	k.nx = (int)std::round(pl.n.x * sN);
+	k.ny = (int)std::round(pl.n.y * sN);
+	k.nz = (int)std::round(pl.n.z * sN);
+	k.d = (int)std::round(d * sD);
+	return k;
+}
+
+struct MirrorCacheEntry {
+	Plane plane;
+	Camera mirrorCam;
+	RenderTarget rt;
+	bool ready = false;
+};
+
+static RenderTarget renderPass(const Camera &cam,
+	const RenderContext &ctx,
+	int recursionDepth,
+	const Plane *excludeCoplanarPlaneOrNull);
+
+static RenderTarget renderPass(const Camera &cam,
+	const RenderContext &ctx,
+	int recursionDepth,
+	const Plane *excludeCoplanarPlaneOrNull) {
+	RenderTarget rt;
+	rt.color.reset(cam.imgW, cam.imgH, ctx.cfg.clearColor);
+	rt.depth.reset(cam.imgW, cam.imgH);
+
+	// Cache planar reflections per plane (per pass)
+	std::unordered_map<PlaneKey, MirrorCacheEntry, PlaneKeyHash> mirrorCache;
+	mirrorCache.reserve(64);
+
+	for (int ti = 0; ti < (int)ctx.tris->size(); ++ti) {
+		const Triangle &t = (*ctx.tris)[ti];
+
+		if (excludeCoplanarPlaneOrNull && triangleCoplanarWithPlane(t, *excludeCoplanarPlaneOrNull)) {
+			continue;
+		}
+
+		Vec2 s0, s1, s2;
+		float invZ0, invZ1, invZ2;
+		float z0, z1, z2;
+
+		bool ok0 = cam.projectToScreen(t.p0, s0, invZ0, z0);
+		bool ok1 = cam.projectToScreen(t.p1, s1, invZ1, z1);
+		bool ok2 = cam.projectToScreen(t.p2, s2, invZ2, z2);
+
+		// Minimal clipping: if any vertex behind near, skip triangle
+		if (!(ok0 && ok1 && ok2))
+			continue;
+
+		ScreenVertex sv[3];
+		sv[0] = { s0, invZ0, t.p0 };
+		sv[1] = { s1, invZ1, t.p1 };
+		sv[2] = { s2, invZ2, t.p2 };
+
+		float areaPx = triangleAreaPixels(sv[0].s, sv[1].s, sv[2].s);
+
+		float minXf = std::floor(std::min({ sv[0].s.x, sv[1].s.x, sv[2].s.x }));
+		float maxXf = std::ceil(std::max({ sv[0].s.x, sv[1].s.x, sv[2].s.x }));
+		float minYf = std::floor(std::min({ sv[0].s.y, sv[1].s.y, sv[2].s.y }));
+		float maxYf = std::ceil(std::max({ sv[0].s.y, sv[1].s.y, sv[2].s.y }));
+
+		int minX = std::clamp((int)minXf, 0, cam.imgW - 1);
+		int maxX = std::clamp((int)maxXf, 0, cam.imgW - 1);
+		int minY = std::clamp((int)minYf, 0, cam.imgH - 1);
+		int maxY = std::clamp((int)maxYf, 0, cam.imgH - 1);
+
+		float triArea = edgeFunction(sv[0].s, sv[1].s, sv[2].s);
+		if (std::abs(triArea) < kEps)
+			continue;
+		float invTriArea = 1.0f / triArea;
+
+		for (int y = minY; y <= maxY; ++y) {
+			for (int x = minX; x <= maxX; ++x) {
+				Vec2 p = { (float)x + 0.5f, (float)y + 0.5f };
+
+				float w0 = edgeFunction(sv[1].s, sv[2].s, p) * invTriArea;
+				float w1 = edgeFunction(sv[2].s, sv[0].s, p) * invTriArea;
+				float w2 = edgeFunction(sv[0].s, sv[1].s, p) * invTriArea;
+
+				if (w0 < -kEps || w1 < -kEps || w2 < -kEps)
+					continue;
+
+				// Perspective-correct interpolation: invZ at pixel
+				float invZ = w0 * sv[0].invZ + w1 * sv[1].invZ + w2 * sv[2].invZ;
+				if (invZ <= kEps)
+					continue;
+				float camZ = 1.0f / invZ;
+
+				float oldZ = rt.depth.get(x, y);
+				if (camZ >= oldZ)
+					continue;
+
+				// Interpolate world position perspective-correctly
+				Vec3 worldP = (w0 * sv[0].worldP * sv[0].invZ + w1 * sv[1].worldP * sv[1].invZ + w2 * sv[2].worldP * sv[2].invZ) / invZ;
+
+				rt.depth.set(x, y, camZ);
+
+				Vec3 outLinear { 0, 0, 0 };
+
+				if (t.mat.type == MaterialType::Diffuse) {
+					outLinear = shadeDiffuse(t, worldP, t.normal, cam, ctx);
+				} else {
+					float refl = std::clamp(t.mat.reflectance, 0.0f, 1.0f);
+
+					bool canRecurse = (refl > 0.0f) && (recursionDepth < ctx.cfg.maxDepth) && (areaPx >= ctx.cfg.minMirrorAreaPixels);
+
+					Vec3 base = shadeDiffuse(t, worldP, t.normal, cam, ctx);
+
+					if (!canRecurse) {
+						outLinear = base;
+					} else {
+						Plane pl = orientedPlaneTowardCamera(t, cam);
+						PlaneKey key = makePlaneKey(pl);
+
+						auto it = mirrorCache.find(key);
+						if (it == mirrorCache.end()) {
+							MirrorCacheEntry entry;
+							entry.plane = pl;
+							entry.mirrorCam = mirrorCameraAcrossPlane(cam, pl);
+
+							// Render mirrored pass, excluding this mirror plane (avoid self)
+							entry.rt = renderPass(entry.mirrorCam, ctx, recursionDepth + 1, &entry.plane);
+							entry.ready = true;
+
+							it = mirrorCache.emplace(key, std::move(entry)).first;
+						}
+
+						const MirrorCacheEntry &entry = it->second;
+
+						Vec2 rxy;
+						float rinvZ, rcamZ;
+						if (entry.ready && entry.mirrorCam.projectToScreen(worldP, rxy, rinvZ, rcamZ)) {
+							float u = rxy.x / (float)entry.rt.color.w;
+							float v = rxy.y / (float)entry.rt.color.h;
+
+							if (u >= 0.0f && u <= 1.0f && v >= 0.0f && v <= 1.0f) {
+								Vec3 sample = entry.rt.color.sampleNearest(u, v);
+								// Ideal mirror: mostly reflection; keep tiny base to avoid "reflection outside screen => black"
+								float baseKeep = 0.08f;
+								outLinear = sample * refl + base * (1.0f - refl);
+								outLinear = outLinear + baseKeep * base;
+							} else {
+								outLinear = base;
+							}
+						} else {
+							outLinear = base;
+						}
+					}
+				}
+
+				rt.color.set(x, y, outLinear);
+			}
+		}
+	}
+
+	return rt;
+}
+
+// --- Scene building helpers ---
+
+static void addQuad(std::vector<Triangle> &tris,
+	const Vec3 &a, const Vec3 &b, const Vec3 &c, const Vec3 &d,
+	const Material &mat,
+	bool ccw = true) {
+	Triangle t1, t2;
+	if (ccw) {
+		t1.p0 = a;
+		t1.p1 = b;
+		t1.p2 = c;
+		t2.p0 = a;
+		t2.p1 = c;
+		t2.p2 = d;
+	} else {
+		t1.p0 = a;
+		t1.p1 = c;
+		t1.p2 = b;
+		t2.p0 = a;
+		t2.p1 = d;
+		t2.p2 = c;
+	}
+	t1.mat = mat;
+	t2.mat = mat;
+	t1.normal = computeFlatNormal(t1);
+	t2.normal = computeFlatNormal(t2);
+	tris.push_back(t1);
+	tris.push_back(t2);
+}
+
+static void addBox(std::vector<Triangle> &tris,
+	const Vec3 &mn, const Vec3 &mx,
+	const Material &mat) {
+	Vec3 p000 { mn.x, mn.y, mn.z };
+	Vec3 p001 { mn.x, mn.y, mx.z };
+	Vec3 p010 { mn.x, mx.y, mn.z };
+	Vec3 p011 { mn.x, mx.y, mx.z };
+	Vec3 p100 { mx.x, mn.y, mn.z };
+	Vec3 p101 { mx.x, mn.y, mx.z };
+	Vec3 p110 { mx.x, mx.y, mn.z };
+	Vec3 p111 { mx.x, mx.y, mx.z };
+
+	addQuad(tris, p000, p001, p011, p010, mat, true); // -X
+	addQuad(tris, p100, p110, p111, p101, mat, true); // +X
+	addQuad(tris, p000, p100, p101, p001, mat, true); // -Y
+	addQuad(tris, p010, p011, p111, p110, mat, true); // +Y
+	addQuad(tris, p000, p010, p110, p100, mat, true); // -Z
+	addQuad(tris, p001, p101, p111, p011, mat, true); // +Z
+}
+
+static std::vector<Triangle> buildCornellBoxScene() {
+	std::vector<Triangle> tris;
+	tris.reserve(256);
+
+	// Room: x in [-1,1], y in [0,2], z in [-1,1]; front is open (no wall at z=+1)
+	float xmin = -1.0f, xmax = 1.0f;
+	float ymin = 0.0f, ymax = 2.0f;
+	float zmin = -1.0f, zmax = 1.0f;
+
+	Material white { MaterialType::Diffuse, { 0.85f, 0.85f, 0.85f }, 0.0f };
+	Material red { MaterialType::Diffuse, { 0.85f, 0.20f, 0.20f }, 0.0f };
+	Material green { MaterialType::Diffuse, { 0.20f, 0.85f, 0.20f }, 0.0f };
+
+	// Floor (y=ymin)
+	addQuad(tris,
+		{ xmin, ymin, zmin }, { xmax, ymin, zmin }, { xmax, ymin, zmax }, { xmin, ymin, zmax },
+		white, true);
+
+	// Ceiling (y=ymax)
+	addQuad(tris,
+		{ xmin, ymax, zmax }, { xmax, ymax, zmax }, { xmax, ymax, zmin }, { xmin, ymax, zmin },
+		white, true);
+
+	// Back wall (z=zmin)
+	addQuad(tris,
+		{ xmin, ymin, zmin }, { xmin, ymax, zmin }, { xmax, ymax, zmin }, { xmax, ymin, zmin },
+		white, true);
+
+	// Left wall (x=xmin)
+	addQuad(tris,
+		{ xmin, ymin, zmax }, { xmin, ymax, zmax }, { xmin, ymax, zmin }, { xmin, ymin, zmin },
+		red, true);
+
+	// Right wall (x=xmax)
+	addQuad(tris,
+		{ xmax, ymin, zmin }, { xmax, ymax, zmin }, { xmax, ymax, zmax }, { xmax, ymin, zmax },
+		green, true);
+
+	// Two metal boxes
+	Material blueMetal { MaterialType::Metal, { 0.10f, 0.20f, 0.95f }, 1.0f };
+	Material yellowMetal { MaterialType::Metal, { 0.95f, 0.85f, 0.10f }, 1.0f };
+
+	addBox(tris,
+		Vec3 { -0.75f, 0.0f, -0.20f },
+		Vec3 { -0.25f, 0.65f, 0.35f },
+		blueMetal);
+
+	addBox(tris,
+		Vec3 { 0.20f, 0.0f, -0.70f },
+		Vec3 { 0.75f, 1.05f, -0.10f },
+		yellowMetal);
+
+	for (auto &t : tris)
+		t.normal = computeFlatNormal(t);
+	return tris;
+}
+
+int main() {
+	const int W = 520;
+	const int H = 520;
+
+	std::vector<Triangle> scene = buildCornellBoxScene();
+
+	// Keep camera outside-ish but close; perspective should be obvious
+	Camera cam = Camera::lookAt(
+		/*eye*/ Vec3 { 0.0f, 1.0f, 2.7f },
+		/*target*/ Vec3 { 0.0f, 1.0f, 0.0f },
+		/*up*/ Vec3 { 0.0f, 1.0f, 0.0f },
+		/*fov*/ 55.0f,
+		/*near*/ 0.05f,
+		/*far*/ 50.0f,
+		/*w,h*/ W, H);
+
+	RenderContext ctx;
+	ctx.tris = &scene;
+
+	ctx.cfg.maxDepth = 2;
+	ctx.cfg.minMirrorAreaPixels = 8.0f;
+	ctx.cfg.clearColor = { 0.0f, 0.0f, 0.0f };
+
+	// Light near ceiling center
+	ctx.lightPos = { 0.0f, 1.95f, -0.1f };
+	ctx.lightColor = { 1.0f, 1.0f, 1.0f };
+	ctx.lightIntensity = 30.0f;
+	ctx.ambient = { 0.06f, 0.06f, 0.06f };
+
+	RenderTarget rt = renderPass(cam, ctx, /*recDepth*/ 0, /*excludePlane*/ nullptr);
+	rt.color.writePPM_P3("output.ppm");
+
+	std::cout << "Wrote output.ppm (" << W << "x" << H << ")\n";
+	std::cout << "Convert if needed:\n";
+	std::cout << "  magick output.ppm output.png\n";
+	return 0;
+}

experiments/rt5.cpp

@@ -0,0 +1,830 @@
+// cornell_patchstep_fixed.cpp
+// g++ -std=c++17 -O2 cornell_patchstep_fixed.cpp -o render && ./render
+// 输出：out.ppm
+//
+// 修复点（对应你的反馈）：
+// - 之前递归时“下一级 viewport 在最终图片中占哪块区域”的信息虽然隐含在 vm.screenUV/clip 中，
+//   但逻辑上不够显式，容易在扩展/改动时导致下级按“全屏”比例写入。
+// - 现在为 renderTriangleWithTriangle / renderViewport 显式增加参数：
+//   `viewportRegion` = 当前 viewport 在最终图片中的屏幕UV三角形(3个二维坐标)。
+// - 所有“投影到屏幕”的计算都通过 viewportRegion 完成；所有写入也强制 clip 在 viewportRegion 内。
+// - 向下递归时，会根据“当前三角形在当前 viewport 上的投影 triScreenUV”计算出下一级 viewportRegion 并传入。
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cmath>
+#include <cstdint>
+#include <fstream>
+#include <iostream>
+#include <limits>
+#include <optional>
+#include <string>
+#include <utility>
+#include <vector>
+
+static constexpr double kEps = 1e-9;
+
+static inline double clamp01(double x) {
+	return x < 0.0 ? 0.0 : (x > 1.0 ? 1.0 : x);
+}
+static inline int clampi(int x, int lo, int hi) {
+	return x < lo ? lo : (x > hi ? hi : x);
+}
+
+struct Vec2 {
+	double x = 0, y = 0;
+	Vec2() = default;
+	Vec2(double xx, double yy) : x(xx), y(yy) {
+	}
+	Vec2 operator+(const Vec2 &o) const {
+		return Vec2 { x + o.x, y + o.y };
+	}
+	Vec2 operator-(const Vec2 &o) const {
+		return Vec2 { x - o.x, y - o.y };
+	}
+	Vec2 operator*(double s) const {
+		return Vec2 { x * s, y * s };
+	}
+};
+
+static inline double dot(const Vec2 &a, const Vec2 &b) {
+	return a.x * b.x + a.y * b.y;
+}
+static inline double cross2(const Vec2 &a, const Vec2 &b) {
+	return a.x * b.y - a.y * b.x;
+}
+
+struct Vec3 {
+	double x = 0, y = 0, z = 0;
+	Vec3() = default;
+	Vec3(double xx, double yy, double zz) : x(xx), y(yy), z(zz) {
+	}
+	Vec3 operator+(const Vec3 &o) const {
+		return Vec3 { x + o.x, y + o.y, z + o.z };
+	}
+	Vec3 operator-(const Vec3 &o) const {
+		return Vec3 { x - o.x, y - o.y, z - o.z };
+	}
+	Vec3 operator*(double s) const {
+		return Vec3 { x * s, y * s, z * s };
+	}
+	Vec3 operator/(double s) const {
+		return Vec3 { x / s, y / s, z / s };
+	}
+};
+
+static inline Vec3 operator*(double s, const Vec3 &v) {
+	return v * s;
+}
+static inline double dot(const Vec3 &a, const Vec3 &b) {
+	return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+static inline Vec3 cross(const Vec3 &a, const Vec3 &b) {
+	return Vec3 {
+		a.y * b.z - a.z * b.y,
+		a.z * b.x - a.x * b.z,
+		a.x * b.y - a.y * b.x,
+	};
+}
+static inline double length(const Vec3 &v) {
+	return std::sqrt(dot(v, v));
+}
+static inline Vec3 normalize(const Vec3 &v) {
+	double len = length(v);
+	if (len < kEps)
+		return Vec3 { 0, 0, 0 };
+	return v / len;
+}
+
+struct Plane {
+	Vec3 n; // unit normal
+	double d; // n·x + d = 0
+};
+
+static inline Plane planeFromTriangle(const Vec3 &a, const Vec3 &b, const Vec3 &c) {
+	Vec3 n = normalize(cross(b - a, c - a));
+	double d = -dot(n, a);
+	return Plane { n, d };
+}
+
+static inline double planeSignedDistance(const Plane &p, const Vec3 &x) {
+	return dot(p.n, x) + p.d;
+}
+
+static inline Vec3 reflectPointAcrossPlane(const Vec3 &point, const Plane &p) {
+	double dist = planeSignedDistance(p, point);
+	return point - 2.0 * dist * p.n;
+}
+
+struct Basis2DOnPlane {
+	Vec3 origin;
+	Vec3 ux;
+	Vec3 uy;
+	Vec3 n;
+};
+
+static inline Basis2DOnPlane makePlaneBasis(const Vec3 &a, const Vec3 &b, const Vec3 &c) {
+	Vec3 n = normalize(cross(b - a, c - a));
+	Vec3 ux = normalize(b - a);
+	Vec3 uy = normalize(cross(n, ux));
+	return Basis2DOnPlane { a, ux, uy, n };
+}
+
+static inline Vec2 to2D(const Basis2DOnPlane &basis, const Vec3 &p) {
+	Vec3 v = p - basis.origin;
+	return Vec2 { dot(v, basis.ux), dot(v, basis.uy) };
+}
+
+static inline Vec3 barycentric2D(const Vec2 &p, const Vec2 &a, const Vec2 &b, const Vec2 &c) {
+	Vec2 v0 = b - a;
+	Vec2 v1 = c - a;
+	Vec2 v2 = p - a;
+	double den = cross2(v0, v1);
+	if (std::fabs(den) < kEps)
+		return Vec3 { -1, -1, -1 };
+	double v = cross2(v2, v1) / den;
+	double w = cross2(v0, v2) / den;
+	double u = 1.0 - v - w;
+	return Vec3 { u, v, w };
+}
+
+static inline bool pointInTri2D(const Vec2 &p, const Vec2 &a, const Vec2 &b, const Vec2 &c) {
+	Vec3 bc = barycentric2D(p, a, b, c);
+	return bc.x >= -1e-12 && bc.y >= -1e-12 && bc.z >= -1e-12;
+}
+
+static inline bool segIntersect2D(const Vec2 &a, const Vec2 &b, const Vec2 &c, const Vec2 &d) {
+	auto orient = [](const Vec2 &p, const Vec2 &q, const Vec2 &r) {
+		return cross2(q - p, r - p);
+	};
+	double o1 = orient(a, b, c);
+	double o2 = orient(a, b, d);
+	double o3 = orient(c, d, a);
+	double o4 = orient(c, d, b);
+
+	auto onSeg = [](const Vec2 &p, const Vec2 &q, const Vec2 &r) {
+		return std::min(p.x, r.x) - 1e-12 <= q.x && q.x <= std::max(p.x, r.x) + 1e-12 && std::min(p.y, r.y) - 1e-12 <= q.y && q.y <= std::max(p.y, r.y) + 1e-12;
+	};
+
+	if ((o1 * o2 < 0) && (o3 * o4 < 0))
+		return true;
+	if (std::fabs(o1) < 1e-12 && onSeg(a, c, b))
+		return true;
+	if (std::fabs(o2) < 1e-12 && onSeg(a, d, b))
+		return true;
+	if (std::fabs(o3) < 1e-12 && onSeg(c, a, d))
+		return true;
+	if (std::fabs(o4) < 1e-12 && onSeg(c, b, d))
+		return true;
+	return false;
+}
+
+static inline bool triOverlap2D(const std::array<Vec2, 3> &t0, const std::array<Vec2, 3> &t1) {
+	for (int i = 0; i < 3; i++) {
+		if (pointInTri2D(t0[i], t1[0], t1[1], t1[2]))
+			return true;
+		if (pointInTri2D(t1[i], t0[0], t0[1], t0[2]))
+			return true;
+	}
+	for (int i = 0; i < 3; i++) {
+		Vec2 a0 = t0[i], b0 = t0[(i + 1) % 3];
+		for (int j = 0; j < 3; j++) {
+			Vec2 a1 = t1[j], b1 = t1[(j + 1) % 3];
+			if (segIntersect2D(a0, b0, a1, b1))
+				return true;
+		}
+	}
+	return false;
+}
+
+// 3D 三角形相交（满足你“Triangle类及相关运算”的要求；渲染主流程不依赖它）
+static inline void triAABB(const Vec3 &a, const Vec3 &b, const Vec3 &c, Vec3 &mn, Vec3 &mx) {
+	mn = Vec3 { std::min({ a.x, b.x, c.x }), std::min({ a.y, b.y, c.y }), std::min({ a.z, b.z, c.z }) };
+	mx = Vec3 { std::max({ a.x, b.x, c.x }), std::max({ a.y, b.y, c.y }), std::max({ a.z, b.z, c.z }) };
+}
+
+static inline bool aabbOverlap(const Vec3 &mn0, const Vec3 &mx0, const Vec3 &mn1, const Vec3 &mx1) {
+	return (mn0.x <= mx1.x + 1e-12 && mx0.x + 1e-12 >= mn1.x) && (mn0.y <= mx1.y + 1e-12 && mx0.y + 1e-12 >= mn1.y) && (mn0.z <= mx1.z + 1e-12 && mx0.z + 1e-12 >= mn1.z);
+}
+
+static inline bool segmentTriangleIntersect(const Vec3 &p0, const Vec3 &p1,
+	const Vec3 &a, const Vec3 &b, const Vec3 &c,
+	double &tOut) {
+	Vec3 dir = p1 - p0;
+	Vec3 e1 = b - a;
+	Vec3 e2 = c - a;
+	Vec3 pvec = cross(dir, e2);
+	double det = dot(e1, pvec);
+	if (std::fabs(det) < 1e-12)
+		return false;
+	double invDet = 1.0 / det;
+
+	Vec3 tvec = p0 - a;
+	double u = dot(tvec, pvec) * invDet;
+	if (u < -1e-12 || u > 1.0 + 1e-12)
+		return false;
+
+	Vec3 qvec = cross(tvec, e1);
+	double v = dot(dir, qvec) * invDet;
+	if (v < -1e-12 || u + v > 1.0 + 1e-12)
+		return false;
+
+	double t = dot(e2, qvec) * invDet;
+	if (t < -1e-12 || t > 1.0 + 1e-12)
+		return false;
+	tOut = t;
+	return true;
+}
+
+static inline bool pointInTriangle3D(const Vec3 &p, const Vec3 &a, const Vec3 &b, const Vec3 &c) {
+	Vec3 n = cross(b - a, c - a);
+	Vec3 n0 = cross(b - a, p - a);
+	Vec3 n1 = cross(c - b, p - b);
+	Vec3 n2 = cross(a - c, p - c);
+	if (dot(n, n0) < -1e-12)
+		return false;
+	if (dot(n, n1) < -1e-12)
+		return false;
+	if (dot(n, n2) < -1e-12)
+		return false;
+	return true;
+}
+
+static inline bool triTriIntersect3D(const Vec3 &a0, const Vec3 &b0, const Vec3 &c0,
+	const Vec3 &a1, const Vec3 &b1, const Vec3 &c1) {
+	Vec3 mn0, mx0, mn1, mx1;
+	triAABB(a0, b0, c0, mn0, mx0);
+	triAABB(a1, b1, c1, mn1, mx1);
+	if (!aabbOverlap(mn0, mx0, mn1, mx1))
+		return false;
+
+	Plane p0 = planeFromTriangle(a0, b0, c0);
+	Plane p1 = planeFromTriangle(a1, b1, c1);
+
+	if (std::fabs(dot(p0.n, p1.n)) > 1.0 - 1e-7 && std::fabs(planeSignedDistance(p0, a1)) < 1e-7) {
+		Vec3 nn = p0.n;
+		int drop = 0;
+		double ax = std::fabs(nn.x), ay = std::fabs(nn.y), az = std::fabs(nn.z);
+		if (ay > ax && ay > az)
+			drop = 1;
+		else if (az > ax && az > ay)
+			drop = 2;
+
+		auto proj = [&](const Vec3 &v) -> Vec2 {
+			if (drop == 0)
+				return Vec2 { v.y, v.z };
+			if (drop == 1)
+				return Vec2 { v.x, v.z };
+			return Vec2 { v.x, v.y };
+		};
+
+		std::array<Vec2, 3> t0 { proj(a0), proj(b0), proj(c0) };
+		std::array<Vec2, 3> t1 { proj(a1), proj(b1), proj(c1) };
+		return triOverlap2D(t0, t1);
+	}
+
+	const Vec3 t0v[3] = { a0, b0, c0 };
+	const Vec3 t1v[3] = { a1, b1, c1 };
+	for (int i = 0; i < 3; i++) {
+		double t = 0;
+		if (segmentTriangleIntersect(t0v[i], t0v[(i + 1) % 3], a1, b1, c1, t))
+			return true;
+		if (segmentTriangleIntersect(t1v[i], t1v[(i + 1) % 3], a0, b0, c0, t))
+			return true;
+	}
+
+	if (pointInTriangle3D(a0, a1, b1, c1))
+		return true;
+	if (pointInTriangle3D(a1, a0, b0, c0))
+		return true;
+	return false;
+}
+
+struct Image {
+	int w = 0, h = 0;
+	std::vector<Vec3> pix;
+
+	Image(int ww, int hh) : w(ww), h(hh), pix((size_t)ww * (size_t)hh, Vec3 { 0, 0, 0 }) {
+	}
+
+	void blendOver(int x, int y, const Vec3 &src, double alpha) {
+		if (x < 0 || x >= w || y < 0 || y >= h)
+			return;
+		alpha = clamp01(alpha);
+		Vec3 dst = pix[(size_t)y * (size_t)w + (size_t)x];
+		Vec3 out = dst * (1.0 - alpha) + src * alpha;
+		pix[(size_t)y * (size_t)w + (size_t)x] = out;
+	}
+
+	void add(int x, int y, const Vec3 &src) {
+		if (x < 0 || x >= w || y < 0 || y >= h)
+			return;
+		Vec3 dst = pix[(size_t)y * (size_t)w + (size_t)x];
+		pix[(size_t)y * (size_t)w + (size_t)x] = Vec3 { dst.x + src.x, dst.y + src.y, dst.z + src.z };
+	}
+
+	void writePPM(const std::string &path) const {
+		std::ofstream out(path, std::ios::binary);
+		if (!out) {
+			std::cerr << "Failed to open output file: " << path << "\n";
+			return;
+		}
+		out << "P6\n"
+			<< w << " " << h << "\n255\n";
+		for (int y = 0; y < h; y++) {
+			for (int x = 0; x < w; x++) {
+				Vec3 c = pix[(size_t)y * (size_t)w + (size_t)x];
+				c.x = clamp01(c.x);
+				c.y = clamp01(c.y);
+				c.z = clamp01(c.z);
+				auto toByte = [](double v) -> unsigned char {
+					v = std::pow(clamp01(v), 1.0 / 2.2);
+					int iv = (int)std::lround(v * 255.0);
+					return (unsigned char)clampi(iv, 0, 255);
+				};
+				unsigned char rgb[3] = { toByte(c.x), toByte(c.y), toByte(c.z) };
+				out.write((char *)rgb, 3);
+			}
+		}
+	}
+};
+
+enum class MaterialType {
+	Curtain,
+	Diffuse,
+	Metal
+};
+
+struct Triangle {
+	int id = -1;
+	std::string name;
+
+	Vec3 p[3];
+	Vec2 uv[3];
+
+	MaterialType mat = MaterialType::Diffuse;
+	Vec3 baseColor { 1, 1, 1 };
+
+	Vec3 normal() const {
+		return normalize(cross(p[1] - p[0], p[2] - p[0]));
+	}
+	Vec3 centroid() const {
+		return (p[0] + p[1] + p[2]) / 3.0;
+	}
+};
+
+struct ProjectedVertex {
+	bool ok = false;
+	Vec3 onPlane;
+	double t = 0.0;
+};
+
+static inline ProjectedVertex projectPointToPlaneAlongOrigin(const Vec3 &origin, const Vec3 &v, const Plane &plane) {
+	Vec3 dir = v - origin;
+	double denom = dot(plane.n, dir);
+	if (std::fabs(denom) < 1e-12)
+		return ProjectedVertex { false, Vec3 {}, 0 };
+	double t = -(dot(plane.n, origin) + plane.d) / denom;
+	if (t <= 1e-9)
+		return ProjectedVertex { false, Vec3 {}, t };
+	Vec3 p = origin + dir * t;
+	return ProjectedVertex { true, p, t };
+}
+
+// 显式的“当前 viewport 在最终图片中的范围”
+// 用屏幕UV三角形表达（更贴合你描述的“两个三角形幕布”与递归中“面片->面片”的映射）
+using ScreenTri = std::array<Vec2, 3>;
+
+static inline bool pointInScreenTri(const ScreenTri &tri, const Vec2 &uv) {
+	return pointInTri2D(uv, tri[0], tri[1], tri[2]);
+}
+
+static inline Vec2 uvFromPixelCenter(int x, int y, int w, int h) {
+	double u = ((double)x + 0.5) / (double)w;
+	double v = 1.0 - (((double)y + 0.5) / (double)h);
+	return Vec2 { u, v };
+}
+
+static inline std::array<Vec2, 3> projectedTriangleToViewport2D(const Basis2DOnPlane &basis,
+	const std::array<Vec3, 3> &proj) {
+	return { to2D(basis, proj[0]), to2D(basis, proj[1]), to2D(basis, proj[2]) };
+}
+
+static inline std::array<Vec2, 3> viewportTriangleTo2D(const Basis2DOnPlane &basis, const Triangle &viewport) {
+	return {
+		to2D(basis, viewport.p[0]),
+		to2D(basis, viewport.p[1]),
+		to2D(basis, viewport.p[2]),
+	};
+}
+
+static inline bool projectTriangleToViewport(const Triangle &tri,
+	const Vec3 &origin,
+	const Triangle &viewport,
+	const Basis2DOnPlane &viewportBasis,
+	const ScreenTri &viewportRegion,
+	std::array<Vec3, 3> &projOnViewportPlane,
+	ScreenTri &triScreenUV) {
+	Plane plane = planeFromTriangle(viewport.p[0], viewport.p[1], viewport.p[2]);
+
+	ProjectedVertex pv[3];
+	for (int i = 0; i < 3; i++) {
+		pv[i] = projectPointToPlaneAlongOrigin(origin, tri.p[i], plane);
+		if (!pv[i].ok)
+			return false;
+		projOnViewportPlane[i] = pv[i].onPlane;
+	}
+
+	auto proj2D = projectedTriangleToViewport2D(viewportBasis, projOnViewportPlane);
+	auto vp2D = viewportTriangleTo2D(viewportBasis, viewport);
+	if (!triOverlap2D(proj2D, vp2D))
+		return false;
+
+	// 用 viewport 顶点 <-> viewportRegion 的三点对应，建立“viewport平面 -> 屏幕UV”的仿射映射
+	Vec2 A2 = vp2D[0], B2 = vp2D[1], C2 = vp2D[2];
+	for (int i = 0; i < 3; i++) {
+		Vec3 bc = barycentric2D(proj2D[i], A2, B2, C2);
+		Vec2 uv = viewportRegion[0] * bc.x + viewportRegion[1] * bc.y + viewportRegion[2] * bc.z;
+		triScreenUV[i] = uv;
+	}
+	return true;
+}
+
+static inline double triAreaPixels(const ScreenTri &screenUV, int w, int h) {
+	Vec2 a = Vec2 { screenUV[0].x * w, screenUV[0].y * h };
+	Vec2 b = Vec2 { screenUV[1].x * w, screenUV[1].y * h };
+	Vec2 c = Vec2 { screenUV[2].x * w, screenUV[2].y * h };
+	double area2 = std::fabs(cross2(b - a, c - a));
+	return area2 * 0.5;
+}
+
+static inline Vec3 sampleProceduralTexture(const Triangle &tri, const Vec2 &uv) {
+	double u = uv.x, v = uv.y;
+	double s = 10.0;
+	int iu = (int)std::floor(u * s);
+	int iv = (int)std::floor(v * s);
+	bool checker = ((iu + iv) & 1) == 0;
+
+	Vec3 base = tri.baseColor;
+	if (tri.mat == MaterialType::Metal) {
+		double stripe = 0.6 + 0.4 * std::sin((u * 40.0 + v * 15.0) * 3.14159);
+		base = base * stripe;
+	} else {
+		double k = checker ? 1.0 : 0.85;
+		base = base * k;
+	}
+	return base;
+}
+
+static inline Vec3 shadeLambert(const Vec3 &color, const Vec3 &n) {
+	Vec3 lightDir = normalize(Vec3 { -0.35, 0.85, 0.25 });
+	double ndl = std::max(0.0, dot(n, lightDir));
+	double amb = 0.20;
+	double diff = 0.90 * ndl;
+	return color * (amb + diff);
+}
+
+static inline void rasterizeTriangleToImage(Image &img,
+	const ScreenTri &triScreenUV,
+	const Triangle &tri,
+	const ScreenTri &viewportRegion,
+	const Vec3 &throughput,
+	double alpha,
+	bool additive) {
+	// 强制只写入 viewportRegion 覆盖的屏幕区域
+	// triScreenUV 是“当前 tri 投影到当前 viewport 后，再映射到最终屏幕”的三角形
+
+	double minU = std::min({ triScreenUV[0].x, triScreenUV[1].x, triScreenUV[2].x });
+	double maxU = std::max({ triScreenUV[0].x, triScreenUV[1].x, triScreenUV[2].x });
+	double minV = std::min({ triScreenUV[0].y, triScreenUV[1].y, triScreenUV[2].y });
+	double maxV = std::max({ triScreenUV[0].y, triScreenUV[1].y, triScreenUV[2].y });
+
+	int x0 = clampi((int)std::floor(minU * img.w) - 1, 0, img.w - 1);
+	int x1 = clampi((int)std::ceil(maxU * img.w) + 1, 0, img.w - 1);
+	int y0 = clampi((int)std::floor((1.0 - maxV) * img.h) - 1, 0, img.h - 1);
+	int y1 = clampi((int)std::ceil((1.0 - minV) * img.h) + 1, 0, img.h - 1);
+
+	Vec2 a = triScreenUV[0], b = triScreenUV[1], c = triScreenUV[2];
+	Vec3 n = tri.normal();
+
+	for (int y = y0; y <= y1; y++) {
+		for (int x = x0; x <= x1; x++) {
+			Vec2 suv = uvFromPixelCenter(x, y, img.w, img.h);
+
+			// 关键：限制写入区域为当前 viewportRegion
+			if (!pointInScreenTri(viewportRegion, suv))
+				continue;
+
+			Vec3 bc = barycentric2D(suv, a, b, c);
+			if (bc.x < -1e-12 || bc.y < -1e-12 || bc.z < -1e-12)
+				continue;
+
+			Vec2 uv = tri.uv[0] * bc.x + tri.uv[1] * bc.y + tri.uv[2] * bc.z;
+
+			Vec3 tex = sampleProceduralTexture(tri, uv);
+			Vec3 lit = shadeLambert(tex, n);
+			Vec3 src = Vec3 { lit.x * throughput.x, lit.y * throughput.y, lit.z * throughput.z };
+
+			if (additive)
+				img.add(x, y, src * alpha);
+			else
+				img.blendOver(x, y, src, alpha);
+		}
+	}
+}
+
+struct RenderConfig {
+	int maxDepth = 3;
+	double minAreaPixels = 3.0;
+};
+
+static void renderViewport(const std::vector<Triangle> &scene,
+	const Vec3 &origin,
+	const Triangle &viewport,
+	const Basis2DOnPlane &viewportBasis,
+	const ScreenTri &viewportRegion,
+	Image &out,
+	const RenderConfig &cfg,
+	int depth,
+	const Vec3 &throughput,
+	int excludeId);
+
+static inline double fresnelSchlick(double cosTheta, double f0) {
+	cosTheta = clamp01(cosTheta);
+	return f0 + (1.0 - f0) * std::pow(1.0 - cosTheta, 5.0);
+}
+
+static void renderTriangleWithTriangle(const std::vector<Triangle> &scene,
+	const Vec3 &origin,
+	const Triangle &viewport,
+	const Basis2DOnPlane &viewportBasis,
+	const ScreenTri &viewportRegion,
+	const Triangle &tri,
+	Image &out,
+	const RenderConfig &cfg,
+	int depth,
+	const Vec3 &throughput,
+	int excludeId) {
+	if (tri.id == excludeId)
+		return;
+	if (tri.mat == MaterialType::Curtain)
+		return;
+
+	std::array<Vec3, 3> projOnPlane {};
+	ScreenTri triScreenUV {};
+	if (!projectTriangleToViewport(tri, origin, viewport, viewportBasis, viewportRegion, projOnPlane, triScreenUV))
+		return;
+
+	double areaPix = triAreaPixels(triScreenUV, out.w, out.h);
+	if (areaPix < 0.25)
+		return;
+
+	if (tri.mat == MaterialType::Diffuse) {
+		// 漫反射：直接贴到最终屏幕，但写入范围必须受 viewportRegion 限制（已在 rasterize 内处理）
+		rasterizeTriangleToImage(out, triScreenUV, tri, viewportRegion, throughput, 1.0, false);
+		return;
+	}
+
+	if (tri.mat == MaterialType::Metal) {
+		// 金属：先贴自身底色，再递归把反射结果“写到它在最终屏幕上的 triScreenUV 区域里”
+		Vec3 n = tri.normal();
+		Vec3 viewDir = normalize(origin - tri.centroid());
+		double cosTheta = std::fabs(dot(n, viewDir));
+		double reflectK = 0.75;
+		double f0 = 0.90;
+		double F = fresnelSchlick(cosTheta, f0);
+		double refl = clamp01(reflectK * F);
+
+		rasterizeTriangleToImage(out, triScreenUV, tri, viewportRegion, throughput, 1.0, false);
+
+		if (depth >= cfg.maxDepth)
+			return;
+		if (areaPix < cfg.minAreaPixels)
+			return;
+
+		Plane triPlane = planeFromTriangle(tri.p[0], tri.p[1], tri.p[2]);
+		Vec3 reflectedOrigin = reflectPointAcrossPlane(origin, triPlane);
+
+		// 关键：下一级 viewport 就是 tri（世界空间），而它在最终图片中的区域就是 triScreenUV
+		const Triangle &childViewport = tri;
+		Basis2DOnPlane childBasis = makePlaneBasis(childViewport.p[0], childViewport.p[1], childViewport.p[2]);
+		ScreenTri childRegion = triScreenUV;
+
+		Vec3 throughputChild = Vec3 { throughput.x * refl, throughput.y * refl, throughput.z * refl };
+
+		renderViewport(scene, reflectedOrigin, childViewport, childBasis, childRegion, out, cfg, depth + 1, throughputChild, tri.id);
+		return;
+	}
+}
+
+static void renderViewport(const std::vector<Triangle> &scene,
+	const Vec3 &origin,
+	const Triangle &viewport,
+	const Basis2DOnPlane &viewportBasis,
+	const ScreenTri &viewportRegion,
+	Image &out,
+	const RenderConfig &cfg,
+	int depth,
+	const Vec3 &throughput,
+	int excludeId) {
+	struct Cand {
+		const Triangle *t;
+		double dist2;
+	};
+	std::vector<Cand> cands;
+	cands.reserve(scene.size());
+
+	for (const Triangle &tri : scene) {
+		if (tri.id == excludeId)
+			continue;
+		if (tri.mat == MaterialType::Curtain)
+			continue;
+
+		std::array<Vec3, 3> projOnPlane {};
+		ScreenTri triScreenUV {};
+		if (!projectTriangleToViewport(tri, origin, viewport, viewportBasis, viewportRegion, projOnPlane, triScreenUV))
+			continue;
+
+		Vec3 c = tri.centroid();
+		Vec3 d = c - origin;
+		double dist2 = dot(d, d);
+		cands.push_back(Cand { &tri, dist2 });
+	}
+
+	std::sort(cands.begin(), cands.end(), [](const Cand &a, const Cand &b) {
+		return a.dist2 > b.dist2;
+	});
+
+	for (const Cand &c : cands) {
+		renderTriangleWithTriangle(scene, origin, viewport, viewportBasis, viewportRegion, *c.t, out, cfg, depth, throughput, excludeId);
+	}
+}
+
+struct Camera {
+	Vec3 origin;
+	Triangle curtainA;
+	Triangle curtainB;
+
+	void render(const std::vector<Triangle> &scene, Image &out) const {
+		RenderConfig cfg;
+		cfg.maxDepth = 3;
+		cfg.minAreaPixels = 3.0;
+
+		// Curtain A：viewportRegion 就是它本身的 uv（三角形覆盖屏幕的一半）
+		{
+			const Triangle &viewport = curtainA;
+			Basis2DOnPlane basis = makePlaneBasis(viewport.p[0], viewport.p[1], viewport.p[2]);
+			ScreenTri region = { viewport.uv[0], viewport.uv[1], viewport.uv[2] };
+			renderViewport(scene, origin, viewport, basis, region, out, cfg, 0, Vec3 { 1, 1, 1 }, -1);
+		}
+
+		// Curtain B
+		{
+			const Triangle &viewport = curtainB;
+			Basis2DOnPlane basis = makePlaneBasis(viewport.p[0], viewport.p[1], viewport.p[2]);
+			ScreenTri region = { viewport.uv[0], viewport.uv[1], viewport.uv[2] };
+			renderViewport(scene, origin, viewport, basis, region, out, cfg, 0, Vec3 { 1, 1, 1 }, -1);
+		}
+	}
+};
+
+static inline Triangle makeTri(int id, const std::string &name,
+	const Vec3 &a, const Vec3 &b, const Vec3 &c,
+	const Vec2 &ua, const Vec2 &ub, const Vec2 &uc,
+	MaterialType mat, const Vec3 &color) {
+	Triangle t;
+	t.id = id;
+	t.name = name;
+	t.p[0] = a;
+	t.p[1] = b;
+	t.p[2] = c;
+	t.uv[0] = ua;
+	t.uv[1] = ub;
+	t.uv[2] = uc;
+	t.mat = mat;
+	t.baseColor = color;
+	return t;
+}
+
+static inline void addQuad(std::vector<Triangle> &out, int &nextId, const std::string &name,
+	const Vec3 &a, const Vec3 &b, const Vec3 &c, const Vec3 &d,
+	const Vec2 &ua, const Vec2 &ub, const Vec2 &uc, const Vec2 &ud,
+	MaterialType mat, const Vec3 &color) {
+	out.push_back(makeTri(nextId++, name + "_t0", a, b, c, ua, ub, uc, mat, color));
+	out.push_back(makeTri(nextId++, name + "_t1", a, c, d, ua, uc, ud, mat, color));
+}
+
+static inline void addBox(std::vector<Triangle> &out, int &nextId, const std::string &name,
+	const Vec3 &mn, const Vec3 &mx,
+	MaterialType mat, const Vec3 &color) {
+	Vec3 p000 { mn.x, mn.y, mn.z };
+	Vec3 p001 { mn.x, mn.y, mx.z };
+	Vec3 p010 { mn.x, mx.y, mn.z };
+	Vec3 p011 { mn.x, mx.y, mx.z };
+	Vec3 p100 { mx.x, mn.y, mn.z };
+	Vec3 p101 { mx.x, mn.y, mx.z };
+	Vec3 p110 { mx.x, mx.y, mn.z };
+	Vec3 p111 { mx.x, mx.y, mx.z };
+
+	Vec2 uv00 { 0, 0 }, uv10 { 1, 0 }, uv11 { 1, 1 }, uv01 { 0, 1 };
+
+	addQuad(out, nextId, name + "_front", p001, p101, p111, p011, uv00, uv10, uv11, uv01, mat, color);
+	addQuad(out, nextId, name + "_back", p100, p000, p010, p110, uv00, uv10, uv11, uv01, mat, color);
+	addQuad(out, nextId, name + "_left", p000, p001, p011, p010, uv00, uv10, uv11, uv01, mat, color);
+	addQuad(out, nextId, name + "_right", p101, p100, p110, p111, uv00, uv10, uv11, uv01, mat, color);
+	addQuad(out, nextId, name + "_top", p010, p011, p111, p110, uv00, uv10, uv11, uv01, mat, color);
+	addQuad(out, nextId, name + "_bottom", p000, p100, p101, p001, uv00, uv10, uv11, uv01, mat, color);
+}
+
+static std::vector<Triangle> buildCornellScene() {
+	std::vector<Triangle> scene;
+	int nextId = 0;
+
+	Vec3 mn { -1, -1, 0 };
+	Vec3 mx { 1, 1, 2 };
+
+	Vec2 uv00 { 0, 0 }, uv10 { 1, 0 }, uv11 { 1, 1 }, uv01 { 0, 1 };
+
+	addQuad(scene, nextId, "wall_back",
+		Vec3 { mn.x, mn.y, mn.z }, Vec3 { mx.x, mn.y, mn.z }, Vec3 { mx.x, mx.y, mn.z }, Vec3 { mn.x, mx.y, mn.z },
+		uv00, uv10, uv11, uv01, MaterialType::Diffuse, Vec3 { 0.95, 0.95, 0.95 });
+
+	addQuad(scene, nextId, "wall_left",
+		Vec3 { mn.x, mn.y, mx.z }, Vec3 { mn.x, mn.y, mn.z }, Vec3 { mn.x, mx.y, mn.z }, Vec3 { mn.x, mx.y, mx.z },
+		uv00, uv10, uv11, uv01, MaterialType::Diffuse, Vec3 { 0.90, 0.25, 0.25 });
+
+	addQuad(scene, nextId, "wall_right",
+		Vec3 { mx.x, mn.y, mn.z }, Vec3 { mx.x, mn.y, mx.z }, Vec3 { mx.x, mx.y, mx.z }, Vec3 { mx.x, mx.y, mn.z },
+		uv00, uv10, uv11, uv01, MaterialType::Diffuse, Vec3 { 0.25, 0.90, 0.25 });
+
+	addQuad(scene, nextId, "floor",
+		Vec3 { mn.x, mn.y, mx.z }, Vec3 { mx.x, mn.y, mx.z }, Vec3 { mx.x, mn.y, mn.z }, Vec3 { mn.x, mn.y, mn.z },
+		uv00, uv10, uv11, uv01, MaterialType::Diffuse, Vec3 { 0.95, 0.95, 0.95 });
+
+	addQuad(scene, nextId, "ceiling",
+		Vec3 { mn.x, mx.y, mn.z }, Vec3 { mx.x, mx.y, mn.z }, Vec3 { mx.x, mx.y, mx.z }, Vec3 { mn.x, mx.y, mx.z },
+		uv00, uv10, uv11, uv01, MaterialType::Diffuse, Vec3 { 0.95, 0.95, 0.95 });
+
+	// 蓝金属盒
+	{
+		Vec3 bmn { -0.75, -1.0, 0.75 };
+		Vec3 bmx { -0.15, -0.40, 1.35 };
+		addBox(scene, nextId, "box_blue_metal", bmn, bmx, MaterialType::Metal, Vec3 { 0.20, 0.40, 0.95 });
+	}
+
+	// 黄金属盒
+	{
+		Vec3 ymn { 0.15, -1.0, 1.10 };
+		Vec3 ymx { 0.70, -0.20, 1.70 };
+		addBox(scene, nextId, "box_yellow_metal", ymn, ymx, MaterialType::Metal, Vec3 { 0.95, 0.85, 0.20 });
+	}
+
+	// 小漫反射柱（辅助反射观感）
+	{
+		Vec3 dmn { -0.10, -1.0, 1.55 };
+		Vec3 dmx { 0.10, -0.70, 1.75 };
+		addBox(scene, nextId, "diffuse_pillar", dmn, dmx, MaterialType::Diffuse, Vec3 { 0.85, 0.85, 0.90 });
+	}
+
+	return scene;
+}
+
+int main() {
+	const int W = 800;
+	const int H = 800;
+
+	Image img(W, H);
+
+	Camera cam;
+	cam.origin = Vec3 { 0.0, 0.0, 3.0 };
+
+	// Curtain（两个三角形）
+	Vec3 s0 { -1.1, -1.1, 2.5 };
+	Vec3 s1 { 1.1, -1.1, 2.5 };
+	Vec3 s2 { 1.1, 1.1, 2.5 };
+	Vec3 s3 { -1.1, 1.1, 2.5 };
+
+	cam.curtainA = makeTri(-100, "curtainA",
+		s0, s1, s2,
+		Vec2 { 0, 0 }, Vec2 { 1, 0 }, Vec2 { 1, 1 },
+		MaterialType::Curtain, Vec3 { 0, 0, 0 });
+	cam.curtainB = makeTri(-101, "curtainB",
+		s0, s2, s3,
+		Vec2 { 0, 0 }, Vec2 { 1, 1 }, Vec2 { 0, 1 },
+		MaterialType::Curtain, Vec3 { 0, 0, 0 });
+
+	auto scene = buildCornellScene();
+
+	// 只是证明 tri-tri 相交存在，不影响渲染
+	if (scene.size() >= 2) {
+		(void)triTriIntersect3D(scene[0].p[0], scene[0].p[1], scene[0].p[2],
+			scene[1].p[0], scene[1].p[1], scene[1].p[2]);
+	}
+
+	cam.render(scene, img);
+	img.writePPM("out.ppm");
+
+	std::cout << "Wrote out.ppm (" << W << "x" << H << ")\n";
+	return 0;
+}

experiments/rt6.cpp

@@ -0,0 +1,918 @@
+// main.cpp
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cmath>
+#include <cstdint>
+#include <fstream>
+#include <iostream>
+#include <limits>
+#include <optional>
+#include <string>
+#include <utility>
+#include <vector>
+
+static constexpr double kEps = 1e-9;
+
+struct Vec2 {
+  double x = 0, y = 0;
+  Vec2() = default;
+  Vec2(double x_, double y_) : x(x_), y(y_) {}
+  Vec2 operator+(const Vec2& o) const { return {x + o.x, y + o.y}; }
+  Vec2 operator-(const Vec2& o) const { return {x - o.x, y - o.y}; }
+  Vec2 operator*(double s) const { return {x * s, y * s}; }
+};
+
+static inline double cross2(const Vec2& a, const Vec2& b) { return a.x * b.y - a.y * b.x; }
+
+struct Vec3 {
+  double x = 0, y = 0, z = 0;
+  Vec3() = default;
+  Vec3(double x_, double y_, double z_) : x(x_), y(y_), z(z_) {}
+  Vec3 operator+(const Vec3& o) const { return {x + o.x, y + o.y, z + o.z}; }
+  Vec3 operator-(const Vec3& o) const { return {x - o.x, y - o.y, z - o.z}; }
+  Vec3 operator*(double s) const { return {x * s, y * s, z * s}; }
+  Vec3 operator/(double s) const { return {x / s, y / s, z / s}; }
+};
+
+static inline double dot(const Vec3& a, const Vec3& b) { return a.x * b.x + a.y * b.y + a.z * b.z; }
+
+static inline Vec3 cross(const Vec3& a, const Vec3& b) {
+  return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x};
+}
+
+static inline double norm2(const Vec3& v) { return dot(v, v); }
+static inline double norm(const Vec3& v) { return std::sqrt(norm2(v)); }
+
+static inline Vec3 normalize(const Vec3& v) {
+  const double n = norm(v);
+  if (n < kEps) return v;
+  return v / n;
+}
+
+struct Color {
+  double r = 0, g = 0, b = 0;
+  Color() = default;
+  Color(double r_, double g_, double b_) : r(r_), g(g_), b(b_) {}
+  Color operator+(const Color& o) const { return {r + o.r, g + o.g, b + o.b}; }
+  Color operator*(double s) const { return {r * s, g * s, b * s}; }
+  Color operator*(const Color& o) const { return {r * o.r, g * o.g, b * o.b}; }
+};
+
+static inline Color clamp01(const Color& c) {
+  auto cl = [](double v) { return std::max(0.0, std::min(1.0, v)); };
+  return {cl(c.r), cl(c.g), cl(c.b)};
+}
+
+struct Plane {
+  Vec3 n; // normalized
+  double d = 0; // n·X + d = 0
+
+  double sd(const Vec3& p) const { return dot(n, p) + d; }
+};
+
+static inline Plane planeFromPointNormal(const Vec3& p, const Vec3& n_unit) {
+  Plane pl;
+  pl.n = n_unit;
+  pl.d = -dot(pl.n, p);
+  return pl;
+}
+
+static inline Plane planeThrough3(const Vec3& a, const Vec3& b, const Vec3& c) {
+  Vec3 n = normalize(cross(b - a, c - a));
+  return planeFromPointNormal(a, n);
+}
+
+struct Mat3 {
+  double m[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
+
+  static Mat3 identity() {
+    Mat3 I;
+    I.m[0][0] = I.m[1][1] = I.m[2][2] = 1;
+    return I;
+  }
+};
+
+static inline Mat3 mul(const Mat3& A, const Mat3& B) {
+  Mat3 C;
+  for (int i = 0; i < 3; ++i) {
+    for (int j = 0; j < 3; ++j) {
+      double s = 0;
+      for (int k = 0; k < 3; ++k) s += A.m[i][k] * B.m[k][j];
+      C.m[i][j] = s;
+    }
+  }
+  return C;
+}
+
+static inline Vec3 mul_h(const Mat3& H, const Vec3& p) {
+  Vec3 r;
+  r.x = H.m[0][0] * p.x + H.m[0][1] * p.y + H.m[0][2] * p.z;
+  r.y = H.m[1][0] * p.x + H.m[1][1] * p.y + H.m[1][2] * p.z;
+  r.z = H.m[2][0] * p.x + H.m[2][1] * p.y + H.m[2][2] * p.z;
+  return r;
+}
+
+static inline bool invertMat3(const Mat3& A, Mat3& invOut) {
+  const double a00 = A.m[0][0], a01 = A.m[0][1], a02 = A.m[0][2];
+  const double a10 = A.m[1][0], a11 = A.m[1][1], a12 = A.m[1][2];
+  const double a20 = A.m[2][0], a21 = A.m[2][1], a22 = A.m[2][2];
+
+  const double c00 = a11 * a22 - a12 * a21;
+  const double c01 = -(a10 * a22 - a12 * a20);
+  const double c02 = a10 * a21 - a11 * a20;
+
+  const double c10 = -(a01 * a22 - a02 * a21);
+  const double c11 = a00 * a22 - a02 * a20;
+  const double c12 = -(a00 * a21 - a01 * a20);
+
+  const double c20 = a01 * a12 - a02 * a11;
+  const double c21 = -(a00 * a12 - a02 * a10);
+  const double c22 = a00 * a11 - a01 * a10;
+
+  const double det = a00 * c00 + a01 * c01 + a02 * c02;
+  if (std::abs(det) < 1e-18) return false;
+  const double invDet = 1.0 / det;
+
+  invOut.m[0][0] = c00 * invDet;
+  invOut.m[0][1] = c10 * invDet;
+  invOut.m[0][2] = c20 * invDet;
+
+  invOut.m[1][0] = c01 * invDet;
+  invOut.m[1][1] = c11 * invDet;
+  invOut.m[1][2] = c21 * invDet;
+
+  invOut.m[2][0] = c02 * invDet;
+  invOut.m[2][1] = c12 * invDet;
+  invOut.m[2][2] = c22 * invDet;
+  return true;
+}
+
+// Solve 8x8 linear system via Gaussian elimination (small, fixed size)
+static inline bool solve8(double A[8][8], double b[8], double x[8]) {
+  for (int col = 0; col < 8; ++col) {
+    int piv = col;
+    double best = std::abs(A[col][col]);
+    for (int r = col + 1; r < 8; ++r) {
+      double v = std::abs(A[r][col]);
+      if (v > best) { best = v; piv = r; }
+    }
+    if (best < 1e-18) return false;
+    if (piv != col) {
+      for (int c = col; c < 8; ++c) std::swap(A[piv][c], A[col][c]);
+      std::swap(b[piv], b[col]);
+    }
+    const double diag = A[col][col];
+    for (int c = col; c < 8; ++c) A[col][c] /= diag;
+    b[col] /= diag;
+
+    for (int r = 0; r < 8; ++r) {
+      if (r == col) continue;
+      const double f = A[r][col];
+      if (std::abs(f) < 1e-18) continue;
+      for (int c = col; c < 8; ++c) A[r][c] -= f * A[col][c];
+      b[r] -= f * b[col];
+    }
+  }
+  for (int i = 0; i < 8; ++i) x[i] = b[i];
+  return true;
+}
+
+// Homography from 4 point correspondences: (x,y)->(u,v), with h33=1
+static inline bool homography4pt(const std::array<Vec2, 4>& src, const std::array<Vec2, 4>& dst, Mat3& H, Mat3& Hinv) {
+  double A[8][8];
+  double b[8];
+  for (int i = 0; i < 8; ++i) {
+    b[i] = 0;
+    for (int j = 0; j < 8; ++j) A[i][j] = 0;
+  }
+
+  for (int i = 0; i < 4; ++i) {
+    const double x = src[i].x, y = src[i].y;
+    const double u = dst[i].x, v = dst[i].y;
+
+    // row for u
+    A[2 * i + 0][0] = x;
+    A[2 * i + 0][1] = y;
+    A[2 * i + 0][2] = 1;
+    A[2 * i + 0][6] = -u * x;
+    A[2 * i + 0][7] = -u * y;
+    b[2 * i + 0] = u;
+
+    // row for v
+    A[2 * i + 1][3] = x;
+    A[2 * i + 1][4] = y;
+    A[2 * i + 1][5] = 1;
+    A[2 * i + 1][6] = -v * x;
+    A[2 * i + 1][7] = -v * y;
+    b[2 * i + 1] = v;
+  }
+
+  double xsol[8];
+  if (!solve8(A, b, xsol)) return false;
+
+  // fill H with h33=1
+  H = Mat3::identity();
+  H.m[0][0] = xsol[0]; H.m[0][1] = xsol[1]; H.m[0][2] = xsol[2];
+  H.m[1][0] = xsol[3]; H.m[1][1] = xsol[4]; H.m[1][2] = xsol[5];
+  H.m[2][0] = xsol[6]; H.m[2][1] = xsol[7]; H.m[2][2] = 1;
+
+  if (!invertMat3(H, Hinv)) return false;
+  return true;
+}
+
+enum class MaterialType { Curtain, Diffuse, Metal };
+
+struct Material {
+  MaterialType type = MaterialType::Diffuse;
+  Color albedo = {1, 1, 1};      // Diffuse base or Metal reflectance
+  double roughness = 0.0;        // unused in ideal mirror
+};
+
+struct Triangle {
+  Vec3 p0, p1, p2;
+  Material mat;
+
+  Plane plane() const { return planeThrough3(p0, p1, p2); }
+
+  Vec3 normalUnit() const { return normalize(cross(p1 - p0, p2 - p0)); }
+
+  Vec3 pointFromUV(const Vec2& uv) const { return p0 + (p1 - p0) * uv.x + (p2 - p0) * uv.y; }
+
+  // Solve X = p0 + u*(p1-p0) + v*(p2-p0) in least-square on plane basis via Gram 2x2.
+  Vec2 uvFromPoint(const Vec3& X) const {
+    const Vec3 e1 = p1 - p0;
+    const Vec3 e2 = p2 - p0;
+    const Vec3 w = X - p0;
+
+    const double a = dot(e1, e1);
+    const double b = dot(e1, e2);
+    const double c = dot(e2, e2);
+    const double d = dot(e1, w);
+    const double e = dot(e2, w);
+
+    const double det = a * c - b * b;
+    if (std::abs(det) < 1e-18) return {0, 0};
+    const double invDet = 1.0 / det;
+    const double u = (d * c - b * e) * invDet;
+    const double v = (a * e - b * d) * invDet;
+    return {u, v};
+  }
+
+  bool containsUV(const Vec2& uv) const {
+    return uv.x >= -1e-9 && uv.y >= -1e-9 && (uv.x + uv.y) <= 1.0 + 1e-9;
+  }
+};
+
+struct Image {
+  int w = 0, h = 0;
+  std::vector<Color> color;
+  std::vector<double> z;
+
+  Image(int w_, int h_) : w(w_), h(h_), color(w_ * h_), z(w_ * h_, std::numeric_limits<double>::infinity()) {}
+
+  void clear(const Color& c) {
+    std::fill(color.begin(), color.end(), c);
+    std::fill(z.begin(), z.end(), std::numeric_limits<double>::infinity());
+  }
+
+  void setIfCloser(int x, int y, double depth, const Color& c) {
+    if (x < 0 || x >= w || y < 0 || y >= h) return;
+    const int idx = y * w + x;
+    if (depth < z[idx]) {
+      z[idx] = depth;
+      color[idx] = c;
+    }
+  }
+
+  void writePPM(const std::string& path) const {
+    std::ofstream f(path, std::ios::binary);
+    f << "P6\n" << w << " " << h << "\n255\n";
+    for (int i = 0; i < w * h; ++i) {
+      Color c = clamp01(color[i]);
+      uint8_t r = (uint8_t)std::lround(c.r * 255.0);
+      uint8_t g = (uint8_t)std::lround(c.g * 255.0);
+      uint8_t b = (uint8_t)std::lround(c.b * 255.0);
+      f.write((char*)&r, 1);
+      f.write((char*)&g, 1);
+      f.write((char*)&b, 1);
+    }
+  }
+};
+
+struct Frustum {
+  std::array<Plane, 5> planes; // 3 side + near + far(optional as large)
+  int count = 0;
+};
+
+static inline std::optional<Vec3> intersectRayPlane(const Vec3& E, const Vec3& dir_unit, const Plane& pl, double& tOut) {
+  const double denom = dot(pl.n, dir_unit);
+  if (std::abs(denom) < 1e-12) return std::nullopt;
+  const double t = -(dot(pl.n, E) + pl.d) / denom;
+  tOut = t;
+  return E + dir_unit * t;
+}
+
+static inline std::vector<Vec3> clipPolyAgainstPlane(const std::vector<Vec3>& poly, const Plane& pl) {
+  std::vector<Vec3> out;
+  if (poly.empty()) return out;
+  auto inside = [&](const Vec3& p) { return pl.sd(p) >= -1e-9; };
+
+  for (size_t i = 0; i < poly.size(); ++i) {
+    const Vec3 S = poly[i];
+    const Vec3 E = poly[(i + 1) % poly.size()];
+    const double ds = pl.sd(S);
+    const double de = pl.sd(E);
+    const bool inS = ds >= -1e-9;
+    const bool inE = de >= -1e-9;
+
+    if (inS && inE) {
+      out.push_back(E);
+    } else if (inS && !inE) {
+      const double t = ds / (ds - de);
+      out.push_back(S + (E - S) * t);
+    } else if (!inS && inE) {
+      const double t = ds / (ds - de);
+      out.push_back(S + (E - S) * t);
+      out.push_back(E);
+    }
+  }
+  return out;
+}
+
+static inline std::vector<Triangle> triangulateFan(const std::vector<Vec3>& poly, const Material& mat) {
+  std::vector<Triangle> tris;
+  if (poly.size() < 3) return tris;
+  for (size_t i = 1; i + 1 < poly.size(); ++i) {
+    Triangle t;
+    t.p0 = poly[0];
+    t.p1 = poly[i];
+    t.p2 = poly[i + 1];
+    t.mat = mat;
+    tris.push_back(t);
+  }
+  return tris;
+}
+
+static inline Frustum buildFrustum(const Vec3& E, const Triangle& Tv, double near_eps, std::optional<double> far_opt) {
+  Frustum fr;
+  fr.count = 0;
+
+  // Ensure Tv normal points away from eye along view direction
+  Vec3 nTv = Tv.normalUnit();
+  Vec3 cTv = (Tv.p0 + Tv.p1 + Tv.p2) / 3.0;
+  Vec3 viewDir = normalize(cTv - E);
+  if (dot(nTv, viewDir) < 0) nTv = nTv * -1.0;
+
+  // Side planes: each passes through E and an edge of Tv; inward means Tv's opposite vertex is inside.
+  auto addSide = [&](const Vec3& A, const Vec3& B, const Vec3& C_opp) {
+    Vec3 v0 = A - E;
+    Vec3 v1 = B - E;
+    Vec3 n = normalize(cross(v0, v1)); // orientation depends
+    Plane pl = planeFromPointNormal(E, n);
+    if (pl.sd(C_opp) < 0) {
+      pl.n = pl.n * -1.0;
+      pl.d = -pl.d;
+    }
+    fr.planes[fr.count++] = pl;
+  };
+  addSide(Tv.p0, Tv.p1, Tv.p2);
+  addSide(Tv.p1, Tv.p2, Tv.p0);
+  addSide(Tv.p2, Tv.p0, Tv.p1);
+
+  // Near plane: perpendicular to viewDir (use nTv) at E + nTv * near_eps
+  fr.planes[fr.count++] = planeFromPointNormal(E + nTv * near_eps, nTv);
+
+  // Far plane if provided: at E + nTv * far, normal facing back (-nTv) to keep inside between near/far
+  if (far_opt.has_value()) {
+    fr.planes[fr.count++] = planeFromPointNormal(E + nTv * (*far_opt), nTv * -1.0);
+  }
+  return fr;
+}
+
+static inline std::vector<Triangle> clipTriangleToFrustum(const Triangle& tri, const Frustum& fr) {
+  std::vector<Vec3> poly = {tri.p0, tri.p1, tri.p2};
+  for (int i = 0; i < fr.count; ++i) {
+    poly = clipPolyAgainstPlane(poly, fr.planes[i]);
+    if (poly.size() < 3) return {};
+  }
+  return triangulateFan(poly, tri.mat);
+}
+
+// 2D Sutherland–Hodgman: clip polygon P by triangle T (given in 2D)
+static inline std::vector<Vec2> clipPolyByTri2D(const std::vector<Vec2>& poly, const std::array<Vec2, 3>& tri) {
+  std::vector<Vec2> out = poly;
+  auto clipByEdge = [&](const Vec2& A, const Vec2& B, const Vec2& insideRef) {
+    std::vector<Vec2> res;
+    if (out.empty()) return res;
+
+    Vec2 e = B - A;
+    double sign = cross2(e, insideRef - A);
+    if (std::abs(sign) < 1e-18) sign = 1.0;
+
+    auto inside = [&](const Vec2& p) { return cross2(e, p - A) * sign >= -1e-9; };
+
+    for (size_t i = 0; i < out.size(); ++i) {
+      Vec2 S = out[i];
+      Vec2 E = out[(i + 1) % out.size()];
+      bool inS = inside(S);
+      bool inE = inside(E);
+
+      auto intersect = [&]() -> Vec2 {
+        Vec2 d = E - S;
+        double num = cross2(e, A - S);
+        double den = cross2(e, d);
+        if (std::abs(den) < 1e-18) return S;
+        double t = num / den;
+        return S + d * t;
+      };
+
+      if (inS && inE) {
+        res.push_back(E);
+      } else if (inS && !inE) {
+        res.push_back(intersect());
+      } else if (!inS && inE) {
+        res.push_back(intersect());
+        res.push_back(E);
+      }
+    }
+    return res;
+  };
+
+  // clip in order by each edge, using opposite vertex as inside reference
+  out = clipByEdge(tri[0], tri[1], tri[2]);
+  out = clipByEdge(tri[1], tri[2], tri[0]);
+  out = clipByEdge(tri[2], tri[0], tri[1]);
+  return out;
+}
+
+static inline double triArea2(const Vec2& a, const Vec2& b, const Vec2& c) {
+  return std::abs(cross2(b - a, c - a)) * 0.5;
+}
+
+static inline bool barycentric2D(const Vec2& p, const Vec2& a, const Vec2& b, const Vec2& c, double& w0, double& w1, double& w2) {
+  const Vec2 v0 = b - a;
+  const Vec2 v1 = c - a;
+  const Vec2 v2 = p - a;
+  const double den = cross2(v0, v1);
+  if (std::abs(den) < 1e-18) return false;
+  w1 = cross2(v2, v1) / den;
+  w2 = cross2(v0, v2) / den;
+  w0 = 1.0 - w1 - w2;
+  return true;
+}
+
+struct Screen {
+  // Root "curtain" is a rectangle in 3D: O + u*U + v*V, u,v in [0,1]
+  Vec3 O, U, V;
+  int W = 0, H = 0;
+
+  Vec3 pointFromUV01(const Vec2& uv01) const { return O + U * uv01.x + V * uv01.y; }
+
+  Vec2 uv01FromPixelCenter(int x, int y) const {
+    // y down
+    double u = (x + 0.5) / (double)W;
+    double v = (y + 0.5) / (double)H;
+    return {u, v};
+  }
+};
+
+struct DepthOverride {
+  Plane writePlane; // first mirror plane in root view
+  bool valid = false;
+};
+
+struct RenderConfig {
+  double near_eps = 1e-4;
+  std::optional<double> far = std::nullopt;
+  int L_max = 4;
+  double A_min_pixels = 2.0;
+};
+
+struct RenderContext {
+  const std::vector<Triangle>* scene = nullptr;
+  Image* img = nullptr;
+  Screen screen;
+  Vec3 rootEye;
+  RenderConfig cfg;
+};
+
+static inline Vec2 applyH(const Mat3& H, const Vec2& p) {
+  Vec3 hp = mul_h(H, Vec3{p.x, p.y, 1.0});
+  if (std::abs(hp.z) < 1e-18) return {hp.x, hp.y};
+  return {hp.x / hp.z, hp.y / hp.z};
+}
+
+static inline std::optional<std::pair<double, Vec3>> intersectRayTrianglePlane(const Vec3& E, const Vec3& dir_unit, const Triangle& tri) {
+  Plane pl = tri.plane();
+  double t = 0;
+  auto Xopt = intersectRayPlane(E, dir_unit, pl, t);
+  if (!Xopt.has_value()) return std::nullopt;
+  return std::make_pair(t, *Xopt);
+}
+
+static inline Vec3 reflectPointAboutPlane(const Vec3& P, const Plane& pl) {
+  // pl is normalized
+  const double s = pl.sd(P);
+  return P - pl.n * (2.0 * s);
+}
+
+static inline double estimateTrianglePixelArea(const Mat3& H_toRoot, const Triangle& Tv_local, const Screen& screen) {
+  // Tv_local canonical coords: (0,0),(1,0),(0,1)
+  Vec2 r0 = applyH(H_toRoot, Vec2{0, 0});
+  Vec2 r1 = applyH(H_toRoot, Vec2{1, 0});
+  Vec2 r2 = applyH(H_toRoot, Vec2{0, 1});
+  Vec2 p0 = {r0.x * screen.W, r0.y * screen.H};
+  Vec2 p1 = {r1.x * screen.W, r1.y * screen.H};
+  Vec2 p2 = {r2.x * screen.W, r2.y * screen.H};
+  return triArea2(p0, p1, p2);
+}
+
+static inline Color shadeDiffuseSimple(const Triangle& tri, const Vec3& X, const Vec3& dir_unit) {
+  Vec3 n = tri.normalUnit();
+  // Simple directional light + ambient
+  Vec3 L = normalize(Vec3{-0.3, -1.0, -0.2}); // light coming from above
+  double ndotl = std::max(0.0, dot(n, L * -1.0));
+  double ambient = 0.08;
+  double intensity = ambient + 0.92 * ndotl;
+
+  // optional: face-forward
+  if (dot(n, dir_unit) > 0) n = n * -1.0;
+
+  return tri.mat.albedo * intensity;
+}
+
+static void renderTriangleWithTriangle(
+    RenderContext& ctx,
+    const Vec3& E_cur,
+    const Triangle& Tv_local,
+    const Mat3& H_accum, const Mat3& H_accum_inv,
+    const Color& throughput,
+    const DepthOverride& depthOverride,
+    int depthLevel);
+
+// Diffuse branch: clip piece already in frustum, project to Tv plane, rasterize in root pixels
+static void renderDiffusePiece(
+    RenderContext& ctx,
+    const Vec3& E_cur,
+    const Triangle& Tv_local,
+    const Triangle& triPiece,
+    const Mat3& H_accum, const Mat3& H_accum_inv,
+    const Color& throughput,
+    const DepthOverride& depthOverride) {
+
+  // Project triPiece vertices to Tv plane via rays from E_cur
+  Plane tvPl = Tv_local.plane();
+  std::array<Vec2, 3> projUV;
+  std::array<Vec3, 3> projP;
+
+  std::array<Vec3, 3> V = {triPiece.p0, triPiece.p1, triPiece.p2};
+  for (int i = 0; i < 3; ++i) {
+    Vec3 dir = normalize(V[i] - E_cur);
+    double t = 0;
+    auto Xopt = intersectRayPlane(E_cur, dir, tvPl, t);
+    if (!Xopt.has_value() || t <= ctx.cfg.near_eps) return;
+    projP[i] = *Xopt;
+    projUV[i] = Tv_local.uvFromPoint(projP[i]); // in Tv_local uv-space (not necessarily inside Tv triangle, but should)
+  }
+
+  // Map projected triangle into root uv01 via H_accum
+  std::array<Vec2, 3> rootUV01 = {
+      applyH(H_accum, projUV[0]),
+      applyH(H_accum, projUV[1]),
+      applyH(H_accum, projUV[2]),
+  };
+
+  // Pixel bbox in root image
+  auto toPix = [&](const Vec2& uv01) -> Vec2 {
+    return Vec2{uv01.x * ctx.screen.W, uv01.y * ctx.screen.H};
+  };
+  Vec2 p0 = toPix(rootUV01[0]);
+  Vec2 p1 = toPix(rootUV01[1]);
+  Vec2 p2 = toPix(rootUV01[2]);
+
+  int xmin = (int)std::floor(std::min({p0.x, p1.x, p2.x}));
+  int xmax = (int)std::ceil (std::max({p0.x, p1.x, p2.x}));
+  int ymin = (int)std::floor(std::min({p0.y, p1.y, p2.y}));
+  int ymax = (int)std::ceil (std::max({p0.y, p1.y, p2.y}));
+  xmin = std::max(xmin, 0); ymin = std::max(ymin, 0);
+  xmax = std::min(xmax, ctx.img->w - 1); ymax = std::min(ymax, ctx.img->h - 1);
+
+  // For each pixel center: root uv01 -> tv uv via inverse H_accum -> inside test -> ray intersection
+  for (int y = ymin; y <= ymax; ++y) {
+    for (int x = xmin; x <= xmax; ++x) {
+      Vec2 uv01 = ctx.screen.uv01FromPixelCenter(x, y);
+      Vec2 uv_tv = applyH(H_accum_inv, uv01);
+
+      double w0, w1, w2;
+      if (!barycentric2D(uv_tv, projUV[0], projUV[1], projUV[2], w0, w1, w2)) continue;
+      if (w0 < -1e-8 || w1 < -1e-8 || w2 < -1e-8) continue;
+
+      // Build point on Tv plane for this uv_tv
+      Vec3 P_on_tv = Tv_local.pointFromUV(uv_tv);
+      Vec3 dir = normalize(P_on_tv - E_cur);
+
+      auto hit = intersectRayTrianglePlane(E_cur, dir, triPiece);
+      if (!hit.has_value()) continue;
+      double t_virtual = hit->first;
+      Vec3 X = hit->second;
+      if (t_virtual <= ctx.cfg.near_eps) continue;
+
+      // Ensure inside triPiece in its own uv
+      Vec2 uv_piece = triPiece.uvFromPoint(X);
+      if (!triPiece.containsUV(uv_piece)) continue;
+
+      // Depth for z-buffer: either real hit depth, or overridden mirror depth in root view
+      double depth = t_virtual;
+      if (depthOverride.valid) {
+        Vec3 P_root = ctx.screen.pointFromUV01(uv01);
+        Vec3 dir_root = normalize(P_root - ctx.rootEye);
+        double t_override = 0;
+        auto Xo = intersectRayPlane(ctx.rootEye, dir_root, depthOverride.writePlane, t_override);
+        if (!Xo.has_value() || t_override <= ctx.cfg.near_eps) continue;
+        depth = t_override;
+      }
+
+      Color base = shadeDiffuseSimple(triPiece, X, dir);
+      Color out = base * throughput;
+      ctx.img->setIfCloser(x, y, depth, out);
+    }
+  }
+}
+
+static void renderMetalTriangle(
+    RenderContext& ctx,
+    const Vec3& E_cur,
+    const Triangle& Tv_local, // parent curtain viewport
+    const Triangle& triMetal, // unclipped original metal tri OR clipped piece; both ok if plane same
+    const Mat3& H_accum, const Mat3& H_accum_inv,
+    const Color& throughput,
+    const DepthOverride& depthOverride,
+    int depthLevel) {
+
+  if (depthLevel >= ctx.cfg.L_max) return;
+
+  Plane metalPl = triMetal.plane(); // normalized
+  // Footprint of parent frustum on metal plane: intersect 3 boundary rays (E_cur -> Tv_local vertices)
+  std::array<Vec3, 3> Q;
+  std::array<Vec3, 3> Sv = {Tv_local.p0, Tv_local.p1, Tv_local.p2};
+  for (int i = 0; i < 3; ++i) {
+    Vec3 dir = normalize(Sv[i] - E_cur);
+    double t = 0;
+    auto Xopt = intersectRayPlane(E_cur, dir, metalPl, t);
+    if (!Xopt.has_value() || t <= ctx.cfg.near_eps) return;
+    Q[i] = *Xopt;
+  }
+
+  // Clip footprint triangle Q by the metal triangle in-plane (2D)
+  // Use metal triangle local 2D coords in its own basis
+  auto to2D_inMetal = [&](const Vec3& X) { return triMetal.uvFromPoint(X); };
+  std::array<Vec2, 3> metalTri2D = {Vec2{0, 0}, Vec2{1, 0}, Vec2{0, 1}};
+  std::vector<Vec2> poly2D = {to2D_inMetal(Q[0]), to2D_inMetal(Q[1]), to2D_inMetal(Q[2])};
+  poly2D = clipPolyByTri2D(poly2D, metalTri2D);
+  if (poly2D.size() < 3) return;
+
+  // Triangulate child viewport polygon on metal plane
+  std::vector<Triangle> childViewports;
+  for (size_t i = 1; i + 1 < poly2D.size(); ++i) {
+    Triangle tv;
+    tv.p0 = triMetal.pointFromUV(poly2D[0]);
+    tv.p1 = triMetal.pointFromUV(poly2D[i]);
+    tv.p2 = triMetal.pointFromUV(poly2D[i + 1]);
+    tv.mat.type = MaterialType::Curtain; // IMPORTANT: child is a viewport, not a drawable
+    tv.mat.albedo = {0, 0, 0};
+    childViewports.push_back(tv);
+  }
+
+  // Mirror camera
+  Vec3 E_mirror = reflectPointAboutPlane(E_cur, metalPl);
+
+  // Decide depth override: lock to the first mirror plane in root view
+  DepthOverride nextOverride = depthOverride;
+  if (!nextOverride.valid) {
+    nextOverride.valid = true;
+    nextOverride.writePlane = metalPl;
+  }
+
+  // Recurse for each child viewport
+  for (const Triangle& Tv_child : childViewports) {
+    // Stop condition by projected pixel area in root
+    // Need H_step: child uv -> parent uv, induced by central projection from E_cur onto parent plane
+    Plane parentPl = Tv_local.plane();
+
+    auto projToParent = [&](const Vec3& X_on_child) -> Vec3 {
+      Vec3 dir = normalize(X_on_child - E_cur);
+      double t = 0;
+      auto Xp = intersectRayPlane(E_cur, dir, parentPl, t);
+      if (!Xp.has_value()) return Tv_local.p0;
+      return *Xp;
+    };
+
+    // 4 correspondences: 3 vertices + centroid
+    std::array<Vec2, 4> src_uv_child = {
+        Vec2{0, 0},
+        Vec2{1, 0},
+        Vec2{0, 1},
+        Vec2{1.0 / 3.0, 1.0 / 3.0},
+    };
+    Vec3 C3 = (Tv_child.p0 + Tv_child.p1 + Tv_child.p2) / 3.0;
+    std::array<Vec3, 4> child3 = {Tv_child.p0, Tv_child.p1, Tv_child.p2, C3};
+    std::array<Vec2, 4> dst_uv_parent;
+    for (int i = 0; i < 4; ++i) {
+      Vec3 Xp = projToParent(child3[i]);
+      dst_uv_parent[i] = Tv_local.uvFromPoint(Xp);
+    }
+
+    Mat3 H_step, H_step_inv;
+    if (!homography4pt(src_uv_child, dst_uv_parent, H_step, H_step_inv)) continue;
+
+    Mat3 H_child_toRoot = mul(H_accum, H_step);
+    Mat3 H_child_toRoot_inv;
+    if (!invertMat3(H_child_toRoot, H_child_toRoot_inv)) continue;
+
+    double areaPx = estimateTrianglePixelArea(H_child_toRoot, Tv_child, ctx.screen);
+    if (areaPx < ctx.cfg.A_min_pixels) continue;
+
+    Color nextThroughput = throughput * triMetal.mat.albedo; // metal reflectance tint
+    renderTriangleWithTriangle(ctx, E_mirror, Tv_child, H_child_toRoot, H_child_toRoot_inv, nextThroughput, nextOverride, depthLevel + 1);
+  }
+}
+
+static void renderTriangleWithTriangle(
+    RenderContext& ctx,
+    const Vec3& E_cur,
+    const Triangle& Tv_local,
+    const Mat3& H_accum, const Mat3& H_accum_inv,
+    const Color& throughput,
+    const DepthOverride& depthOverride,
+    int depthLevel) {
+
+  if (Tv_local.mat.type != MaterialType::Curtain) {
+    // In this design, only Curtain triangles are viewports.
+    // (Metal recursion creates Tv_child as Curtain.)
+    return;
+  }
+
+  // Build frustum from E_cur and current viewport triangle
+  Frustum fr = buildFrustum(E_cur, Tv_local, ctx.cfg.near_eps, ctx.cfg.far);
+
+  // Collect candidates: clip each scene triangle against frustum
+  for (const Triangle& tri : *ctx.scene) {
+    if (tri.mat.type == MaterialType::Curtain) continue; // do not render curtain geometry
+    std::vector<Triangle> pieces = clipTriangleToFrustum(tri, fr);
+    for (const Triangle& piece : pieces) {
+      if (piece.mat.type == MaterialType::Diffuse) {
+        renderDiffusePiece(ctx, E_cur, Tv_local, piece, H_accum, H_accum_inv, throughput, depthOverride);
+      } else if (piece.mat.type == MaterialType::Metal) {
+        // Metal is recursive, no direct color; use parent frustum footprint method
+        renderMetalTriangle(ctx, E_cur, Tv_local, piece, H_accum, H_accum_inv, throughput, depthOverride, depthLevel);
+      }
+    }
+  }
+}
+
+// Build Cornell Box (5 faces) + 2 metal boxes
+static std::vector<Triangle> buildScene() {
+  std::vector<Triangle> s;
+
+  auto addQuad = [&](Vec3 a, Vec3 b, Vec3 c, Vec3 d, const Material& m) {
+    // (a,b,c) and (a,c,d)
+    Triangle t1{a, b, c, m};
+    Triangle t2{a, c, d, m};
+    s.push_back(t1);
+    s.push_back(t2);
+  };
+
+  // Cornell dimensions
+  // Coordinate system: x right, y up, z forward (into the box)
+  const double W = 2.0;
+  const double H = 2.0;
+  const double D = 2.5;
+
+  Vec3 A{-W/2, 0, 0};
+  Vec3 B{ W/2, 0, 0};
+  Vec3 C{ W/2, H, 0};
+  Vec3 Dd{-W/2, H, 0};
+
+  Vec3 A2{-W/2, 0, D};
+  Vec3 B2{ W/2, 0, D};
+  Vec3 C2{ W/2, H, D};
+  Vec3 D2{-W/2, H, D};
+
+  Material white{MaterialType::Diffuse, {0.75, 0.75, 0.75}};
+  Material red{MaterialType::Diffuse, {0.75, 0.15, 0.15}};
+  Material green{MaterialType::Diffuse, {0.15, 0.75, 0.15}};
+
+  // Floor: A..B..B2..A2
+  addQuad(A, B, B2, A2, white);
+  // Ceiling: Dd..C..C2..D2
+  addQuad(Dd, C, C2, D2, white);
+  // Back wall: A2..B2..C2..D2
+  addQuad(A2, B2, C2, D2, white);
+  // Left wall: A..A2..D2..Dd
+  addQuad(A, A2, D2, Dd, red);
+  // Right wall: B..C..C2..B2
+  addQuad(B, C, C2, B2, green);
+
+  auto addBox = [&](Vec3 minP, Vec3 maxP, const Material& m) {
+    Vec3 p000{minP.x, minP.y, minP.z};
+    Vec3 p100{maxP.x, minP.y, minP.z};
+    Vec3 p110{maxP.x, maxP.y, minP.z};
+    Vec3 p010{minP.x, maxP.y, minP.z};
+
+    Vec3 p001{minP.x, minP.y, maxP.z};
+    Vec3 p101{maxP.x, minP.y, maxP.z};
+    Vec3 p111{maxP.x, maxP.y, maxP.z};
+    Vec3 p011{minP.x, maxP.y, maxP.z};
+
+    // 6 faces
+    addQuad(p000, p100, p110, p010, m); // front (z=min)
+    addQuad(p001, p011, p111, p101, m); // back  (z=max)
+    addQuad(p000, p010, p011, p001, m); // left
+    addQuad(p100, p101, p111, p110, m); // right
+    addQuad(p010, p110, p111, p011, m); // top
+    addQuad(p000, p001, p101, p100, m); // bottom
+  };
+
+  Material metalBlue{MaterialType::Metal, {0.35, 0.45, 0.95}};
+  Material metalYellow{MaterialType::Metal, {0.95, 0.85, 0.25}};
+
+  // Two boxes inside (raise above floor a bit)
+  addBox(Vec3{-0.6, 0.0, 0.7}, Vec3{-0.1, 0.9, 1.2}, metalBlue);
+  addBox(Vec3{ 0.1, 0.0, 1.2}, Vec3{ 0.7, 1.4, 1.9}, metalYellow);
+
+  return s;
+}
+
+struct Camera {
+  Vec3 E;
+  Triangle Tv0, Tv1; // Curtain triangles covering screen
+  Screen screen;
+
+  static Camera makeDefault(int W, int H) {
+    Camera cam;
+    cam.E = Vec3{0, 1.0, -3.2};
+
+    // Screen rectangle in world: put in front of eye
+    // Define 4 corners of screen quad in world (z=-1.0 plane, spanning [-1,1]x[0,2])
+    Vec3 a{-1.0, 0.0, -1.0};
+    Vec3 b{ 1.0, 0.0, -1.0};
+    Vec3 c{ 1.0, 2.0, -1.0};
+    Vec3 d{-1.0, 2.0, -1.0};
+
+    Material curtain{MaterialType::Curtain, {0, 0, 0}};
+    cam.Tv0 = Triangle{a, b, c, curtain};
+    cam.Tv1 = Triangle{a, c, d, curtain};
+
+    cam.screen.O = a;
+    cam.screen.U = (b - a);
+    cam.screen.V = (d - a);
+    cam.screen.W = W;
+    cam.screen.H = H;
+
+    return cam;
+  }
+
+  void render(const std::vector<Triangle>& scene, Image& img, const RenderConfig& cfg) const {
+    RenderContext ctx;
+    ctx.scene = &scene;
+    ctx.img = &img;
+    ctx.screen = screen;
+    ctx.rootEye = E;
+    ctx.cfg = cfg;
+
+    Mat3 H0 = Mat3::identity();
+    Mat3 H0inv = Mat3::identity();
+    DepthOverride none;
+    none.valid = false;
+
+    Color throughput{1, 1, 1};
+
+    renderTriangleWithTriangle(ctx, E, Tv0, H0, H0inv, throughput, none, 0);
+    renderTriangleWithTriangle(ctx, E, Tv1, H0, H0inv, throughput, none, 0);
+  }
+};
+
+int main(int argc, char** argv) {
+  std::string out = "out.ppm";
+  if (argc >= 2) out = argv[1];
+
+  int W = 640, H = 480;
+  Image img(W, H);
+  img.clear(Color{0.0, 0.0, 0.0});
+
+  std::vector<Triangle> scene = buildScene();
+  Camera cam = Camera::makeDefault(W, H);
+
+  RenderConfig cfg;
+  cfg.near_eps = 1e-4;
+  cfg.far = std::nullopt; // or 10.0
+  cfg.L_max = 4;
+  cfg.A_min_pixels = 2.0;
+
+  cam.render(scene, img, cfg);
+  img.writePPM(out);
+
+  std::cerr << "Wrote " << out << "\n";
+  return 0;
+}

experiments/rt7.cpp

@@ -0,0 +1,941 @@
+// main.cpp
+// 一个“以面片为处理单位”的步进式递归渲染器（非逐像素光线追踪），输出 PPM。
+// 思路要点：
+// - 相机 viewport 被拆成 2 个三角形 Curtain；渲染时遍历场景三角形，把三角形“投影变形”到当前 viewport 三角形平面上
+// - 采用“由远到近”排序的 painter 覆盖关系（O(n log n)）
+// - Diffuse：只贴纹理/颜色（不递归）
+// - Metal：先贴自身，再把相机原点关于该金属三角形平面对称，令该金属三角形成为下一层 viewport，递归渲染反射并合成到金属区域
+//
+// 编译：g++ -O2 -std=c++17 main.cpp -o render
+// 运行：./render
+// 输出：out.ppm
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cmath>
+#include <cstdint>
+#include <fstream>
+#include <iostream>
+#include <limits>
+#include <optional>
+#include <string>
+#include <tuple>
+#include <utility>
+#include <vector>
+
+static constexpr double kEps = 1e-9;
+
+static inline double clamp01(double x) {
+	return x < 0 ? 0 : (x > 1 ? 1 : x);
+}
+
+struct Vec2 {
+	double x = 0, y = 0;
+	Vec2() = default;
+	Vec2(double xx, double yy) : x(xx), y(yy) {
+	}
+	Vec2 operator+(const Vec2 &r) const {
+		return { x + r.x, y + r.y };
+	}
+	Vec2 operator-(const Vec2 &r) const {
+		return { x - r.x, y - r.y };
+	}
+	Vec2 operator*(double s) const {
+		return { x * s, y * s };
+	}
+};
+
+static inline double cross2(const Vec2 &a, const Vec2 &b) {
+	return a.x * b.y - a.y * b.x;
+}
+static inline double dot2(const Vec2 &a, const Vec2 &b) {
+	return a.x * b.x + a.y * b.y;
+}
+
+struct Vec3 {
+	double x = 0, y = 0, z = 0;
+	Vec3() = default;
+	Vec3(double xx, double yy, double zz) : x(xx), y(yy), z(zz) {
+	}
+
+	Vec3 operator+(const Vec3 &r) const {
+		return { x + r.x, y + r.y, z + r.z };
+	}
+	Vec3 operator-(const Vec3 &r) const {
+		return { x - r.x, y - r.y, z - r.z };
+	}
+	Vec3 operator*(double s) const {
+		return { x * s, y * s, z * s };
+	}
+	Vec3 operator/(double s) const {
+		return { x / s, y / s, z / s };
+	}
+
+	Vec3 &operator+=(const Vec3 &r) {
+		x += r.x;
+		y += r.y;
+		z += r.z;
+		return *this;
+	}
+};
+
+static inline double dot3(const Vec3 &a, const Vec3 &b) {
+	return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+
+static inline Vec3 cross3(const Vec3 &a, const Vec3 &b) {
+	return {
+		a.y * b.z - a.z * b.y,
+		a.z * b.x - a.x * b.z,
+		a.x * b.y - a.y * b.x
+	};
+}
+
+static inline double length3(const Vec3 &v) {
+	return std::sqrt(dot3(v, v));
+}
+
+static inline Vec3 normalize3(const Vec3 &v) {
+	double len = length3(v);
+	if (len < kEps)
+		return { 0, 0, 0 };
+	return v / len;
+}
+
+static inline Vec3 hadamard(const Vec3 &a, const Vec3 &b) {
+	return { a.x * b.x, a.y * b.y, a.z * b.z };
+}
+
+struct ScreenTri {
+	Vec2 p0, p1, p2;
+};
+
+static inline double triArea2D(const Vec2 &a, const Vec2 &b, const Vec2 &c) {
+	return 0.5 * std::abs(cross2(b - a, c - a));
+}
+
+static inline double triArea2D(const ScreenTri &t) {
+	return triArea2D(t.p0, t.p1, t.p2);
+}
+
+static inline std::array<double, 3> barycentric2D(const Vec2 &p, const Vec2 &a, const Vec2 &b, const Vec2 &c) {
+	// 返回 (w0, w1, w2)，满足 p = w0*a + w1*b + w2*c，且 w0+w1+w2=1（在非退化情况下）
+	Vec2 v0 = b - a;
+	Vec2 v1 = c - a;
+	Vec2 v2 = p - a;
+	double den = cross2(v0, v1);
+	if (std::abs(den) < kEps)
+		return { -1, -1, -1 };
+	double w1 = cross2(v2, v1) / den;
+	double w2 = cross2(v0, v2) / den;
+	double w0 = 1.0 - w1 - w2;
+	return { w0, w1, w2 };
+}
+
+static inline bool pointInTri2D(const Vec2 &p, const Vec2 &a, const Vec2 &b, const Vec2 &c, double eps = 1e-8) {
+	auto w = barycentric2D(p, a, b, c);
+	return w[0] >= -eps && w[1] >= -eps && w[2] >= -eps;
+}
+
+static inline int orient(const Vec2 &a, const Vec2 &b, const Vec2 &c) {
+	double v = cross2(b - a, c - a);
+	if (v > 1e-12)
+		return 1;
+	if (v < -1e-12)
+		return -1;
+	return 0;
+}
+
+static inline bool onSegment(const Vec2 &a, const Vec2 &b, const Vec2 &p) {
+	return std::min(a.x, b.x) - 1e-12 <= p.x && p.x <= std::max(a.x, b.x) + 1e-12 && std::min(a.y, b.y) - 1e-12 <= p.y && p.y <= std::max(a.y, b.y) + 1e-12 && std::abs(cross2(b - a, p - a)) < 1e-10;
+}
+
+static inline bool segIntersects(const Vec2 &a, const Vec2 &b, const Vec2 &c, const Vec2 &d) {
+	int o1 = orient(a, b, c);
+	int o2 = orient(a, b, d);
+	int o3 = orient(c, d, a);
+	int o4 = orient(c, d, b);
+
+	if (o1 != o2 && o3 != o4)
+		return true;
+	if (o1 == 0 && onSegment(a, b, c))
+		return true;
+	if (o2 == 0 && onSegment(a, b, d))
+		return true;
+	if (o3 == 0 && onSegment(c, d, a))
+		return true;
+	if (o4 == 0 && onSegment(c, d, b))
+		return true;
+	return false;
+}
+
+static inline bool triOverlap2D(const ScreenTri &A, const ScreenTri &B) {
+	// 顶点包含测试
+	if (pointInTri2D(A.p0, B.p0, B.p1, B.p2) || pointInTri2D(A.p1, B.p0, B.p1, B.p2) || pointInTri2D(A.p2, B.p0, B.p1, B.p2))
+		return true;
+	if (pointInTri2D(B.p0, A.p0, A.p1, A.p2) || pointInTri2D(B.p1, A.p0, A.p1, A.p2) || pointInTri2D(B.p2, A.p0, A.p1, A.p2))
+		return true;
+
+	// 边相交测试
+	std::array<Vec2, 3> a = { A.p0, A.p1, A.p2 };
+	std::array<Vec2, 3> b = { B.p0, B.p1, B.p2 };
+	for (int i = 0; i < 3; i++) {
+		Vec2 a0 = a[i], a1 = a[(i + 1) % 3];
+		for (int j = 0; j < 3; j++) {
+			Vec2 b0 = b[j], b1 = b[(j + 1) % 3];
+			if (segIntersects(a0, a1, b0, b1))
+				return true;
+		}
+	}
+	return false;
+}
+
+enum class MaterialType {
+	Curtain,
+	Diffuse,
+	Metal
+};
+
+struct Material {
+	MaterialType type = MaterialType::Diffuse;
+	Vec3 baseColor { 1, 1, 1 };
+	double reflectivity = 0.85; // 仅 Metal 使用
+	bool checker = false;
+	double checkerScale = 8.0;
+};
+
+struct Triangle {
+	int id = -1;
+	Vec3 v0, v1, v2;
+	Vec2 uv0 { 0, 0 }, uv1 { 1, 0 }, uv2 { 0, 1 };
+	Material mat;
+
+	Vec3 normal() const {
+		return normalize3(cross3(v1 - v0, v2 - v0));
+	}
+	Vec3 centroid() const {
+		return (v0 + v1 + v2) / 3.0;
+	}
+};
+
+struct Image {
+	int w = 0, h = 0;
+	int ox = 0, oy = 0; // 全局坐标偏移（用于子 buffer）
+	bool masked = false; // true：未写入像素默认“无效”
+	std::vector<Vec3> pix;
+	std::vector<uint8_t> mask; // masked=true 时使用
+
+	Image() = default;
+	Image(int ww, int hh, int offx = 0, int offy = 0, bool useMask = false)
+		: w(ww), h(hh), ox(offx), oy(offy), masked(useMask), pix((size_t)ww * (size_t)hh, { 0, 0, 0 }) {
+		if (masked)
+			mask.assign((size_t)ww * (size_t)hh, 0);
+	}
+
+	bool inBoundsGlobal(int x, int y) const {
+		return x >= ox && x < ox + w && y >= oy && y < oy + h;
+	}
+
+	size_t idxGlobal(int x, int y) const {
+		return (size_t)(y - oy) * (size_t)w + (size_t)(x - ox);
+	}
+
+	Vec3 get(int x, int y) const {
+		if (!inBoundsGlobal(x, y))
+			return { 0, 0, 0 };
+		size_t i = idxGlobal(x, y);
+		if (masked && mask[i] == 0)
+			return { 0, 0, 0 };
+		return pix[i];
+	}
+
+	bool has(int x, int y) const {
+		if (!inBoundsGlobal(x, y))
+			return false;
+		if (!masked)
+			return true;
+		return mask[idxGlobal(x, y)] != 0;
+	}
+
+	void set(int x, int y, const Vec3 &c) {
+		if (!inBoundsGlobal(x, y))
+			return;
+		size_t i = idxGlobal(x, y);
+		pix[i] = c;
+		if (masked)
+			mask[i] = 1;
+	}
+
+	void writePPM(const std::string &path) const {
+		// 仅支持 ox=oy=0 且 masked=false 的整图输出
+		std::ofstream out(path, std::ios::binary);
+		out << "P6\n"
+			<< w << " " << h << "\n255\n";
+		for (int y = 0; y < h; y++) {
+			for (int x = 0; x < w; x++) {
+				Vec3 c = pix[(size_t)y * (size_t)w + (size_t)x];
+				// gamma 2.2
+				auto toByte = [](double v) -> uint8_t {
+					v = clamp01(v);
+					v = std::pow(v, 1.0 / 2.2);
+					int b = (int)std::lround(v * 255.0);
+					if (b < 0)
+						b = 0;
+					if (b > 255)
+						b = 255;
+					return (uint8_t)b;
+				};
+				uint8_t r = toByte(c.x);
+				uint8_t g = toByte(c.y);
+				uint8_t b = toByte(c.z);
+				out.write((const char *)&r, 1);
+				out.write((const char *)&g, 1);
+				out.write((const char *)&b, 1);
+			}
+		}
+	}
+};
+
+struct ViewportFrame {
+	Vec3 p0; // viewport v0
+	Vec3 n; // plane normal (unit)
+	Vec3 axisX; // in-plane basis
+	Vec3 axisY; // in-plane basis
+	Vec2 v0_2 { 0, 0 };
+	Vec2 v1_2 { 0, 0 };
+	Vec2 v2_2 { 0, 0 };
+};
+
+static inline ViewportFrame makeViewportFrame(const Triangle &viewport) {
+	ViewportFrame f;
+	f.p0 = viewport.v0;
+	Vec3 e01 = viewport.v1 - viewport.v0;
+	Vec3 e02 = viewport.v2 - viewport.v0;
+	f.n = normalize3(cross3(e01, e02));
+	f.axisX = normalize3(e01);
+	f.axisY = normalize3(cross3(f.n, f.axisX));
+
+	f.v0_2 = { 0, 0 };
+	f.v1_2 = { dot3(e01, f.axisX), dot3(e01, f.axisY) };
+	f.v2_2 = { dot3(e02, f.axisX), dot3(e02, f.axisY) };
+	return f;
+}
+
+static inline Vec2 toViewport2D(const ViewportFrame &f, const Vec3 &p) {
+	Vec3 d = p - f.p0;
+	return { dot3(d, f.axisX), dot3(d, f.axisY) };
+}
+
+static inline Vec3 reflectPointAcrossPlane(const Vec3 &p, const Vec3 &planePoint, const Vec3 &planeNormalUnit) {
+	// 反射点：p' = p - 2*dot(n, (p-planePoint))*n
+	double d = dot3(planeNormalUnit, p - planePoint);
+	return p - planeNormalUnit * (2.0 * d);
+}
+
+struct ProjectedTri {
+	ScreenTri screen; // 投影到最终输出（全局像素坐标）的三角形
+	std::array<double, 3> invW; // “投影深度倒数”等价量（用于透视矫正插值）
+};
+
+static inline std::optional<ProjectedTri> projectTriangleOntoViewport(
+	const Triangle &tri,
+	const Vec3 &origin,
+	const Triangle &viewportWorld,
+	const ScreenTri &viewportScreen,
+	const ViewportFrame &vf) {
+	// 把 tri 的三个顶点沿着 origin->vertex 的直线投影到 viewportWorld 的平面上，
+	// 再通过 viewportWorld 的重心坐标映射到 viewportScreen（像素三角形）上。
+	Vec3 n = vf.n;
+	Vec3 planeP = vf.p0;
+
+	auto projectPoint = [&](const Vec3 &P, double &outT, Vec3 &outProj) -> bool {
+		Vec3 dir = P - origin;
+		double denom = dot3(n, dir);
+		if (std::abs(denom) < 1e-12)
+			return false;
+		double t = dot3(n, planeP - origin) / denom;
+
+		// 关键：t>1 表示平面在 P 的“更远处”，即 P 位于 origin 与平面之间（不应被该 viewport 看见）
+		// t<=0 表示交点在 origin 反方向
+		if (!(t > 1e-9 && t <= 1.0 + 1e-7))
+			return false;
+
+		outT = t;
+		outProj = origin + dir * t;
+		return true;
+	};
+
+	std::array<Vec3, 3> P = { tri.v0, tri.v1, tri.v2 };
+	std::array<Vec3, 3> Q;
+	std::array<double, 3> t;
+
+	for (int i = 0; i < 3; i++) {
+		if (!projectPoint(P[i], t[i], Q[i]))
+			return std::nullopt;
+	}
+
+	// 投影点 Q 都在 viewport 平面上：计算它们相对 viewportWorld 的重心坐标
+	auto screenFromQ = [&](const Vec3 &q) -> std::optional<Vec2> {
+		Vec2 q2 = toViewport2D(vf, q);
+		auto w = barycentric2D(q2, vf.v0_2, vf.v1_2, vf.v2_2);
+		if (w[0] < -1e-6 || w[1] < -1e-6 || w[2] < -1e-6) {
+			// 允许在 viewport 外（仍可能与 viewport 相交），所以这里不做强制 inside
+			// 只要不是退化即可
+		}
+		if (!std::isfinite(w[0]) || !std::isfinite(w[1]) || !std::isfinite(w[2]))
+			return std::nullopt;
+
+		Vec2 s = viewportScreen.p0 * w[0] + viewportScreen.p1 * w[1] + viewportScreen.p2 * w[2];
+		return s;
+	};
+
+	std::array<Vec2, 3> S;
+	for (int i = 0; i < 3; i++) {
+		auto s = screenFromQ(Q[i]);
+		if (!s)
+			return std::nullopt;
+		S[i] = *s;
+	}
+
+	ProjectedTri out;
+	out.screen = { S[0], S[1], S[2] };
+
+	// 透视矫正：在“固定 origin + 固定 viewport 平面”下，t 等价于 1/depth（类比 plane z=1 时 t=1/z）
+	out.invW = { t[0], t[1], t[2] };
+	return out;
+}
+
+static inline Vec3 sampleMaterial(const Triangle &tri, const Vec2 &uv) {
+	// 简易纹理：checker 或纯色
+	Vec3 c = tri.mat.baseColor;
+	if (tri.mat.checker) {
+		double u = uv.x * tri.mat.checkerScale;
+		double v = uv.y * tri.mat.checkerScale;
+		int iu = (int)std::floor(u);
+		int iv = (int)std::floor(v);
+		bool odd = ((iu + iv) & 1) != 0;
+		double k = odd ? 0.55 : 1.0;
+		c = c * k;
+	}
+	return c;
+}
+
+static inline Vec3 shadeSimple(const Triangle &tri, const Vec3 &base) {
+	// 简易定向光 + 环境光，避免因法线翻转导致全黑：使用 abs(dot)
+	Vec3 n = tri.normal();
+	Vec3 lightDir = normalize3(Vec3 { -0.3, 0.9, -0.2 });
+	double ndl = std::abs(dot3(n, lightDir));
+	double ambient = 0.18;
+	double diff = ambient + (1.0 - ambient) * ndl;
+	return base * diff;
+}
+
+struct RasterMask {
+	int w = 0, h = 0;
+	int ox = 0, oy = 0;
+	std::vector<uint8_t> m;
+	RasterMask() = default;
+	RasterMask(int ww, int hh, int offx, int offy) : w(ww), h(hh), ox(offx), oy(offy), m((size_t)ww * (size_t)hh, 0) {
+	}
+
+	bool inBoundsGlobal(int x, int y) const {
+		return x >= ox && x < ox + w && y >= oy && y < oy + h;
+	}
+	size_t idxGlobal(int x, int y) const {
+		return (size_t)(y - oy) * (size_t)w + (size_t)(x - ox);
+	}
+
+	void set(int x, int y) {
+		if (!inBoundsGlobal(x, y))
+			return;
+		m[idxGlobal(x, y)] = 1;
+	}
+	bool get(int x, int y) const {
+		if (!inBoundsGlobal(x, y))
+			return false;
+		return m[idxGlobal(x, y)] != 0;
+	}
+};
+
+static inline void rasterizeProjectedTriangle(
+	Image &target,
+	const Triangle &tri,
+	const ProjectedTri &proj,
+	const ScreenTri &viewportScreen,
+	RasterMask *outMaskOrNull) {
+	// 在目标 target 上对 proj.screen 做三角形光栅化，并且裁剪在 viewportScreen 内（防止越界 spill）
+	ScreenTri st = proj.screen;
+
+	double minx = std::floor(std::min({ st.p0.x, st.p1.x, st.p2.x }));
+	double maxx = std::ceil(std::max({ st.p0.x, st.p1.x, st.p2.x }));
+	double miny = std::floor(std::min({ st.p0.y, st.p1.y, st.p2.y }));
+	double maxy = std::ceil(std::max({ st.p0.y, st.p1.y, st.p2.y }));
+
+	int ix0 = (int)minx;
+	int ix1 = (int)maxx;
+	int iy0 = (int)miny;
+	int iy1 = (int)maxy;
+
+	for (int y = iy0; y <= iy1; y++) {
+		for (int x = ix0; x <= ix1; x++) {
+			Vec2 p { (double)x + 0.5, (double)y + 0.5 };
+			if (!pointInTri2D(p, st.p0, st.p1, st.p2))
+				continue;
+			if (!pointInTri2D(p, viewportScreen.p0, viewportScreen.p1, viewportScreen.p2))
+				continue;
+			if (!target.inBoundsGlobal(x, y))
+				continue;
+
+			auto w = barycentric2D(p, st.p0, st.p1, st.p2);
+			if (w[0] < -1e-8 || w[1] < -1e-8 || w[2] < -1e-8)
+				continue;
+
+			// 透视矫正插值 UV
+			double iw0 = proj.invW[0], iw1 = proj.invW[1], iw2 = proj.invW[2];
+			double denom = w[0] * iw0 + w[1] * iw1 + w[2] * iw2;
+			if (std::abs(denom) < 1e-12)
+				continue;
+
+			Vec2 uv = (tri.uv0 * (w[0] * iw0) + tri.uv1 * (w[1] * iw1) + tri.uv2 * (w[2] * iw2)) * (1.0 / denom);
+
+			Vec3 base = sampleMaterial(tri, uv);
+			Vec3 col = shadeSimple(tri, base);
+
+			target.set(x, y, col);
+			if (outMaskOrNull)
+				outMaskOrNull->set(x, y);
+		}
+	}
+}
+
+// ---------（可选）三角形相交：这里给一个基础实现（不一定用于主流程）---------
+
+struct RayHit {
+	double t = 0;
+	Vec3 p;
+	Vec3 n;
+};
+
+static inline std::optional<RayHit> intersectRayTriangle(const Vec3 &ro, const Vec3 &rd, const Triangle &tri) {
+	// Möller–Trumbore（用于几何工具，主算法不按逐像素 ray casting）
+	Vec3 e1 = tri.v1 - tri.v0;
+	Vec3 e2 = tri.v2 - tri.v0;
+	Vec3 pvec = cross3(rd, e2);
+	double det = dot3(e1, pvec);
+	if (std::abs(det) < 1e-12)
+		return std::nullopt;
+	double invDet = 1.0 / det;
+
+	Vec3 tvec = ro - tri.v0;
+	double u = dot3(tvec, pvec) * invDet;
+	if (u < 0 || u > 1)
+		return std::nullopt;
+
+	Vec3 qvec = cross3(tvec, e1);
+	double v = dot3(rd, qvec) * invDet;
+	if (v < 0 || u + v > 1)
+		return std::nullopt;
+
+	double t = dot3(e2, qvec) * invDet;
+	if (t < 0)
+		return std::nullopt;
+
+	RayHit hit;
+	hit.t = t;
+	hit.p = ro + rd * t;
+	hit.n = tri.normal();
+	return hit;
+}
+
+static inline bool triangleTriangleIntersectRough(const Triangle &a, const Triangle &b) {
+	// 粗略：边与对方三角形的射线相交 + 顶点包含（足够作为“相关运算”示意）
+	auto testEdge = [&](const Vec3 &p0, const Vec3 &p1, const Triangle &tri) -> bool {
+		Vec3 d = p1 - p0;
+		double len = length3(d);
+		if (len < 1e-12)
+			return false;
+		Vec3 rd = d / len;
+		auto hit = intersectRayTriangle(p0, rd, tri);
+		if (!hit)
+			return false;
+		return hit->t >= 0 && hit->t <= len;
+	};
+
+	std::array<Vec3, 3> av = { a.v0, a.v1, a.v2 };
+	std::array<Vec3, 3> bv = { b.v0, b.v1, b.v2 };
+
+	for (int i = 0; i < 3; i++) {
+		if (testEdge(av[i], av[(i + 1) % 3], b))
+			return true;
+		if (testEdge(bv[i], bv[(i + 1) % 3], a))
+			return true;
+	}
+	return false;
+}
+
+// --------- 核心递归渲染：renderTriangleWithTriangle ---------
+
+struct RenderSettings {
+	int maxDepth = 4;
+	double minViewportAreaPx = 4.0; // 1~5 像素级阈值，这里取 4
+};
+
+struct Candidate {
+	const Triangle *tri = nullptr;
+	ProjectedTri proj;
+	double dist = 0;
+};
+
+static void renderTriangleWithTriangle(
+	const std::vector<Triangle> &scene,
+	const Vec3 &cameraOrigin,
+	const Triangle &curtainTriWorld, // 保留形参以贴合你的描述；本实现不强依赖它
+	const Triangle &currentViewportWorld, // 当前 viewport 面片（世界空间三角形）
+	const ScreenTri &viewportInImage, // 当前 viewport 面片在最终输出图上的三角形区域（像素三点）
+	Image &outTarget,
+	const RenderSettings &settings,
+	int depth) {
+	(void)curtainTriWorld;
+
+	if (depth > settings.maxDepth)
+		return;
+	if (triArea2D(viewportInImage) < settings.minViewportAreaPx)
+		return;
+
+	ViewportFrame vf = makeViewportFrame(currentViewportWorld);
+
+	std::vector<Candidate> candidates;
+	candidates.reserve(scene.size());
+
+	for (const Triangle &tri : scene) {
+		if (tri.id == currentViewportWorld.id && tri.id != -1)
+			continue; // viewport 自身不参与渲染，避免递归自反馈
+
+		auto projOpt = projectTriangleOntoViewport(tri, cameraOrigin, currentViewportWorld, viewportInImage, vf);
+		if (!projOpt)
+			continue;
+
+		// 投影三角形必须与 viewport 区域有重叠，否则不处理
+		if (!triOverlap2D(projOpt->screen, viewportInImage))
+			continue;
+
+		Candidate c;
+		c.tri = &tri;
+		c.proj = *projOpt;
+		c.dist = length3(tri.centroid() - cameraOrigin);
+		candidates.push_back(c);
+	}
+
+	// 覆盖关系：由远到近 painter（O(n log n)）
+	std::sort(candidates.begin(), candidates.end(), [](const Candidate &a, const Candidate &b) {
+		return a.dist > b.dist;
+	});
+
+	for (const Candidate &c : candidates) {
+		const Triangle &tri = *c.tri;
+
+		if (tri.mat.type == MaterialType::Diffuse) {
+			rasterizeProjectedTriangle(outTarget, tri, c.proj, viewportInImage, nullptr);
+			continue;
+		}
+
+		if (tri.mat.type == MaterialType::Metal) {
+			// 1) 先贴金属自身底色（并记录金属可见区域 mask）
+			ScreenTri metalScreen = c.proj.screen;
+
+			int bbMinX = (int)std::floor(std::min({ metalScreen.p0.x, metalScreen.p1.x, metalScreen.p2.x }));
+			int bbMaxX = (int)std::ceil(std::max({ metalScreen.p0.x, metalScreen.p1.x, metalScreen.p2.x }));
+			int bbMinY = (int)std::floor(std::min({ metalScreen.p0.y, metalScreen.p1.y, metalScreen.p2.y }));
+			int bbMaxY = (int)std::ceil(std::max({ metalScreen.p0.y, metalScreen.p1.y, metalScreen.p2.y }));
+
+			int bbW = std::max(1, bbMaxX - bbMinX + 1);
+			int bbH = std::max(1, bbMaxY - bbMinY + 1);
+
+			RasterMask metalMask(bbW, bbH, bbMinX, bbMinY);
+
+			rasterizeProjectedTriangle(outTarget, tri, c.proj, viewportInImage, &metalMask);
+
+			// 2) 计算“关于当前金属面片”的相机原点对称点，作为下一层递归的 origin
+			Vec3 n = tri.normal();
+			Vec3 originRef = reflectPointAcrossPlane(cameraOrigin, tri.v0, n);
+
+			// 3) 递归渲染反射：让当前金属面片 tri 自身成为下一层 viewport
+			//    注意：反射结果渲染到一个子 buffer（避免直接 blend 导致 painter 合成错误）
+			Image reflBuf(bbW, bbH, bbMinX, bbMinY, true /*masked*/);
+
+			// 递归终止也会受 metalScreen 面积限制（通过 viewportInImage 面积判断）
+			renderTriangleWithTriangle(
+				scene,
+				originRef,
+				curtainTriWorld,
+				tri, // 下一层 viewport = 当前金属三角形
+				metalScreen, // 下一层 viewport 在最终图片中的区域 = 当前金属区域（投影三角形）
+				reflBuf,
+				settings,
+				depth + 1);
+
+			// 4) 合成：只在 metalMask 覆盖到的像素上，把 reflBuf 以 reflectivity 混合到 outTarget
+			double a = clamp01(tri.mat.reflectivity);
+			for (int y = bbMinY; y <= bbMaxY; y++) {
+				for (int x = bbMinX; x <= bbMaxX; x++) {
+					if (!metalMask.get(x, y))
+						continue; // 只在“金属可见区域”合成
+					if (!reflBuf.has(x, y))
+						continue; // 反射缓冲没写入则不改变底色
+
+					Vec3 base = outTarget.get(x, y);
+					Vec3 refl = reflBuf.get(x, y);
+					Vec3 out = base * (1.0 - a) + refl * a;
+					outTarget.set(x, y, out);
+				}
+			}
+
+			continue;
+		}
+
+		// Curtain 类型一般不在 scene 里；若出现，忽略
+	}
+}
+
+// --------- Scene：Cornell Box + 两个金属盒子（蓝/黄）---------
+
+static int gNextTriId = 1;
+
+static inline Triangle makeTri(const Vec3 &a, const Vec3 &b, const Vec3 &c,
+	const Vec2 &uva, const Vec2 &uvb, const Vec2 &uvc,
+	const Material &m) {
+	Triangle t;
+	t.id = gNextTriId++;
+	t.v0 = a;
+	t.v1 = b;
+	t.v2 = c;
+	t.uv0 = uva;
+	t.uv1 = uvb;
+	t.uv2 = uvc;
+	t.mat = m;
+	return t;
+}
+
+static inline void addQuad(std::vector<Triangle> &out,
+	const Vec3 &a, const Vec3 &b, const Vec3 &c, const Vec3 &d,
+	const Material &m) {
+	// (a,b,c) + (a,c,d)
+	out.push_back(makeTri(a, b, c, { 0, 0 }, { 1, 0 }, { 1, 1 }, m));
+	out.push_back(makeTri(a, c, d, { 0, 0 }, { 1, 1 }, { 0, 1 }, m));
+}
+
+static inline Vec3 rotateY(const Vec3 &p, double rad) {
+	double cs = std::cos(rad), sn = std::sin(rad);
+	return { p.x * cs + p.z * sn, p.y, -p.x * sn + p.z * cs };
+}
+
+static inline void addBox(std::vector<Triangle> &out,
+	const Vec3 &center,
+	const Vec3 &size, // (sx, sy, sz)
+	double rotYRad,
+	const Material &m) {
+	Vec3 h = size * 0.5;
+
+	// 8 corners in local space
+	std::array<Vec3, 8> v = {
+		Vec3 { -h.x, -h.y, -h.z }, // 0
+		Vec3 { h.x, -h.y, -h.z }, // 1
+		Vec3 { h.x, h.y, -h.z }, // 2
+		Vec3 { -h.x, h.y, -h.z }, // 3
+		Vec3 { -h.x, -h.y, h.z }, // 4
+		Vec3 { h.x, -h.y, h.z }, // 5
+		Vec3 { h.x, h.y, h.z }, // 6
+		Vec3 { -h.x, h.y, h.z } // 7
+	};
+
+	for (auto &p : v)
+		p = rotateY(p, rotYRad) + center;
+
+	// faces: each as quad (a,b,c,d) with consistent uv
+	// Front (-z): 0,1,2,3
+	addQuad(out, v[0], v[1], v[2], v[3], m);
+	// Back (+z): 5,4,7,6 (swap order to vary orientation; shading使用abs不敏感)
+	addQuad(out, v[5], v[4], v[7], v[6], m);
+	// Left (-x): 4,0,3,7
+	addQuad(out, v[4], v[0], v[3], v[7], m);
+	// Right (+x): 1,5,6,2
+	addQuad(out, v[1], v[5], v[6], v[2], m);
+	// Bottom (-y): 4,5,1,0
+	addQuad(out, v[4], v[5], v[1], v[0], m);
+	// Top (+y): 3,2,6,7
+	addQuad(out, v[3], v[2], v[6], v[7], m);
+}
+
+static inline std::vector<Triangle> buildCornellScene() {
+	std::vector<Triangle> tris;
+	tris.reserve(128);
+
+	// Cornell box 尺寸（前方开口，便于相机观察）
+	// x in [-1,1], y in [0,2], z in [0,2]
+	Vec3 L { -1, 0, 0 }, R { 1, 0, 0 };
+	(void)L;
+	(void)R;
+
+	Material floorM;
+	floorM.type = MaterialType::Diffuse;
+	floorM.baseColor = { 0.9, 0.9, 0.9 };
+	floorM.checker = true;
+	floorM.checkerScale = 6;
+	Material leftM;
+	leftM.type = MaterialType::Diffuse;
+	leftM.baseColor = { 0.9, 0.2, 0.2 };
+	Material rightM;
+	rightM.type = MaterialType::Diffuse;
+	rightM.baseColor = { 0.2, 0.9, 0.2 };
+	Material backM;
+	backM.type = MaterialType::Diffuse;
+	backM.baseColor = { 0.95, 0.95, 0.95 };
+
+	// Floor y=0
+	addQuad(tris,
+		Vec3 { -1, 0, 0 }, Vec3 { 1, 0, 0 }, Vec3 { 1, 0, 2 }, Vec3 { -1, 0, 2 },
+		floorM);
+
+	// Left wall x=-1
+	addQuad(tris,
+		Vec3 { -1, 0, 0 }, Vec3 { -1, 0, 2 }, Vec3 { -1, 2, 2 }, Vec3 { -1, 2, 0 },
+		leftM);
+
+	// Right wall x=1
+	addQuad(tris,
+		Vec3 { 1, 0, 0 }, Vec3 { 1, 2, 0 }, Vec3 { 1, 2, 2 }, Vec3 { 1, 0, 2 },
+		rightM);
+
+	// Back wall z=2
+	addQuad(tris,
+		Vec3 { -1, 0, 2 }, Vec3 { 1, 0, 2 }, Vec3 { 1, 2, 2 }, Vec3 { -1, 2, 2 },
+		backM);
+
+	// 两个金属盒子（蓝/黄），放在盒子内部
+	Material blueMetal;
+	blueMetal.type = MaterialType::Metal;
+	blueMetal.baseColor = { 0.15, 0.25, 0.95 };
+	blueMetal.reflectivity = 0.85;
+	blueMetal.checker = false;
+	Material yellowMetal;
+	yellowMetal.type = MaterialType::Metal;
+	yellowMetal.baseColor = { 0.95, 0.85, 0.15 };
+	yellowMetal.reflectivity = 0.80;
+	yellowMetal.checker = false;
+
+	addBox(tris, Vec3 { -0.45, 0.50, 1.05 }, Vec3 { 0.55, 1.00, 0.55 }, 0.30, blueMetal);
+	addBox(tris, Vec3 { 0.45, 0.35, 1.45 }, Vec3 { 0.65, 0.70, 0.65 }, -0.45, /*yellowMetal*/rightM);
+
+	return tris;
+}
+
+// --------- Camera：viewport 两三角形 Curtain，调用两次渲染并输出 PPM ---------
+
+struct Camera {
+	Vec3 origin { 0, 1, -3 };
+	Vec3 lookAt { 0, 1, 1 };
+	Vec3 up { 0, 1, 0 };
+
+	int width = 800;
+	int height = 600;
+	double fovYDeg = 50.0;
+	double focalDist = 1.0;
+
+	Triangle curtainA; // world
+	Triangle curtainB; // world
+	ScreenTri screenA; // image region
+	ScreenTri screenB; // image region
+
+	void buildCurtain() {
+		Vec3 forward = normalize3(lookAt - origin);
+		Vec3 right = normalize3(cross3(forward, up));
+		Vec3 up2 = normalize3(cross3(right, forward));
+
+		double aspect = (double)width / (double)height;
+		double fovYRad = fovYDeg * M_PI / 180.0;
+		double halfH = std::tan(fovYRad * 0.5) * focalDist;
+		double halfW = halfH * aspect;
+
+		Vec3 center = origin + forward * focalDist;
+		Vec3 tl = center + up2 * halfH - right * halfW;
+		Vec3 tr = center + up2 * halfH + right * halfW;
+		Vec3 bl = center - up2 * halfH - right * halfW;
+		Vec3 br = center - up2 * halfH + right * halfW;
+
+		Material curtainM;
+		curtainM.type = MaterialType::Curtain;
+		curtainM.baseColor = { 0, 0, 0 };
+
+		curtainA.id = -1001;
+		curtainA.v0 = tl;
+		curtainA.v1 = tr;
+		curtainA.v2 = bl;
+		curtainA.mat = curtainM;
+
+		curtainB.id = -1002;
+		curtainB.v0 = br;
+		curtainB.v1 = bl;
+		curtainB.v2 = tr;
+		curtainB.mat = curtainM;
+
+		// 像素三角形：覆盖整个图像矩形（对角线划分）
+		// 注意：图像坐标原点在左上，y 向下
+		screenA = { Vec2 { 0, 0 }, Vec2 { (double)(width - 1), 0 }, Vec2 { 0, (double)(height - 1) } };
+		screenB = { Vec2 { (double)(width - 1), (double)(height - 1) }, Vec2 { 0, (double)(height - 1) }, Vec2 { (double)(width - 1), 0 } };
+	}
+
+	void render(const std::vector<Triangle> &scene, const std::string &outPath) {
+		buildCurtain();
+
+		Image img(width, height, 0, 0, false);
+		// 背景（默认黑）
+		for (auto &p : img.pix)
+			p = Vec3 { 0.0, 0.0, 0.0 };
+
+		RenderSettings settings;
+		settings.maxDepth = 4;
+		settings.minViewportAreaPx = 4.0;
+
+		// CurtainA
+		renderTriangleWithTriangle(
+			scene,
+			origin,
+			curtainA,
+			curtainA,
+			screenA,
+			img,
+			settings,
+			0);
+
+		// CurtainB
+		renderTriangleWithTriangle(
+			scene,
+			origin,
+			curtainB,
+			curtainB,
+			screenB,
+			img,
+			settings,
+			0);
+
+		img.writePPM(outPath);
+	}
+};
+
+int main() {
+	std::vector<Triangle> scene = buildCornellScene();
+
+	Camera cam;
+	cam.width = 900;
+	cam.height = 700;
+	cam.origin = Vec3 { 0.0, 1.0, -3.2 };
+	cam.lookAt = Vec3 { 0.0, 1.0, 1.0 };
+	cam.fovYDeg = 52.0;
+	cam.focalDist = 1.0;
+
+	cam.render(scene, "out.ppm");
+
+	std::cerr << "Wrote out.ppm\n";
+	return 0;
+}

experiments/rt8.cpp

@@ -0,0 +1,606 @@
+#include <algorithm>
+#include <array>
+#include <cmath>
+#include <cstdint>
+#include <fstream>
+#include <iostream>
+#include <limits>
+#include <string>
+#include <vector>
+
+static constexpr double kEps = 1e-9;
+
+static inline double clamp01(double v) { return std::max(0.0, std::min(1.0, v)); }
+static inline int clampInt(int v, int lo, int hi) { return std::max(lo, std::min(hi, v)); }
+
+struct Vec2 {
+  double x = 0.0, y = 0.0;
+
+  Vec2() = default;
+  Vec2(double xx, double yy) : x(xx), y(yy) {}
+
+  Vec2 operator+(const Vec2& r) const { return Vec2(x + r.x, y + r.y); }
+  Vec2 operator-(const Vec2& r) const { return Vec2(x - r.x, y - r.y); }
+  Vec2 operator*(double s) const { return Vec2(x * s, y * s); }
+  Vec2 operator/(double s) const { return Vec2(x / s, y / s); }
+};
+
+static inline Vec2 operator*(double s, const Vec2& v) { return v * s; }
+
+static inline double dot(const Vec2& a, const Vec2& b) { return a.x * b.x + a.y * b.y; }
+static inline double cross2(const Vec2& a, const Vec2& b) { return a.x * b.y - a.y * b.x; }
+static inline double orient2D(const Vec2& a, const Vec2& b, const Vec2& c) { return cross2(b - a, c - a); }
+
+struct Vec3 {
+  double x = 0.0, y = 0.0, z = 0.0;
+
+  Vec3() = default;
+  Vec3(double xx, double yy, double zz) : x(xx), y(yy), z(zz) {}
+
+  Vec3 operator+(const Vec3& r) const { return Vec3(x + r.x, y + r.y, z + r.z); }
+  Vec3 operator-(const Vec3& r) const { return Vec3(x - r.x, y - r.y, z - r.z); }
+  Vec3 operator*(double s) const { return Vec3(x * s, y * s, z * s); }
+  Vec3 operator/(double s) const { return Vec3(x / s, y / s, z / s); }
+
+  Vec3 operator*(const Vec3& r) const { return Vec3(x * r.x, y * r.y, z * r.z); }
+  Vec3 operator/(const Vec3& r) const { return Vec3(x / r.x, y / r.y, z / r.z); }
+};
+
+static inline Vec3 operator*(double s, const Vec3& v) { return v * s; }
+
+static inline double dot(const Vec3& a, const Vec3& b) { return a.x * b.x + a.y * b.y + a.z * b.z; }
+static inline Vec3 cross(const Vec3& a, const Vec3& b) {
+  return Vec3(a.y * b.z - a.z * b.y,
+              a.z * b.x - a.x * b.z,
+              a.x * b.y - a.y * b.x);
+}
+static inline double length(const Vec3& v) { return std::sqrt(dot(v, v)); }
+static inline Vec3 normalize(const Vec3& v) {
+  double len = length(v);
+  if (len < kEps) return Vec3(0, 0, 0);
+  return v / len;
+}
+static inline Vec3 clamp01(const Vec3& c) { return Vec3(clamp01(c.x), clamp01(c.y), clamp01(c.z)); }
+
+struct Triangle2D {
+  Vec2 a, b, c;
+
+  double areaAbs() const { return std::abs(orient2D(a, b, c)) * 0.5; }
+
+  Vec2 minXY() const {
+    return Vec2(std::min({a.x, b.x, c.x}), std::min({a.y, b.y, c.y}));
+  }
+  Vec2 maxXY() const {
+    return Vec2(std::max({a.x, b.x, c.x}), std::max({a.y, b.y, c.y}));
+  }
+};
+
+static inline bool barycentric2D(const Vec2& p, const Vec2& a, const Vec2& b, const Vec2& c, Vec3& wOut) {
+  double denom = orient2D(a, b, c);
+  if (std::abs(denom) < kEps) return false;
+  double w0 = orient2D(p, b, c) / denom;
+  double w1 = orient2D(a, p, c) / denom;
+  double w2 = 1.0 - w0 - w1;
+  wOut = Vec3(w0, w1, w2);
+  return true;
+}
+
+static inline bool pointInTri2D(const Vec2& p, const Triangle2D& t, double eps = 1e-8) {
+  Vec3 w;
+  if (!barycentric2D(p, t.a, t.b, t.c, w)) return false;
+  return (w.x >= -eps && w.y >= -eps && w.z >= -eps);
+}
+
+static inline bool onSegment(const Vec2& a, const Vec2& b, const Vec2& p, double eps = 1e-9) {
+  if (std::abs(orient2D(a, b, p)) > eps) return false;
+  return (std::min(a.x, b.x) - eps <= p.x && p.x <= std::max(a.x, b.x) + eps &&
+          std::min(a.y, b.y) - eps <= p.y && p.y <= std::max(a.y, b.y) + eps);
+}
+
+static inline bool segmentsIntersect2D(const Vec2& p1, const Vec2& p2, const Vec2& q1, const Vec2& q2) {
+  double o1 = orient2D(p1, p2, q1);
+  double o2 = orient2D(p1, p2, q2);
+  double o3 = orient2D(q1, q2, p1);
+  double o4 = orient2D(q1, q2, p2);
+
+  auto sgn = [](double v) -> int {
+    if (v > 1e-12) return 1;
+    if (v < -1e-12) return -1;
+    return 0;
+  };
+
+  int s1 = sgn(o1), s2 = sgn(o2), s3 = sgn(o3), s4 = sgn(o4);
+
+  if (s1 * s2 < 0 && s3 * s4 < 0) return true;
+
+  if (s1 == 0 && onSegment(p1, p2, q1)) return true;
+  if (s2 == 0 && onSegment(p1, p2, q2)) return true;
+  if (s3 == 0 && onSegment(q1, q2, p1)) return true;
+  if (s4 == 0 && onSegment(q1, q2, p2)) return true;
+
+  return false;
+}
+
+static inline bool trianglesOverlap2D(const Triangle2D& t1, const Triangle2D& t2) {
+  Vec2 min1 = t1.minXY(), max1 = t1.maxXY();
+  Vec2 min2 = t2.minXY(), max2 = t2.maxXY();
+  if (max1.x < min2.x || max2.x < min1.x || max1.y < min2.y || max2.y < min1.y) return false;
+
+  if (pointInTri2D(t1.a, t2) || pointInTri2D(t1.b, t2) || pointInTri2D(t1.c, t2)) return true;
+  if (pointInTri2D(t2.a, t1) || pointInTri2D(t2.b, t1) || pointInTri2D(t2.c, t1)) return true;
+
+  std::array<Vec2, 3> e1a{t1.a, t1.b, t1.c};
+  std::array<Vec2, 3> e1b{t1.b, t1.c, t1.a};
+  std::array<Vec2, 3> e2a{t2.a, t2.b, t2.c};
+  std::array<Vec2, 3> e2b{t2.b, t2.c, t2.a};
+
+  for (int i = 0; i < 3; ++i) {
+    for (int j = 0; j < 3; ++j) {
+      if (segmentsIntersect2D(e1a[i], e1b[i], e2a[j], e2b[j])) return true;
+    }
+  }
+  return false;
+}
+
+enum class MaterialType { Curtain, Diffuse, Metal };
+
+struct Material {
+  MaterialType type = MaterialType::Diffuse;
+  Vec3 baseColor = Vec3(1, 1, 1);
+  double reflectance = 0.85;
+};
+
+struct Triangle {
+  int id = -1;
+  Vec3 a, b, c;
+  Vec2 uvA, uvB, uvC;
+  Material mat;
+
+  Vec3 normal() const { return normalize(cross(b - a, c - a)); }
+  Vec3 centroid() const { return (a + b + c) / 3.0; }
+};
+
+struct Image {
+  int w = 0, h = 0;
+  std::vector<Vec3> px;
+
+  Image(int width, int height) : w(width), h(height), px((size_t)width * (size_t)height, Vec3(0, 0, 0)) {}
+
+  void clear(const Vec3& c) { std::fill(px.begin(), px.end(), c); }
+
+  Vec3 get(int x, int y) const { return px[(size_t)y * (size_t)w + (size_t)x]; }
+
+  void blendPixel(int x, int y, const Vec3& src, double alpha) {
+    if (x < 0 || x >= w || y < 0 || y >= h) return;
+    alpha = clamp01(alpha);
+    Vec3& dst = px[(size_t)y * (size_t)w + (size_t)x];
+    dst = dst * (1.0 - alpha) + src * alpha;
+  }
+
+  void writePPM(const std::string& path) const {
+    std::ofstream out(path, std::ios::binary);
+    if (!out) {
+      std::cerr << "Cannot open output file: " << path << "\n";
+      return;
+    }
+    out << "P6\n" << w << " " << h << "\n255\n";
+    for (int y = 0; y < h; ++y) {
+      for (int x = 0; x < w; ++x) {
+        Vec3 c = clamp01(get(x, y));
+        auto toSRGB8 = [](double v) -> unsigned char {
+          v = clamp01(v);
+          v = std::pow(v, 1.0 / 2.2);
+          int iv = (int)std::lround(v * 255.0);
+          iv = clampInt(iv, 0, 255);
+          return (unsigned char)iv;
+        };
+        unsigned char r = toSRGB8(c.x);
+        unsigned char g = toSRGB8(c.y);
+        unsigned char b = toSRGB8(c.z);
+        out.write((char*)&r, 1);
+        out.write((char*)&g, 1);
+        out.write((char*)&b, 1);
+      }
+    }
+  }
+};
+
+static inline Vec3 reflectPointAcrossPlane(const Vec3& p, const Vec3& planePoint, const Vec3& planeNormalUnit) {
+  double d = dot(p - planePoint, planeNormalUnit);
+  return p - planeNormalUnit * (2.0 * d);
+}
+
+static inline bool projectPointToPlaneFromOrigin(const Vec3& origin,
+                                                const Vec3& point,
+                                                const Vec3& planePoint,
+                                                const Vec3& planeNormalUnit,
+                                                Vec3& hit,
+                                                double& tOut) {
+  Vec3 dir = point - origin;
+  double denom = dot(dir, planeNormalUnit);
+  if (denom <= 1e-12) return false;
+  double t = dot(planePoint - origin, planeNormalUnit) / denom;
+  if (t <= 1e-12) return false;
+  hit = origin + dir * t;
+  tOut = t;
+  return true;
+}
+
+static inline double wrap01(double u) {
+  u = u - std::floor(u);
+  if (u < 0) u += 1.0;
+  return u;
+}
+
+static inline Vec3 sampleCheckerUV(const Vec2& uv, const Vec3& base) {
+  double u = wrap01(uv.x);
+  double v = wrap01(uv.y);
+
+  const double scale = 10.0;
+  int iu = (int)std::floor(u * scale);
+  int iv = (int)std::floor(v * scale);
+
+  double checker = ((iu + iv) & 1) ? 0.82 : 1.0;
+
+  double fu = u * scale - std::floor(u * scale);
+  double fv = v * scale - std::floor(v * scale);
+  double line = (fu < 0.05 || fv < 0.05) ? 0.55 : 1.0;
+
+  return base * (checker * line);
+}
+
+struct RenderSettings {
+  int maxDepth = 3;
+  double minViewportAreaPx = 3.0;
+  double minReflectAreaPx = 8.0;
+};
+
+struct RenderLayer {
+  Vec3 tint = Vec3(1, 1, 1);
+  double alpha = 1.0;
+};
+
+struct Candidate {
+  const Triangle* tri = nullptr;
+  Triangle2D projPlane;
+  Triangle2D projScreen;
+  double depthMetric = 0.0;
+};
+
+static inline Vec2 mapPlaneToScreen(const Vec2& pPlane, const Triangle2D& viewportPlaneTri, const Triangle2D& viewportScreenTri) {
+  Vec3 w;
+  if (!barycentric2D(pPlane, viewportPlaneTri.a, viewportPlaneTri.b, viewportPlaneTri.c, w)) return viewportScreenTri.a;
+  return viewportScreenTri.a * w.x + viewportScreenTri.b * w.y + viewportScreenTri.c * w.z;
+}
+
+static Vec3 shadeTriangle(const Triangle& tri, const Vec2& uv, const Vec3& viewOrigin) {
+  Vec3 n = tri.normal();
+  Vec3 lightDir = normalize(Vec3(-0.35, 0.9, -0.25)); // 方向光：从上方略偏前
+  double ndotl = std::max(0.0, dot(n, lightDir));
+
+  Vec3 albedo = tri.mat.baseColor;
+  if (tri.mat.type == MaterialType::Diffuse) {
+    albedo = sampleCheckerUV(uv, albedo);
+    double ambient = 0.22;
+    double diff = ambient + (1.0 - ambient) * ndotl;
+    return albedo * diff;
+  }
+
+  if (tri.mat.type == MaterialType::Metal) {
+    double ambient = 0.05;
+    double diff = ambient + (1.0 - ambient) * std::pow(ndotl, 0.35);
+    return albedo * diff;
+  }
+
+  return albedo;
+}
+
+static void rasterizeTriangleToImage(const Triangle& tri,
+                                     const Triangle2D& triScreen,
+                                     const Triangle2D& clipScreen,
+                                     Image& img,
+                                     const Vec3& viewOrigin,
+                                     const RenderLayer& layer) {
+  Vec2 bbMin = triScreen.minXY();
+  Vec2 bbMax = triScreen.maxXY();
+
+  int minX = clampInt((int)std::floor(bbMin.x), 0, img.w - 1);
+  int maxX = clampInt((int)std::ceil(bbMax.x), 0, img.w - 1);
+  int minY = clampInt((int)std::floor(bbMin.y), 0, img.h - 1);
+  int maxY = clampInt((int)std::ceil(bbMax.y), 0, img.h - 1);
+
+  for (int y = minY; y <= maxY; ++y) {
+    for (int x = minX; x <= maxX; ++x) {
+      Vec2 p((double)x + 0.5, (double)y + 0.5);
+
+      if (!pointInTri2D(p, clipScreen)) continue;
+
+      Vec3 w;
+      if (!barycentric2D(p, triScreen.a, triScreen.b, triScreen.c, w)) continue;
+      if (w.x < -1e-8 || w.y < -1e-8 || w.z < -1e-8) continue;
+
+      Vec2 uv = tri.uvA * w.x + tri.uvB * w.y + tri.uvC * w.z;
+
+      Vec3 c = shadeTriangle(tri, uv, viewOrigin);
+      c = c * layer.tint;
+      img.blendPixel(x, y, c, layer.alpha);
+    }
+  }
+}
+
+static void renderTriangleWithTriangle(const std::vector<Triangle>& scene,
+                                      const Vec3& origin,
+                                      const Triangle& viewportWorld,
+                                      const Triangle2D& viewportScreen,
+                                      Image& img,
+                                      int depth,
+                                      const RenderSettings& settings,
+                                      const RenderLayer& layer,
+                                      int ignoreTriId) {
+  if (depth > settings.maxDepth) return;
+
+  double viewportArea = viewportScreen.areaAbs();
+  if (viewportArea < settings.minViewportAreaPx) return;
+
+  Vec3 planePoint = viewportWorld.a;
+  Vec3 n = normalize(cross(viewportWorld.b - viewportWorld.a, viewportWorld.c - viewportWorld.a));
+  if (length(n) < 1e-12) return;
+
+  if (dot(planePoint - origin, n) < 0.0) n = n * -1.0;
+
+  double planeDist = dot(planePoint - origin, n);
+  if (planeDist <= 1e-9) return;
+
+  Vec3 u3 = normalize(viewportWorld.b - viewportWorld.a);
+  if (length(u3) < 1e-12) return;
+  Vec3 v3 = normalize(cross(n, u3));
+  if (length(v3) < 1e-12) return;
+
+  Triangle2D viewportPlane;
+  viewportPlane.a = Vec2(0.0, 0.0);
+  viewportPlane.b = Vec2(dot(viewportWorld.b - viewportWorld.a, u3), dot(viewportWorld.b - viewportWorld.a, v3));
+  viewportPlane.c = Vec2(dot(viewportWorld.c - viewportWorld.a, u3), dot(viewportWorld.c - viewportWorld.a, v3));
+
+  std::vector<Candidate> candidates;
+  candidates.reserve(scene.size());
+
+  for (const Triangle& tri : scene) {
+    if (tri.id == ignoreTriId) continue;
+    if (tri.mat.type == MaterialType::Curtain) continue;
+
+    std::array<Vec3, 3> vtx{tri.a, tri.b, tri.c};
+    std::array<Vec2, 3> proj2;
+    std::array<double, 3> denom;
+    bool ok = true;
+
+    for (int i = 0; i < 3; ++i) {
+      Vec3 hit;
+      double t;
+      if (!projectPointToPlaneFromOrigin(origin, vtx[i], planePoint, n, hit, t)) { ok = false; break; }
+
+      if (t >= 1.0 - 1e-6) { ok = false; break; }
+
+      proj2[i] = Vec2(dot(hit - planePoint, u3), dot(hit - planePoint, v3));
+      denom[i] = dot(vtx[i] - origin, n);
+      if (denom[i] <= 1e-9) { ok = false; break; }
+    }
+    if (!ok) continue;
+
+    Triangle2D projPlane{proj2[0], proj2[1], proj2[2]};
+    if (!trianglesOverlap2D(projPlane, viewportPlane)) continue;
+
+    Triangle2D projScreen;
+    projScreen.a = mapPlaneToScreen(projPlane.a, viewportPlane, viewportScreen);
+    projScreen.b = mapPlaneToScreen(projPlane.b, viewportPlane, viewportScreen);
+    projScreen.c = mapPlaneToScreen(projPlane.c, viewportPlane, viewportScreen);
+
+    double depthMetric = (denom[0] + denom[1] + denom[2]) / 3.0;
+
+    candidates.push_back(Candidate{&tri, projPlane, projScreen, depthMetric});
+  }
+
+  std::sort(candidates.begin(), candidates.end(),
+            [](const Candidate& lhs, const Candidate& rhs) { return lhs.depthMetric > rhs.depthMetric; });
+
+  bool enableCull = (depth == 0);
+
+  for (const Candidate& cand : candidates) {
+    const Triangle& tri = *cand.tri;
+
+    if (enableCull) {
+      Vec3 nn = tri.normal();
+      Vec3 toOrigin = origin - tri.centroid();
+      if (dot(nn, toOrigin) <= 0.0) continue;
+    }
+
+    rasterizeTriangleToImage(tri, cand.projScreen, viewportScreen, img, origin, layer);
+
+    if (tri.mat.type == MaterialType::Metal) {
+      double triAreaPx = cand.projScreen.areaAbs();
+      if (triAreaPx < settings.minReflectAreaPx) continue;
+      if (depth >= settings.maxDepth) continue;
+
+      Vec3 mirrorN = tri.normal();
+      if (length(mirrorN) < 1e-12) continue;
+
+      Vec3 mirroredOrigin = reflectPointAcrossPlane(origin, tri.a, mirrorN);
+
+      RenderLayer childLayer;
+      childLayer.tint = layer.tint * tri.mat.baseColor;
+      childLayer.alpha = layer.alpha * clamp01(tri.mat.reflectance);
+
+      if (childLayer.alpha < 1e-4) continue;
+
+      renderTriangleWithTriangle(scene,
+                                 mirroredOrigin,
+                                 tri,
+                                 cand.projScreen,
+                                 img,
+                                 depth + 1,
+                                 settings,
+                                 childLayer,
+                                 tri.id);
+    }
+  }
+}
+
+static Triangle makeTri(int& idCounter,
+                        const Vec3& a, const Vec3& b, const Vec3& c,
+                        const Vec2& uvA, const Vec2& uvB, const Vec2& uvC,
+                        const Material& mat) {
+  Triangle t;
+  t.id = idCounter++;
+  t.a = a; t.b = b; t.c = c;
+  t.uvA = uvA; t.uvB = uvB; t.uvC = uvC;
+  t.mat = mat;
+  return t;
+}
+
+static void addQuad(std::vector<Triangle>& out, int& idCounter,
+                    const Vec3& p00, const Vec3& p10, const Vec3& p11, const Vec3& p01,
+                    const Material& mat,
+                    bool windingForGivenNormal = true) {
+  Vec2 uv00(0, 0), uv10(1, 0), uv11(1, 1), uv01(0, 1);
+
+  if (windingForGivenNormal) {
+    out.push_back(makeTri(idCounter, p00, p11, p10, uv00, uv11, uv10, mat));
+    out.push_back(makeTri(idCounter, p00, p01, p11, uv00, uv01, uv11, mat));
+  } else {
+    out.push_back(makeTri(idCounter, p00, p10, p11, uv00, uv10, uv11, mat));
+    out.push_back(makeTri(idCounter, p00, p11, p01, uv00, uv11, uv01, mat));
+  }
+}
+
+static void addAxisAlignedBox(std::vector<Triangle>& out, int& idCounter,
+                             const Vec3& bmin, const Vec3& bmax,
+                             const Material& mat) {
+  Vec3 p000(bmin.x, bmin.y, bmin.z);
+  Vec3 p100(bmax.x, bmin.y, bmin.z);
+  Vec3 p110(bmax.x, bmax.y, bmin.z);
+  Vec3 p010(bmin.x, bmax.y, bmin.z);
+
+  Vec3 p001(bmin.x, bmin.y, bmax.z);
+  Vec3 p101(bmax.x, bmin.y, bmax.z);
+  Vec3 p111(bmax.x, bmax.y, bmax.z);
+  Vec3 p011(bmin.x, bmax.y, bmax.z);
+
+  addQuad(out, idCounter, p001, p101, p111, p011, mat, true);   // front  +z
+  addQuad(out, idCounter, p100, p000, p010, p110, mat, true);   // back   -z
+  addQuad(out, idCounter, p000, p001, p011, p010, mat, true);   // left   -x
+  addQuad(out, idCounter, p101, p100, p110, p111, mat, true);   // right  +x
+  addQuad(out, idCounter, p010, p011, p111, p110, mat, true);   // top    +y
+  addQuad(out, idCounter, p000, p100, p101, p001, mat, true);   // bottom -y
+}
+
+struct Camera {
+  Vec3 origin;
+  Triangle viewportWorld0;
+  Triangle viewportWorld1;
+  Triangle2D viewportScreen0;
+  Triangle2D viewportScreen1;
+
+  void render(const std::vector<Triangle>& scene, Image& img, const RenderSettings& settings) const {
+    RenderLayer rootLayer;
+    rootLayer.tint = Vec3(1, 1, 1);
+    rootLayer.alpha = 1.0;
+
+    renderTriangleWithTriangle(scene, origin, viewportWorld0, viewportScreen0, img, 0, settings, rootLayer, -1);
+    renderTriangleWithTriangle(scene, origin, viewportWorld1, viewportScreen1, img, 0, settings, rootLayer, -1);
+  }
+};
+
+int main() {
+  const int W = 800;
+  const int H = 600;
+
+  Image img(W, H);
+  img.clear(Vec3(0.02, 0.02, 0.025));
+
+  RenderSettings settings;
+  settings.maxDepth = 3;
+  settings.minViewportAreaPx = 2.0;
+  settings.minReflectAreaPx = 14.0;
+
+  std::vector<Triangle> scene;
+  scene.reserve(128);
+  int idCounter = 0;
+
+  Material redWall;    redWall.type = MaterialType::Diffuse; redWall.baseColor = Vec3(0.78, 0.16, 0.16);
+  Material greenWall;  greenWall.type = MaterialType::Diffuse; greenWall.baseColor = Vec3(0.16, 0.78, 0.18);
+  Material whiteWall;  whiteWall.type = MaterialType::Diffuse; whiteWall.baseColor = Vec3(0.82, 0.82, 0.82);
+
+  Material metalBlue;   metalBlue.type = MaterialType::Metal; metalBlue.baseColor = Vec3(0.12, 0.35, 1.00); metalBlue.reflectance = 0.85;
+  Material metalYellow; metalYellow.type = MaterialType::Metal; metalYellow.baseColor = Vec3(1.00, 0.86, 0.18); metalYellow.reflectance = 0.85;
+
+  // Cornell Box: x [-1,1], y [0,2], z [0,2]
+  // floor (y=0), normal +y
+  addQuad(scene, idCounter,
+          Vec3(-1, 0, 0), Vec3( 1, 0, 0), Vec3( 1, 0, 2), Vec3(-1, 0, 2),
+          whiteWall, true);
+
+  // ceiling (y=2), normal -y：用反 winding
+  addQuad(scene, idCounter,
+          Vec3(-1, 2, 2), Vec3( 1, 2, 2), Vec3( 1, 2, 0), Vec3(-1, 2, 0),
+          whiteWall, true);
+
+  // back wall (z=2), normal -z
+  addQuad(scene, idCounter,
+          Vec3(-1, 0, 2), Vec3( 1, 0, 2), Vec3( 1, 2, 2), Vec3(-1, 2, 2),
+          whiteWall, false);
+
+  // left wall (x=-1), normal +x
+  addQuad(scene, idCounter,
+          Vec3(-1, 0, 0), Vec3(-1, 0, 2), Vec3(-1, 2, 2), Vec3(-1, 2, 0),
+          redWall, true);
+
+  // right wall (x=1), normal -x
+  addQuad(scene, idCounter,
+          Vec3( 1, 0, 2), Vec3( 1, 0, 0), Vec3( 1, 2, 0), Vec3( 1, 2, 2),
+          greenWall, true);
+
+  // Two metallic boxes (axis-aligned for simplicity)
+  addAxisAlignedBox(scene, idCounter, Vec3(-0.65, 0.0, 0.55), Vec3(-0.10, 0.70, 1.10), metalBlue);
+  addAxisAlignedBox(scene, idCounter, Vec3( 0.10, 0.0, 1.05), Vec3( 0.70, 0.95, 1.70), metalYellow);
+
+  // Camera + viewport (two triangles)
+  Camera cam;
+  cam.origin = Vec3(0.0, 1.0, -3.0);
+
+  Material curtain; curtain.type = MaterialType::Curtain; curtain.baseColor = Vec3(0, 0, 0);
+
+  Vec3 bl(-1.0, 0.0, -1.0);
+  Vec3 br( 1.0, 0.0, -1.0);
+  Vec3 tr( 1.0, 2.0, -1.0);
+  Vec3 tl(-1.0, 2.0, -1.0);
+
+  {
+    Triangle t0;
+    t0.id = -100;
+    t0.a = bl; t0.b = br; t0.c = tl;
+    t0.uvA = Vec2(0, 1); t0.uvB = Vec2(1, 1); t0.uvC = Vec2(0, 0);
+    t0.mat = curtain;
+    cam.viewportWorld0 = t0;
+
+    Triangle t1;
+    t1.id = -101;
+    t1.a = br; t1.b = tr; t1.c = tl;
+    t1.uvA = Vec2(1, 1); t1.uvB = Vec2(1, 0); t1.uvC = Vec2(0, 0);
+    t1.mat = curtain;
+    cam.viewportWorld1 = t1;
+  }
+
+  // Screen triangles cover whole image rectangle
+  Vec2 sbl(0.0, (double)H - 1.0);
+  Vec2 sbr((double)W - 1.0, (double)H - 1.0);
+  Vec2 str((double)W - 1.0, 0.0);
+  Vec2 stl(0.0, 0.0);
+
+  cam.viewportScreen0 = Triangle2D{sbl, sbr, stl};
+  cam.viewportScreen1 = Triangle2D{sbr, str, stl};
+
+  cam.render(scene, img, settings);
+
+  img.writePPM("output.ppm");
+  std::cerr << "Done. Wrote output.ppm\n";
+  return 0;
+}

experiments/rt_orig.cpp

@@ -0,0 +1,291 @@
+#define _USE_MATH_DEFINES
+/*
+ * 基于三角形面片的步进式纹理变换康奈尔盒渲染器（无递归，无AO/反射，仅面片遮挡关系）
+ * 编译: g++ cornell_box_tri_step_transform.cpp -std=c++11 -O2 -o cornell_box_tri
+ * 运行: ./cornell_box_tri
+ */
+
+#include <algorithm>
+#include <cmath>
+#include <cstdio>
+#include <iostream>
+#include <vector>
+
+constexpr float EPS = 1e-6f;
+constexpr float INF = 1e30f;
+
+struct Vec3 {
+	float x, y, z;
+	Vec3(float xx = 0, float yy = 0, float zz = 0) : x(xx), y(yy), z(zz) {
+	}
+	Vec3 operator+(const Vec3 &b) const {
+		return Vec3(x + b.x, y + b.y, z + b.z);
+	}
+	Vec3 operator-(const Vec3 &b) const {
+		return Vec3(x - b.x, y - b.y, z - b.z);
+	}
+	Vec3 operator*(float s) const {
+		return Vec3(x * s, y * s, z * s);
+	}
+	float dot(const Vec3 &b) const {
+		return x * b.x + y * b.y + z * b.z;
+	}
+	Vec3 cross(const Vec3 &b) const {
+		return Vec3(
+			y * b.z - z * b.y,
+			z * b.x - x * b.z,
+			x * b.y - y * b.x);
+	}
+	float length() const {
+		return std::sqrt(x * x + y * y + z * z);
+	}
+	Vec3 normalized() const {
+		float l = length();
+		return (*this) * (1.0f / l);
+	}
+};
+
+struct Color {
+	float r, g, b;
+	Color(float rr = 0, float gg = 0, float bb = 0) : r(rr), g(gg), b(bb) {
+	}
+	Color operator*(float s) const {
+		return Color(r * s, g * s, b * s);
+	}
+	Color operator+(const Color &c) const {
+		return Color(r + c.r, g + c.g, b + c.b);
+	}
+	void clamp() {
+		r = fmaxf(0.0f, fminf(1.0f, r));
+		g = fmaxf(0.0f, fminf(1.0f, g));
+		b = fmaxf(0.0f, fminf(1.0f, b));
+	}
+};
+
+struct Texture {
+	virtual Color at(float u, float v) const = 0;
+	virtual ~Texture() {
+	}
+};
+struct SolidTexture : Texture {
+	Color c;
+	SolidTexture(Color cc) : c(cc) {
+	}
+	Color at(float, float) const override {
+		return c;
+	}
+};
+struct CheckerTexture : Texture {
+	Color a, b;
+	float scale;
+	CheckerTexture(Color c1, Color c2, float s = 10) : a(c1), b(c2), scale(s) {
+	}
+	Color at(float u, float v) const override {
+		int xx = int(floor(u * scale)), yy = int(floor(v * scale));
+		return ((xx + yy) % 2 == 0) ? a : b;
+	}
+};
+struct MetalTexture : Texture {
+	Color tint;
+	MetalTexture(Color tt) : tint(tt) {
+	}
+	Color at(float, float) const override {
+		return tint;
+	}
+};
+
+struct Tri {
+	Vec3 v0, v1, v2;
+	Vec3 n; // 法线
+	Vec3 uv0, uv1, uv2; // uv.xy
+	Texture *tex;
+	Tri(Vec3 a, Vec3 b, Vec3 c, Vec3 t0, Vec3 t1, Vec3 t2, Texture *tx)
+		: v0(a), v1(b), v2(c), uv0(t0), uv1(t1), uv2(t2), tex(tx) {
+		n = (v1 - v0).cross(v2 - v0).normalized();
+	}
+	// 射线相交
+	bool intersect(const Vec3 &o, const Vec3 &d, float &t, float &u, float &v) const {
+		// Moller-Trumbore
+		Vec3 e1 = v1 - v0, e2 = v2 - v0, h = d.cross(e2), s = o - v0;
+		float a = e1.dot(h);
+		if (fabs(a) < EPS)
+			return false;
+		float f = 1.f / a;
+		u = f * s.dot(h);
+		if (u < 0 || u > 1)
+			return false;
+		Vec3 q = s.cross(e1);
+		v = f * d.dot(q);
+		if (v < 0 || u + v > 1)
+			return false;
+		t = f * e2.dot(q);
+		return t > EPS;
+	}
+	// barycentric -> uv
+	void bary2uv(float b0, float b1, float b2, float &u, float &v) const {
+		u = uv0.x * b0 + uv1.x * b1 + uv2.x * b2;
+		v = uv0.y * b0 + uv1.y * b1 + uv2.y * b2;
+	}
+	// 在射线上与面片交点对应的纹理坐标
+	bool texcoord_at_hit(const Vec3 &o, const Vec3 &d, float &t, float &outu, float &outv) const {
+		float uu, vv;
+		if (!intersect(o, d, t, uu, vv))
+			return false;
+		float w = 1 - uu - vv;
+		bary2uv(w, uu, vv, outu, outv);
+		return true;
+	}
+};
+
+struct Camera {
+	Vec3 pos, target, up;
+	float fov;
+	Camera(Vec3 p, Vec3 t, Vec3 u, float f) : pos(p), target(t), up(u), fov(f) {
+	}
+};
+
+// Cornell box三角分割，每个面（矩形）分两个三角
+struct Scene {
+	std::vector<Tri> tris;
+	std::vector<Texture *> textures; // 管理资源释放
+	~Scene() {
+		for (Texture *t : textures)
+			delete t;
+	}
+	Scene() {
+		// 盒体(-1~1)
+		Texture *red = new SolidTexture(Color(0.8, 0.15, 0.15)),
+				*green = new SolidTexture(Color(0.15, 0.8, 0.15)),
+				*white = new SolidTexture(Color(0.8, 0.8, 0.8)),
+				*checker = new CheckerTexture(Color(0.9, 0.9, 0.9), Color(0.1, 0.1, 0.1), 8);
+		textures = { red, green, white, checker };
+
+		// --- 左壁(红)
+		pushQuad(-1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, red);
+		// --- 右壁(绿)
+		pushQuad(1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, green);
+		// --- 地板(棋盘)
+		pushQuad(-1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, checker);
+		// --- 顶
+		pushQuad(-1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, white);
+		// --- 背面(白)
+		pushQuad(-1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, white);
+
+		// 添加一个立方体（中心(-0.4,-0.5,0.2)，尺寸0.4）
+		pushBox(-0.4f, -0.7f, 0.2f, 0.20f, white);
+	}
+	// 面片顶点uv为(0,0),(1,0),(1,1),(0,1)
+	void pushQuad(float x0, float y0, float z0, float x1, float y1, float z1,
+		float x2, float y2, float z2, float x3, float y3, float z3, Texture *t) {
+		tris.emplace_back(Vec3(x0, y0, z0), Vec3(x1, y1, z1), Vec3(x2, y2, z2),
+			Vec3(0, 0, 0), Vec3(1, 0, 0), Vec3(1, 1, 0), t);
+		tris.emplace_back(Vec3(x0, y0, z0), Vec3(x2, y2, z2), Vec3(x3, y3, z3),
+			Vec3(0, 0, 0), Vec3(1, 1, 0), Vec3(0, 1, 0), t);
+	}
+	// 六面体
+	void pushBox(float cx, float cy, float cz, float r, Texture *t) {
+		float x = cx, y = cy, z = cz, s = r;
+		float X[2] = { x - s, x + s }, Y[2] = { y - s, y + s }, Z[2] = { z - s, z + s };
+		// 六面六个pushQuad
+		pushQuad(X[0], Y[0], Z[0], X[1], Y[0], Z[0], X[1], Y[1], Z[0], X[0], Y[1], Z[0], t); // 后
+		pushQuad(X[0], Y[0], Z[1], X[1], Y[0], Z[1], X[1], Y[1], Z[1], X[0], Y[1], Z[1], t); // 前
+		pushQuad(X[0], Y[0], Z[0], X[0], Y[1], Z[0], X[0], Y[1], Z[1], X[0], Y[0], Z[1], t); // 左
+		pushQuad(X[1], Y[0], Z[0], X[1], Y[1], Z[0], X[1], Y[1], Z[1], X[1], Y[0], Z[1], t); // 右
+		pushQuad(X[0], Y[1], Z[0], X[1], Y[1], Z[0], X[1], Y[1], Z[1], X[0], Y[1], Z[1], t); // 上
+		pushQuad(X[0], Y[0], Z[0], X[1], Y[0], Z[0], X[1], Y[0], Z[1], X[0], Y[0], Z[1], t); // 下
+	}
+};
+
+struct Viewport {
+	int w, h;
+	std::vector<Color> pixels;
+	Viewport(int W, int H) : w(W), h(H), pixels(W * H) {
+	}
+	void set(int x, int y, const Color &c) {
+		if (x >= 0 && y >= 0 && x < w && y < h)
+			pixels[y * w + x] = c;
+	}
+	const Color &get(int x, int y) const {
+		return pixels[y * w + x];
+	}
+};
+
+struct Cand {
+	float t; // 距离
+	Color c;
+	Cand(float _t, const Color &_c) : t(_t), c(_c) {
+	}
+};
+bool dist_cmp(const Cand &a, const Cand &b) {
+	return a.t > b.t;
+}
+
+// 主渲染器
+void render(const Scene &scene, const Camera &cam, Viewport &vp) {
+	// 视锥参数
+	Vec3 forward = (cam.target - cam.pos).normalized();
+	Vec3 right = forward.cross(cam.up).normalized();
+	Vec3 up = right.cross(forward);
+	float aspect = 1.0 * vp.w / vp.h;
+	float imagePlaneDist = 1.0;
+	float scale = tanf(cam.fov * 0.5f * M_PI / 180.f) * imagePlaneDist;
+
+	for (int y = 0; y < vp.h; ++y)
+		for (int x = 0; x < vp.w; ++x) {
+			float fx = (2 * (x + 0.5f) / vp.w - 1) * aspect * scale;
+			float fy = (1 - 2 * (y + 0.5f) / vp.h) * scale;
+			Vec3 dir = (forward * imagePlaneDist + right * fx + up * fy).normalized();
+
+			std::vector<Cand> cands;
+			for (const auto &tri : scene.tris) {
+				float t, u, v;
+				if (tri.intersect(cam.pos, dir, t, u, v)) {
+					float w = 1 - u - v, uu, vv;
+					tri.bary2uv(w, u, v, uu, vv);
+					Color col = tri.tex->at(uu, vv);
+					cands.emplace_back(t, col);
+				}
+			}
+			if (cands.empty()) {
+				vp.set(x, y, Color(0, 0, 0));
+				continue;
+			}
+			std::sort(cands.begin(), cands.end(), dist_cmp);
+			Color col = cands.front().c;
+			col.clamp();
+			vp.set(x, y, col);
+		}
+	std::cerr << "Rendered." << std::endl;
+}
+
+void writePPM(const Viewport &vp, const char *fn) {
+	FILE *f = fopen(fn, "wb");
+	fprintf(f, "P6\n%d %d\n255\n", vp.w, vp.h);
+	for (int y = 0; y < vp.h; ++y)
+		for (int x = 0; x < vp.w; ++x) {
+			Color c = vp.get(x, y);
+			c.clamp();
+			unsigned char rr = (unsigned char)(pow(c.r, 1 / 2.2f) * 255);
+			unsigned char gg = (unsigned char)(pow(c.g, 1 / 2.2f) * 255);
+			unsigned char bb = (unsigned char)(pow(c.b, 1 / 2.2f) * 255);
+			fwrite(&rr, 1, 1, f);
+			fwrite(&gg, 1, 1, f);
+			fwrite(&bb, 1, 1, f);
+		}
+	fclose(f);
+}
+
+int main() {
+	int width = 512, height = 512;
+	Scene scene;
+	Camera cam(
+		Vec3(0, 0, 4),
+		Vec3(0, 0, 0),
+		Vec3(0, 1, 0),
+		50.f);
+	Viewport vp(width, height);
+	render(scene, cam, vp);
+	writePPM(vp, "out.ppm");
+	std::cout << "Saved to out.ppm\n";
+	return 0;
+}

include/basic/math.h

@@ -0,0 +1,11 @@
+#ifndef ARE_INCLUDE_BASIC_MATH_H
+#define ARE_INCLUDE_BASIC_MATH_H
+
+namespace are {
+
+// A small epsilon value for geometric calculations
+constexpr double GEOMETRY_EPSILON = 1e-12;
+
+}
+
+#endif

include/basic/plane.h

@@ -0,0 +1,25 @@
+#ifndef ARE_INCLUDE_BASIC_PLANE_H
+#define ARE_INCLUDE_BASIC_PLANE_H
+
+#include <basic/vec3.h>
+#include <basic/ray.h>
+
+namespace are {
+
+// Plane represented in the form: normal * P + d = 0
+struct Plane {
+	Vec3 normal;
+	double d;
+
+	// Constructors
+	Plane() = default;
+	Plane(Vec3 normal_, double d_);
+	Plane(const Point3 &p, const Vec3 &n);
+
+	// Function to check ray-plane intersection.
+	bool intersect_ray(const Ray &ray, Point3 &intersection) const;
+};
+
+}
+
+#endif

include/basic/ray.h

@@ -0,0 +1,22 @@
+#ifndef ARE_INCLUDE_BASIC_RAY_H
+#define ARE_INCLUDE_BASIC_RAY_H
+
+#include <basic/vec3.h>
+
+namespace are {
+
+struct Ray {
+	Point3 Q;
+	Vec3 D;
+
+	// Constructors
+	Ray() = default;
+	Ray(const Point3 &origin, const Vec3 &direction); // direction should be normalized
+
+	// Get point at geometric distance t along the ray
+	Point3 at(double t);
+};
+
+}
+
+#endif

include/basic/vec3.h

@@ -0,0 +1,88 @@
+#ifndef ARE_INCLUDE_BASIC_VEC3_H
+#define ARE_INCLUDE_BASIC_VEC3_H
+
+#include <cmath>
+#include <sys/cdefs.h>
+
+namespace are {
+
+class Vec3 {
+private:
+	double e_[3]; // x, y, z value
+
+public:
+	// Constructors
+	Vec3();
+	Vec3(double e0, double e1, double e2);
+
+	// Copy constructor
+	Vec3(const Vec3 &other);
+
+	// Destructor
+	~Vec3() = default;
+
+	// Component access
+	double *e();
+	double x() const;
+	double y() const;
+	double z() const;
+
+	// Vector operations
+	Vec3 operator-() const; // Negation
+	double operator[](int i) const;
+	double &operator[](int i);
+
+	// Vector assignment
+	Vec3 &operator=(const Vec3 &other);
+
+	// Compound assignment operations
+	Vec3 &operator+=(const Vec3 &v);
+	Vec3 &operator-=(const Vec3 &v);
+	Vec3 &operator*=(double t);
+	Vec3 &operator/=(double t); // Returns invalid vector (NaN) if division by zero
+
+	// Vector length operations
+	double length() const;
+	double length_squared() const;
+
+	// Normalization - returns invalid vector (NaN) if length is zero
+	Vec3 &normalize();
+	Vec3 normalized() const;
+
+	// Dot product
+	double dot(const Vec3 &v) const;
+
+	// Cross product
+	Vec3 cross(const Vec3 &v) const;
+
+	// Check if vector is near zero
+	bool near_zero() const;
+
+	// Friend function declarations
+	friend Vec3 operator+(const Vec3 &u, const Vec3 &v);
+	friend Vec3 operator-(const Vec3 &u, const Vec3 &v);
+	friend Vec3 operator*(const Vec3 &u, const Vec3 &v);
+	friend Vec3 operator*(double t, const Vec3 &v);
+	friend Vec3 operator*(const Vec3 &v, double t);
+	friend Vec3 operator/(const Vec3 &v, double t); // Returns invalid vector (NaN) if division by zero
+};
+
+// Vector operation friend function declarations
+Vec3 operator+(const Vec3 &u, const Vec3 &v);
+Vec3 operator-(const Vec3 &u, const Vec3 &v);
+Vec3 operator*(const Vec3 &u, const Vec3 &v);
+Vec3 operator*(double t, const Vec3 &v);
+Vec3 operator*(const Vec3 &v, double t);
+Vec3 operator/(const Vec3 &v, double t); // Returns invalid vector (NaN) if division by zero
+
+// Utility functions
+Vec3 reflect(const Vec3 &v, const Vec3 &n);
+Vec3 refract(const Vec3 &uv, const Vec3 &n, double etai_over_etat); // Returns invalid vector (NaN) if total internal reflection occurs
+
+// Some other type based on Vec3 class
+using Point3 = Vec3;
+using Color3 = Vec3;
+
+}
+
+#endif

include/material/diffuse.h

@@ -0,0 +1,25 @@
+#ifndef ARE_INCLUDE_MATERIAL_DIFFUSE_H
+#define ARE_INCLUDE_MATERIAL_DIFFUSE_H
+
+#include <basic/vec3.h>
+#include <basic/plane.h>
+#include <material/material.h>
+
+namespace are {
+
+// Diffuse material class, derived from class Material.
+class Diffuse : public Material {
+public:
+	// Constructor to initialize a Diffuse object.
+	Diffuse() = default;
+
+	// Destructors
+	~Diffuse() override = default;
+
+	// Calculate the new viewport origin after reflection.
+	bool reflect(const Plane &viewport_plane, const Point3 &viewport_origin, Point3 &new_viewport_origin) const override;
+};
+
+}
+
+#endif

include/material/material.h

@@ -0,0 +1,33 @@
+#ifndef ARE_INCLUDE_MATERIAL_MATERIAL_H
+#define ARE_INCLUDE_MATERIAL_MATERIAL_H
+
+#include <basic/plane.h>
+#include <basic/vec3.h>
+
+namespace are {
+
+// Material base cass
+class Material {
+protected:
+	// Declare the constructor in protected section.
+	Material() = default;
+
+public:
+	// Constructors
+	Material(const Material &) = delete; // Delete the copy constructor
+	Material &operator=(const Material &) = delete;
+	Material(Material &) = delete; // Delete the move constructor
+	Material &operator=(Material &) = delete;
+
+	// Destructor
+	virtual ~Material();
+
+	// Virtual function interface declaration
+
+	// Calculate the new viewport origin after reflection.
+	virtual bool reflect(const Plane &viewport_plane, const Point3 &viewport_origin, Point3 &new_viewport_origin) const;
+};
+
+}
+
+#endif

include/material/reflective.h

@@ -0,0 +1,29 @@
+#ifndef ARE_INCLUDE_MATERIAL_REFLECTIVE_H
+#define ARE_INCLUDE_MATERIAL_REFLECTIVE_H
+
+#include <basic/vec3.h>
+#include <basic/plane.h>
+#include <material/material.h>
+
+namespace are {
+
+// Reflective material class, derived from class Material.
+class Reflective : public Material {
+public:
+	// Constructor to initialize a Reflective object.
+	Reflective() = delete;
+	Reflective(double reflectivity);
+
+	// Destructors
+	~Reflective() override = default;
+
+	// Calculate the new viewport origin after reflection.
+	bool reflect(const Plane &viewport_plane, const Point3 &viewport_origin, Point3 &new_viewport_origin) const override;
+
+	double reflectivity_;
+private:
+};
+
+}
+
+#endif

include/object/object.h

@@ -0,0 +1,43 @@
+#ifndef ARE_INCLUDE_OBJECT_OBJECT_H
+#define ARE_INCLUDE_OBJECT_OBJECT_H
+
+#include <basic/ray.h>
+#include <basic/vec3.h>
+#include <texture.h>
+
+namespace are {
+
+// The declaration of ObjectSet to avoid circular dependency(forward declaration), please see object_set.h for the detailed definition.
+struct ObjectSet;
+
+// Object base class
+class Object {
+protected:
+	// Declare the constructor in protected section.
+	Object() = default;
+
+public:
+	// Constructors
+	Object(const Object &) = delete; // Delete the copy constructor
+	Object &operator=(const Object &) = delete;
+	Object(Object &) = delete; // Delete the move constructor
+	Object &operator=(Object &) = delete;
+
+	// Destructor
+	virtual ~Object();
+
+	// Virtual function interface declaration
+
+	// Function to check if a point is inside the polygon.
+	virtual bool point_in(const Point3 &point) const;
+
+	// Function to check ray-quad intersection.
+	virtual bool intersect_ray(const Ray &ray, Point3 &hit_point) const;
+
+	// Function to trace texture for polygon objects.
+	virtual Texture trace_texture(const ObjectSet &object_set, const Point3 &viewport_origin_point) const;
+};
+
+}
+
+#endif

include/object/object_set.h

@@ -0,0 +1,16 @@
+#ifndef ARE_INCLUDE_OBJECT_OBJECT_SET_H
+#define ARE_INCLUDE_OBJECT_OBJECT_SET_H
+
+#include <object/object.h>
+#include <object/polygon.h>
+
+namespace are {
+
+// Unified container for all objects.
+struct ObjectSet {
+	std::vector<Polygon *> object_set;
+};
+
+}
+
+#endif

include/object/polygon.h

@@ -0,0 +1,45 @@
+#ifndef ARE_INCLUDE_OBJECT_POLYGON_H
+#define ARE_INCLUDE_OBJECT_POLYGON_H
+
+#include <basic/plane.h>
+#include <basic/ray.h>
+#include <basic/vec3.h>
+#include <material/material.h>
+#include <object/object.h>
+#include <texture.h>
+#include <vector>
+
+namespace are {
+
+// Polygon object class, derived from class Object.
+class Polygon : public Object {
+public:
+	// Constructor to initialize a Polygon object.
+	Polygon() = delete;
+	Polygon(const std::vector<Point3> &vertices, Material *material, Texture *texture);
+
+	// Destructors
+	~Polygon() override = default;
+
+	// Function to check if a point is inside the polygon.
+	bool point_in(const Point3 &point) const override;
+
+	// Function to check ray-polygon intersection.
+	bool intersect_ray(const Ray &ray, Point3 &hit_point) const override;
+
+	// Function to trace texture for polygon objects.
+	Texture trace_texture(const ObjectSet &object_set, const Point3 &viewport_origin_point) const override;
+
+	// Object properties
+	std::vector<Point3> vertices_; // Vertices of the polygon
+	Plane plane_; // The plane that based on
+
+private:
+	// Graphic properties
+	Material *material_;
+	Texture *texture_;
+};
+
+}
+
+#endif

include/texture.h

@@ -0,0 +1,36 @@
+#ifndef ARE_INCLUDE_TEXTURE_H
+#define ARE_INCLUDE_TEXTURE_H
+
+#include <basic/vec3.h>
+#include <string>
+#include <utility>
+
+namespace are {
+
+class Texture {
+public:
+	// Constructors
+	Texture() = default; // Allow default constructor.
+	Texture(const std::string &image_path); // Initialize the image by loading from file (currently support .ppm format).
+	Texture(int width, int height, const Color3 &fill_color); // Initialize the image by filling with a color.
+
+	// Destructor
+	~Texture();
+
+	Color3 &pixel(int x, int y);
+
+	// Paste src_texture into this image with given four corners.
+	void paste(const Texture &src_texture, const std::pair<int, int> &left_top, const std::pair<int, int> &right_top, const std::pair<int, int> &left_bottom, const std::pair<int, int> &right_bottom);
+
+	// Save the texture to a file (currently support .ppm format)
+	bool save_texture(const std::string &file_path) const;
+
+	int width_, height_; // The image width and height.
+
+private:
+	Color3 **image_ = nullptr; // The raw pixel data.
+};
+
+}
+
+#endif

scripts/code_counter.sh

@@ -0,0 +1,407 @@
+#!/usr/bin/env bash
+
+set -uo pipefail
+
+# Colors map
+declare -A COLOR_MAP=(
+	["Cyan"]="\e[36m"
+	["Green"]="\e[32m"
+	["Yellow"]="\e[33m"
+	["Magenta"]="\e[35m"
+	["Blue"]="\e[34m"
+	["Red"]="\e[31m"
+	["White"]="\e[97m"
+	["Gray"]="\e[90m"
+	["DarkYellow"]="\e[33m"
+	["Reset"]="\e[0m"
+)
+
+# Configuration: Type → Extension list, Color
+declare -A TYPE_COLOR
+declare -A TYPE_EXTS
+TYPE_COLOR["C/C++"]="Cyan"
+TYPE_EXTS["C/C++"]='c cpp cc cxx h hpp hh hxx'
+
+TYPE_COLOR["C#"]="Green"
+TYPE_EXTS["C#"]='cs'
+
+TYPE_COLOR["Java"]="Yellow"
+TYPE_EXTS["Java"]='java'
+
+TYPE_COLOR["Python"]="Magenta"
+TYPE_EXTS["Python"]='py pyw'
+
+TYPE_COLOR["JavaScript"]="Blue"
+TYPE_EXTS["JavaScript"]='js jsx ts tsx'
+
+TYPE_COLOR["Web"]="Red"
+TYPE_EXTS["Web"]='html htm css scss less sass'
+
+TYPE_COLOR["Shell"]="White"
+TYPE_EXTS["Shell"]='sh bash ps1 psm1 psd1'
+
+TYPE_COLOR["Config/Data"]="Gray"
+TYPE_EXTS["Config/Data"]='xml json yaml yml ini cfg config'
+
+TYPE_COLOR["Other Code"]="DarkYellow"
+TYPE_EXTS["Other Code"]='go rs rb php swift kt scala'
+
+# Show usage
+show_usage() {
+	printf "Usage: %s [OPTIONS] [DIRECTORY]\n\n" "$(basename "$0")"
+	printf "Options:\n"
+	printf "  -h, --help     Show this help message\n"
+	printf "  -d, --dir DIR  Specify directory to scan\n"
+	printf "\nExamples:\n"
+	printf "  %s                    # Scan current directory\n" "$(basename "$0")"
+	printf "  %s /path/to/project   # Scan specified directory\n" "$(basename "$0")"
+	printf "  %s -d /path/to/project\n" "$(basename "$0")"
+}
+
+# Parse command line arguments
+scan_dir=""
+while [[ $# -gt 0 ]]; do
+	case "$1" in
+		-h|--help)
+			show_usage
+			exit 0
+			;;
+		-d|--dir)
+			if [[ -n "${2:-}" ]]; then
+				scan_dir="$2"
+				shift 2
+			else
+				printf "Error: --dir requires a directory argument\n" >&2
+				exit 1
+			fi
+			;;
+		-*)
+			printf "Error: Unknown option: %s\n" "$1" >&2
+			show_usage
+			exit 1
+			;;
+		*)
+			if [[ -z "$scan_dir" ]]; then
+				scan_dir="$1"
+			else
+				printf "Error: Multiple directories specified\n" >&2
+				exit 1
+			fi
+			shift
+			;;
+	esac
+done
+
+# Default to current directory if not specified
+if [[ -z "$scan_dir" ]]; then
+	scan_dir="$(pwd)"
+fi
+
+# Validate directory
+if [[ ! -d "$scan_dir" ]]; then
+	printf "Error: Directory does not exist: %s\n" "$scan_dir" >&2
+	exit 1
+fi
+
+# Convert to absolute path using readlink or realpath
+if command -v realpath >/dev/null 2>&1; then
+	target_dir="$(realpath "$scan_dir")"
+elif command -v readlink >/dev/null 2>&1 && readlink -f / >/dev/null 2>&1; then
+	target_dir="$(readlink -f "$scan_dir")"
+else
+	# Fallback: use cd + pwd
+	target_dir="$(cd "$scan_dir" && pwd)"
+fi
+
+if [[ -z "$target_dir" || ! -d "$target_dir" ]]; then
+	printf "Error: Cannot resolve directory: %s\n" "$scan_dir" >&2
+	exit 1
+fi
+
+# Build suffix → type mapping (lowercase, without dot)
+declare -A SUFFIX_TYPE
+for t in "${!TYPE_EXTS[@]}"; do
+	for ext in ${TYPE_EXTS[$t]}; do
+		ext_lower="$(printf '%s' "$ext" | tr '[:upper:]' '[:lower:]')"
+		SUFFIX_TYPE["$ext_lower"]="$t"
+	done
+done
+
+# Build regex pattern for find
+# Create a single regex pattern matching all extensions
+all_extensions=()
+for t in "${!TYPE_EXTS[@]}"; do
+	for ext in ${TYPE_EXTS[$t]}; do
+		all_extensions+=("$ext")
+	done
+done
+
+# Title
+printf "%b========================================%b\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+printf "%b       Code Line Counter%b\n" "${COLOR_MAP[Yellow]}" "${COLOR_MAP[Reset]}"
+printf "%b========================================%b\n\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+
+printf "%bScanning directory: %s%b\n\n" "${COLOR_MAP[Gray]}" "$target_dir" "${COLOR_MAP[Reset]}"
+
+# Statistics variables
+total_lines=0
+total_files=0
+declare -A type_files
+declare -A type_lines
+declare -A ext_files
+declare -A ext_lines
+declare -a FILE_INFO_LIST
+start_time_ns=$(date +%s%N)
+
+# Initialize type statistics
+for t in "${!TYPE_EXTS[@]}"; do
+	type_files["$t"]=0
+	type_lines["$t"]=0
+done
+
+printf "%bCollecting files...%b\n" "${COLOR_MAP[Gray]}" "${COLOR_MAP[Reset]}"
+
+# Collect ALL regular files first, then filter by extension
+# This avoids any issues with find's -iname pattern matching
+declare -A SEEN_FILES
+ALL_FILES=()
+
+# Use find to get all files, then filter in bash
+# This is more reliable than multiple find calls with -iname
+while IFS= read -r -d '' file; do
+	# Skip empty
+	[[ -z "$file" ]] && continue
+	
+	# Get filename and extension
+	filename="${file##*/}"
+	
+	# Skip files without extension
+	[[ "$filename" != *.* ]] && continue
+	
+	# Get extension (lowercase, without dot)
+	ext="${filename##*.}"
+	ext_lower="$(printf '%s' "$ext" | tr '[:upper:]' '[:lower:]')"
+	
+	# Check if this extension is in our list
+	if [[ -n "${SUFFIX_TYPE[$ext_lower]+isset}" ]]; then
+		# Deduplicate
+		if [[ -z "${SEEN_FILES["$file"]+isset}" ]]; then
+			SEEN_FILES["$file"]=1
+			ALL_FILES+=("$file")
+		fi
+	fi
+done < <(find "$target_dir" -type f -print0 2>/dev/null)
+
+total_to_process=${#ALL_FILES[@]}
+
+if (( total_to_process == 0 )); then
+	printf "%bNo source code files found!%b\n" "${COLOR_MAP[Red]}" "${COLOR_MAP[Reset]}"
+	printf "%bPlease check if the directory contains source code files.%b\n" "${COLOR_MAP[Gray]}" "${COLOR_MAP[Reset]}"
+	exit 0
+fi
+
+printf "%bFound %d files to process...%b\n\n" "${COLOR_MAP[Gray]}" "$total_to_process" "${COLOR_MAP[Reset]}"
+
+processed=0
+
+pad_right() {
+	local s="$1" w="$2" len=${#1}
+	if (( len < w )); then
+		printf "%s%*s" "$s" $((w-len)) ""
+	else
+		printf "%s" "$s"
+	fi
+}
+
+count_non_empty_lines() {
+	local file="$1"
+	local count
+	count=$(grep -c '[^[:space:]]' "$file" 2>/dev/null) || count=0
+	printf '%d' "$count"
+}
+
+# Statistics loop
+for file in "${ALL_FILES[@]}"; do
+	((processed++))
+	percent=$(( processed * 100 / total_to_process ))
+
+	base="${file##*/}"
+	printf "\rCounting code lines | Processing: %s | Progress: %d / %d | %3d%%" \
+		"$(pad_right "$base" 30)" "$processed" "$total_to_process" "$percent"
+
+	if [[ ! -r "$file" ]]; then
+		printf "\n%b  Warning: Cannot read file %s%b\n" "${COLOR_MAP[Red]}" "$base" "${COLOR_MAP[Reset]}"
+		continue
+	fi
+
+	lines=$(count_non_empty_lines "$file")
+
+	(( total_lines += lines ))
+	(( total_files++ ))
+
+	# Get extension (lowercase, without dot)
+	ext="${base##*.}"
+	ext_lower="$(printf '%s' "$ext" | tr '[:upper:]' '[:lower:]')"
+	suffix=".${ext_lower}"
+
+	t="${SUFFIX_TYPE[$ext_lower]:-}"
+	if [[ -n "$t" ]]; then
+		(( type_files["$t"] += 1 ))
+		(( type_lines["$t"] += lines ))
+
+		ext_key="${t}|${suffix}"
+		(( ext_files["$ext_key"] = ${ext_files["$ext_key"]:-0} + 1 ))
+		(( ext_lines["$ext_key"] = ${ext_lines["$ext_key"]:-0} + lines ))
+
+		file_dir="$(dirname "$file")"
+		file_name="$(basename "$file")"
+		FILE_INFO_LIST+=("${t}|${suffix}|${file_dir}|${file_name}|${lines}")
+	fi
+done
+
+printf "\n"
+
+# Duration
+end_time_ns=$(date +%s%N)
+duration_ns=$(( end_time_ns - start_time_ns ))
+total_ms=$(( duration_ns / 1000000 ))
+mm=$(( (total_ms / 60000) % 60 ))
+ss=$(( (total_ms / 1000) % 60 ))
+ms=$(( total_ms % 1000 ))
+
+# Detailed statistics
+printf "\n%b========================================%b\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+printf "%b         Statistics Details%b\n" "${COLOR_MAP[Yellow]}" "${COLOR_MAP[Reset]}"
+printf "%b========================================%b\n\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+
+types_sorted=()
+while IFS= read -r line; do
+	[[ -n "$line" ]] && types_sorted+=("$line")
+done < <(
+	for t in "${!TYPE_EXTS[@]}"; do
+		if (( ${type_files["$t"]:-0} > 0 )); then
+			printf "%s\t%d\n" "$t" "${type_lines["$t"]}"
+		fi
+	done | sort -k2,2nr | awk -F'\t' '{print $1}'
+)
+
+for t in "${types_sorted[@]}"; do
+	files=${type_files["$t"]}
+	lines=${type_lines["$t"]}
+	if (( files > 0 )); then
+		percent=0
+		if (( total_lines > 0 )); then
+			percent=$(awk -v a="$lines" -v b="$total_lines" 'BEGIN{printf("%.2f", (b>0)?(a*100.0/b):0)}')
+		fi
+		color_name="${TYPE_COLOR[$t]}"
+		color="${COLOR_MAP[$color_name]}"
+		reset="${COLOR_MAP[Reset]}"
+		printf "%b%-15s Files: %4d  Lines: %8d  (%6s%%)%b\n" "$color" "$t" "$files" "$lines" "$percent" "$reset"
+	fi
+done
+
+# Summary
+printf "\n%b========================================%b\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+printf "%bSummary Statistics%b\n" "${COLOR_MAP[Yellow]}" "${COLOR_MAP[Reset]}"
+printf "%b========================================%b\n" "${COLOR_MAP[White]}" "${COLOR_MAP[Reset]}"
+
+printf "%bTotal Files:  %d%b\n" "${COLOR_MAP[Cyan]}" "$total_files" "${COLOR_MAP[Reset]}"
+printf "%bTotal Lines:  %d%b\n" "${COLOR_MAP[Green]}" "$total_lines" "${COLOR_MAP[Reset]}"
+printf "%bProcessed:    %d / %d%b\n" "${COLOR_MAP[Gray]}" "$processed" "$total_to_process" "${COLOR_MAP[Reset]}"
+printf "%bDuration:     %02d:%02d.%03d%b\n" "${COLOR_MAP[Magenta]}" "$mm" "$ss" "$ms" "${COLOR_MAP[Reset]}"
+
+# File size statistics
+total_size_bytes=0
+stat_size() {
+	local f="$1"
+	if stat --version >/dev/null 2>&1; then
+		stat -c %s -- "$f" 2>/dev/null
+	else
+		stat -f %z -- "$f" 2>/dev/null
+	fi
+}
+for f in "${ALL_FILES[@]}"; do
+	if sz=$(stat_size "$f"); then
+		(( total_size_bytes += sz ))
+	fi
+done
+avg_size_bytes=0
+if (( total_files > 0 )); then
+	avg_size_bytes=$(( total_size_bytes / total_files ))
+fi
+to_mb=$(awk -v b="$total_size_bytes" 'BEGIN{printf("%.2f", b/1024/1024)}')
+avg_kb=$(awk -v b="$avg_size_bytes"  'BEGIN{printf("%.2f", b/1024)}')
+
+printf "%bTotal File Size: %s MB%b\n" "${COLOR_MAP[Blue]}" "$to_mb" "${COLOR_MAP[Reset]}"
+printf "%bAverage File Size: %s KB%b\n" "${COLOR_MAP[Blue]}" "$avg_kb" "${COLOR_MAP[Reset]}"
+
+# Export CSV
+printf "\n"
+read -r -p "Export statistics to CSV file? (Y/N) " exportChoice
+if [[ "$exportChoice" == "Y" || "$exportChoice" == "y" ]]; then
+	timestamp="$(date +%Y%m%d_%H%M%S)"
+	csv_path="${target_dir}/code_stats_${timestamp}.csv"
+
+	{
+		# CSV Header for file details
+		printf "Directory,File Name,Language,Extension,Lines\n"
+
+		# Sort by directory -> language -> extension -> filename
+		printf '%s\n' "${FILE_INFO_LIST[@]}" | sort -t'|' -k3,3 -k1,1 -k2,2 -k4,4 | while IFS='|' read -r ftype fsuffix fdir fname flines; do
+			[[ -z "$ftype" ]] && continue
+
+			# Escape fields for CSV
+			escaped_dir="${fdir//\"/\"\"}"
+			escaped_fname="${fname//\"/\"\"}"
+			escaped_type="${ftype//\"/\"\"}"
+			escaped_suffix="${fsuffix//\"/\"\"}"
+
+			printf '"%s","%s","%s","%s",%d\n' \
+				"$escaped_dir" "$escaped_fname" "$escaped_type" "$escaped_suffix" "$flines"
+		done
+
+		printf "\n"
+		printf -- "--- Extension Summary ---\n"
+		printf "Language,Extension,File Count,Line Count,Percentage\n"
+		for t in "${types_sorted[@]}"; do
+			for key in "${!ext_lines[@]}"; do
+				if [[ "$key" == "${t}|"* ]]; then
+					suffix="${key#*|}"
+					ext_file_count=${ext_files["$key"]:-0}
+					ext_line_count=${ext_lines["$key"]:-0}
+					if (( ext_file_count > 0 )); then
+						ext_percent=$(awk -v a="$ext_line_count" -v b="$total_lines" 'BEGIN{printf("%.2f", (b>0)?(a*100.0/b):0)}')
+						escaped_t="${t//\"/\"\"}"
+						escaped_s="${suffix//\"/\"\"}"
+						printf '"%s","%s",%d,%d,%s\n' "$escaped_t" "$escaped_s" "$ext_file_count" "$ext_line_count" "$ext_percent"
+					fi
+				fi
+			done
+		done
+
+		printf "\n"
+		printf -- "--- Language Summary ---\n"
+		printf "Language,File Count,Line Count,Percentage\n"
+		for t in "${types_sorted[@]}"; do
+			files=${type_files["$t"]}
+			lines=${type_lines["$t"]}
+			if (( files > 0 )); then
+				percent=$(awk -v a="$lines" -v b="$total_lines" 'BEGIN{printf("%.2f", (b>0)?(a*100.0/b):0)}')
+				escaped_t="${t//\"/\"\"}"
+				printf '"%s",%d,%d,%s\n' "$escaped_t" "$files" "$lines" "$percent"
+			fi
+		done
+
+		printf "\n"
+		printf -- "--- Total ---\n"
+		printf "Total Files,Total Lines\n"
+		printf "%d,%d\n" "$total_files" "$total_lines"
+
+	} > "$csv_path"
+
+	printf "%bStatistics exported to: %s%b\n" "${COLOR_MAP[Green]}" "$csv_path" "${COLOR_MAP[Reset]}"
+fi
+
+printf "\n%bStatistics complete! Press any key to exit...%b" "${COLOR_MAP[Gray]}" "${COLOR_MAP[Reset]}"
+read -rsn1 _ 2>/dev/null || true
+printf "\n"

src/basic/plane.cpp

@@ -0,0 +1,29 @@
+#include <basic/math.h>
+#include <basic/plane.h>
+#include <cstdlib>
+
+namespace are {
+
+Plane::Plane(Vec3 normal_, double d_) : normal(normal_), d(d_) {
+}
+
+Plane::Plane(const Point3 &p, const Vec3 &n) : normal(n.normalized()), d(-normal.dot(p)) {
+}
+
+bool Plane::intersect_ray(const Ray &ray, Point3 &intersection) const {
+	double denom = normal.dot(ray.D);
+	if (std::abs(denom) < GEOMETRY_EPSILON) {
+		return false;
+	}
+
+	double t = -(normal.dot(ray.Q) + d) / denom;
+	if (t < GEOMETRY_EPSILON) {
+		return false;
+	}
+
+	intersection = ray.Q + t * ray.D;
+
+	return true;
+}
+
+}

src/basic/ray.cpp

@@ -0,0 +1,12 @@
+#include <basic/ray.h>
+
+namespace are {
+
+Ray::Ray(const Point3 &origin, const Vec3 &direction) : Q(origin), D(direction.normalized()) {
+}
+
+Point3 Ray::at(double t) {
+	return Q + D.normalized() * t;
+}
+
+}

src/basic/vec3.cpp

@@ -0,0 +1,201 @@
+#include <basic/vec3.h>
+
+namespace are {
+
+// Default constructor - creates zero vector
+Vec3::Vec3()
+	: e_ { 0, 0, 0 } {
+}
+
+// Parameterized constructor
+Vec3::Vec3(double e0, double e1, double e2)
+	: e_ { e0, e1, e2 } {
+}
+
+// Copy constructor
+Vec3::Vec3(const Vec3 &other)
+	: e_ { other.e_[0], other.e_[1], other.e_[2] } {
+}
+
+// Get e_ array
+double *Vec3::e() {
+	return e_;
+}
+// Get x component
+double Vec3::x() const {
+	return e_[0];
+}
+
+// Get y component
+double Vec3::y() const {
+	return e_[1];
+}
+
+// Get z component
+double Vec3::z() const {
+	return e_[2];
+}
+
+// Negation operator
+Vec3 Vec3::operator-() const {
+	return Vec3(-e_[0], -e_[1], -e_[2]);
+}
+
+// Const index access
+double Vec3::operator[](int i) const {
+	return e_[i];
+}
+
+// Non-const index access
+double &Vec3::operator[](int i) {
+	return e_[i];
+}
+
+// Assignment operator
+Vec3 &Vec3::operator=(const Vec3 &other) {
+	if (this != &other) {
+		e_[0] = other.e_[0];
+		e_[1] = other.e_[1];
+		e_[2] = other.e_[2];
+	}
+	return *this;
+}
+
+// Compound addition assignment
+Vec3 &Vec3::operator+=(const Vec3 &v) {
+	e_[0] += v.e_[0];
+	e_[1] += v.e_[1];
+	e_[2] += v.e_[2];
+	return *this;
+}
+
+// Compound subtraction assignment
+Vec3 &Vec3::operator-=(const Vec3 &v) {
+	e_[0] -= v.e_[0];
+	e_[1] -= v.e_[1];
+	e_[2] -= v.e_[2];
+	return *this;
+}
+
+// Compound multiplication assignment
+Vec3 &Vec3::operator*=(double t) {
+	e_[0] *= t;
+	e_[1] *= t;
+	e_[2] *= t;
+	return *this;
+}
+
+// Compound division assignment - returns invalid vector (NaN) if division by
+// zero
+Vec3 &Vec3::operator/=(double t) {
+	if (t == 0.0) {
+		e_[0] = e_[1] = e_[2] = NAN;
+		return *this;
+	}
+	e_[0] /= t;
+	e_[1] /= t;
+	e_[2] /= t;
+	return *this;
+}
+
+// Calculate vector length
+double Vec3::length() const {
+	return std::sqrt(length_squared());
+}
+
+// Calculate squared vector length
+double Vec3::length_squared() const {
+	return e_[0] * e_[0] + e_[1] * e_[1] + e_[2] * e_[2];
+}
+
+// Normalize this vector - returns invalid vector (NaN) if length is zero
+Vec3 &Vec3::normalize() {
+	double len = length();
+	if (len == 0.0) {
+		e_[0] = e_[1] = e_[2] = NAN;
+		return *this;
+	}
+	*this /= len;
+	return *this;
+}
+
+// Return normalized copy - returns invalid vector (NaN) if length is zero
+Vec3 Vec3::normalized() const {
+	double len = length();
+	if (len == 0.0) {
+		return Vec3(NAN, NAN, NAN);
+	}
+	return *this / len;
+}
+
+// Dot product with another vector
+double Vec3::dot(const Vec3 &v) const {
+	return e_[0] * v.e_[0] + e_[1] * v.e_[1] + e_[2] * v.e_[2];
+}
+
+// Cross product with another vector
+Vec3 Vec3::cross(const Vec3 &v) const {
+	return Vec3(e_[1] * v.e_[2] - e_[2] * v.e_[1], e_[2] * v.e_[0] - e_[0] * v.e_[2],
+		e_[0] * v.e_[1] - e_[1] * v.e_[0]);
+}
+
+// Check if vector is near zero (for floating point precision)
+bool Vec3::near_zero() const {
+	const auto s = 1e-8;
+	return (std::fabs(e_[0]) < s) && (std::fabs(e_[1]) < s) && (std::fabs(e_[2]) < s);
+}
+
+// Vector addition
+Vec3 operator+(const Vec3 &u, const Vec3 &v) {
+	return Vec3(u.e_[0] + v.e_[0], u.e_[1] + v.e_[1], u.e_[2] + v.e_[2]);
+}
+
+// Vector subtraction
+Vec3 operator-(const Vec3 &u, const Vec3 &v) {
+	return Vec3(u.e_[0] - v.e_[0], u.e_[1] - v.e_[1], u.e_[2] - v.e_[2]);
+}
+
+// Component-wise multiplication
+Vec3 operator*(const Vec3 &u, const Vec3 &v) {
+	return Vec3(u.e_[0] * v.e_[0], u.e_[1] * v.e_[1], u.e_[2] * v.e_[2]);
+}
+
+// Scalar multiplication (scalar first)
+Vec3 operator*(double t, const Vec3 &v) {
+	return Vec3(t * v.e_[0], t * v.e_[1], t * v.e_[2]);
+}
+
+// Scalar multiplication (scalar second)
+Vec3 operator*(const Vec3 &v, double t) {
+	return t * v;
+}
+
+// Scalar division - returns invalid vector (NaN) if division by zero
+Vec3 operator/(const Vec3 &v, double t) {
+	if (t == 0.0) {
+		return Vec3(NAN, NAN, NAN);
+	}
+	return (1 / t) * v;
+}
+
+// Reflection vector calculation
+Vec3 reflect(const Vec3 &v, const Vec3 &n) {
+	return v - 2 * v.dot(n) * n;
+}
+
+// Refraction vector calculation - returns invalid vector (NaN) if total
+// internal reflection occurs
+Vec3 refract(const Vec3 &uv, const Vec3 &n, double etai_over_etat) {
+	auto cos_theta = std::fmin((-uv).dot(n), 1.0);
+	Vec3 r_out_perp = etai_over_etat * (uv + cos_theta * n);
+	Vec3 r_out_parallel = -std::sqrt(std::fabs(1.0 - r_out_perp.length_squared())) * n;
+
+	// Check for total internal reflection
+	if (std::isnan(r_out_parallel.length()) || std::isinf(r_out_parallel.length())) {
+		return Vec3(NAN, NAN, NAN);
+	}
+
+	return r_out_perp + r_out_parallel;
+}
+
+} // namespace are

src/material/diffuse.cpp

@@ -0,0 +1,9 @@
+#include <material/diffuse.h>
+
+namespace are {
+
+bool Diffuse::reflect(const Plane &viewport_plane, const Point3 &viewport_origin, Point3 &new_viewport_origin) const {
+	return false;
+}
+
+}

src/material/material.cpp

@@ -0,0 +1,11 @@
+#include <material/material.h>
+
+namespace are {
+
+Material::~Material() = default;
+
+bool Material::reflect(const Plane &viewport_plane, const Point3 &viewport_origin, Point3 &new_viewport_origin) const {
+	return false;
+}
+
+}

src/material/reflective.cpp

@@ -0,0 +1,28 @@
+#include <basic/math.h>
+#include <material/reflective.h>
+
+namespace are {
+
+Reflective::Reflective(double reflectivity) : reflectivity_(reflectivity) {
+}
+
+bool Reflective::reflect(const Plane &viewport_plane, const Point3 &viewport_origin, Point3 &new_viewport_origin) const {
+	// Calculate the denominator
+    double denom = viewport_plane.normal.length_squared();
+    if (denom < GEOMETRY_EPSILON) { // Illegal plane
+        return false; 
+    }
+
+	// Calculate the numerator
+    double numer = viewport_plane.normal.dot(viewport_origin) + viewport_plane.d;
+
+	// Calculate the k value
+    double k = 2.0 * numer / denom;
+
+    // New viewport origin point
+    new_viewport_origin = viewport_origin - k * viewport_plane.normal;
+
+    return true;
+}
+
+}

src/object/object.cpp

@@ -0,0 +1,19 @@
+#include <object/object.h>
+
+namespace are {
+
+Object::~Object() = default;
+
+bool Object::point_in(const Point3 &point) const {
+	return false;
+}
+
+bool Object::intersect_ray(const Ray &ray, Point3 &hit_point) const {
+	return false;
+}
+
+Texture Object::trace_texture(const ObjectSet &object_set, const Point3 &viewport_origin_point) const {
+	return Texture();
+}
+
+}

src/object/polygon.cpp

@@ -0,0 +1,643 @@
+#include <algorithm>
+#include <basic/math.h>
+#include <iostream>
+#include <object/object_set.h>
+#include <object/polygon.h>
+
+namespace are {
+
+Polygon::Polygon(const std::vector<Point3> &vertices, Material *material, Texture *texture) : material_(material), texture_(texture), vertices_(vertices) {
+	// Initialize plane based on vertices.
+	// Assumes the polygon is planar and defined by at least 3 non-collinear vertices.
+	if (vertices_.size() < 3) {
+		// Degenerate polygon: assign default plane to avoid undefined behavior.
+		plane_.normal = Vec3(0, 1, 0);
+		plane_.d = 0;
+		return;
+	}
+
+	// Compute normal using the first three vertices.
+	Vec3 v0 = vertices_[0];
+	Vec3 v1 = vertices_[1];
+	Vec3 v2 = vertices_[2];
+
+	Vec3 u = v1 - v0;
+	Vec3 v = v2 - v0;
+	Vec3 n = u.cross(v);
+
+	double len = n.length();
+	if (len > GEOMETRY_EPSILON) {
+		plane_.normal = n / len;
+	} else {
+		// Degenerate case (collinear points), try to find a valid normal or default
+		plane_.normal = Vec3(0, 0, 0);
+	}
+
+	// Calculate plane constant d: N . P + d = 0 => d = -N . P
+	plane_.d = -plane_.normal.dot(v0);
+}
+
+bool Polygon::point_in(const Point3 &point) const {
+	if (vertices_.size() < 3) {
+		return false;
+	}
+
+	// Step 1: Check if the point lies on the polygon's plane.
+	double dist = plane_.normal.dot(point) + plane_.d;
+	if (std::fabs(dist) > GEOMETRY_EPSILON) {
+		return false;
+	}
+
+	// Step 2: Check if the point is within the polygon boundaries.
+	// Using the same-side method for convex polygons.
+	// The point must be on the same side of all edges defined by the polygon vertices.
+
+	Vec3 n = plane_.normal;
+	int n_verts = vertices_.size();
+
+	// Determine the expected sign of the cross product relative to the normal.
+	// We check the first edge to establish the reference side (or check all against the normal).
+	// Robust approach: Check that all cross products have the same sign (positive or negative) relative to N.
+
+	bool sign_determined = false;
+	bool positive_side = false;
+
+	for (int i = 0; i < n_verts; ++i) {
+		const Point3 &curr = vertices_[i];
+		const Point3 &next = vertices_[(i + 1) % n_verts];
+
+		// Edge vector
+		Vec3 edge = next - curr;
+		// Vector from vertex to point
+		Vec3 vec_to_p = point - curr;
+
+		// Cross product: edge x vec_to_p.
+		// The direction of this vector indicates which side of the edge the point is on.
+		Vec3 cross_prod = edge.cross(vec_to_p);
+
+		// Dot product with polygon normal to get signed distance (scaled)
+		double dot_val = cross_prod.dot(n);
+
+		// If the point is exactly on the edge (within epsilon), the dot_val is close to 0.
+		// Otherwise, we check consistency of the sign.
+		if (std::fabs(dot_val) > GEOMETRY_EPSILON) {
+			if (!sign_determined) {
+				sign_determined = true;
+				positive_side = (dot_val > 0);
+			} else {
+				// If the current sign differs from the reference sign, point is outside.
+				if ((dot_val > 0) != positive_side) {
+					return false;
+				}
+			}
+		}
+	}
+
+	return true;
+}
+
+bool Polygon::intersect_ray(const Ray &ray, Point3 &hit_point) const {
+	// Step 1: Intersect ray with the infinite plane.
+	// Plane equation: N . P + d = 0
+	// Ray equation: P(t) = Q + t * D
+	// Substitute: N . (Q + t * D) + d = 0
+	// Solve for t: t = -(N . Q + d) / (N . D)
+
+	double denom = plane_.normal.dot(ray.D);
+
+	// Check if ray is parallel to the plane.
+	if (std::fabs(denom) < GEOMETRY_EPSILON) {
+		return false;
+	}
+
+	double t = -(plane_.normal.dot(ray.Q) + plane_.d) / denom;
+
+	// Check if intersection is behind the ray origin.
+	if (t < GEOMETRY_EPSILON) {
+		return false;
+	}
+
+	// Calculate the candidate intersection point.
+	Point3 candidate_point = ray.Q + t * ray.D;
+
+	// Step 2: Check if the intersection point lies inside the polygon boundaries.
+	if (point_in(candidate_point)) {
+		hit_point = candidate_point;
+		return true;
+	}
+
+	return false;
+}
+
+static int diguicishu = 0;
+
+Texture Polygon::trace_texture(const ObjectSet &object_set, const Point3 &viewport_origin_point) const {
+	// 1. 拷贝当前纹理的副本作为返回值
+	Texture result(texture_->width_, texture_->height_, Color3(0, 0, 0));
+	for (int y = 0; y < texture_->height_; ++y) {
+		for (int x = 0; x < texture_->width_; ++x) {
+			result.pixel(x, y) = texture_->pixel(x, y);
+		}
+	}
+
+	// 2. 检测当前纹理是否需要处理反射
+	Point3 dummy_new_origin;
+	if (!material_->reflect(plane_, viewport_origin_point, dummy_new_origin) || ++diguicishu >= 10) {
+		// 不需要处理反射，直接返回拷贝的副本
+		return result;
+	}
+
+	// 3. 建立当前Polygon平面的局部2D坐标系
+	Vec3 normal = plane_.normal.normalized();
+
+	// 选择两个正交的基向量 u_axis 和 v_axis
+	Vec3 u_axis, v_axis;
+	if (std::abs(normal.x()) < 0.9) {
+		u_axis = normal.cross(Vec3(1, 0, 0)).normalized();
+	} else {
+		u_axis = normal.cross(Vec3(0, 1, 0)).normalized();
+	}
+	v_axis = normal.cross(u_axis).normalized();
+
+	// 计算当前polygon顶点在平面坐标系中的UV边界（最小包围盒）
+	Point3 plane_origin = vertices_[0];
+	double min_u_self = std::numeric_limits<double>::max();
+	double max_u_self = std::numeric_limits<double>::lowest();
+	double min_v_self = std::numeric_limits<double>::max();
+	double max_v_self = std::numeric_limits<double>::lowest();
+
+	std::vector<std::pair<double, double>> self_uvs;
+	for (const auto &vertex : vertices_) {
+		Vec3 rel = vertex - plane_origin;
+		double u = rel.dot(u_axis);
+		double v = rel.dot(v_axis);
+		self_uvs.push_back({ u, v });
+		min_u_self = std::min(min_u_self, u);
+		max_u_self = std::max(max_u_self, u);
+		min_v_self = std::min(min_v_self, v);
+		max_v_self = std::max(max_v_self, v);
+	}
+
+	double width_self = max_u_self - min_u_self;
+	double height_self = max_v_self - min_v_self;
+
+	// 4. 构建视锥体边界平面（由viewport_origin_point和当前polygon的边组成）
+	std::vector<Plane> frustum_planes;
+	int n_verts = static_cast<int>(vertices_.size());
+
+	// 计算当前polygon的中心点
+	Point3 self_centroid(0, 0, 0);
+	for (const auto &v : vertices_) {
+		self_centroid += v;
+	}
+	self_centroid = self_centroid / static_cast<double>(n_verts);
+
+	for (int i = 0; i < n_verts; ++i) {
+		const Point3 &v1 = vertices_[i];
+		const Point3 &v2 = vertices_[(i + 1) % n_verts];
+
+		// 构建由viewport_origin_point, v1, v2三点确定的平面
+		Vec3 edge = v2 - v1;
+		Vec3 to_v1 = v1 - viewport_origin_point;
+		Vec3 frustum_normal = edge.cross(to_v1);
+
+		if (frustum_normal.near_zero()) {
+			continue; // 退化情况，跳过
+		}
+		frustum_normal.normalize();
+
+		// 确保法向量指向视锥体内部（朝向polygon中心）
+		Vec3 to_centroid = self_centroid - viewport_origin_point;
+		if (frustum_normal.dot(to_centroid) < 0) {
+			frustum_normal = -frustum_normal;
+		}
+
+		frustum_planes.push_back(Plane(viewport_origin_point, frustum_normal));
+	}
+
+	// 添加viewport平面本身（确保物体在viewport的正面）
+	Vec3 view_dir = (self_centroid - viewport_origin_point).normalized();
+	Plane near_plane(viewport_origin_point, view_dir);
+
+	// 5. 遍历object_set，找出与视锥体相交的polygon
+	struct PolygonDistance {
+		Polygon *polygon;
+		double distance;
+		Point3 centroid;
+	};
+	std::vector<PolygonDistance> intersected_polygons;
+
+	for (Polygon *obj : object_set.object_set) {
+		// 跳过自身
+		if (obj == this) {
+			continue;
+		}
+
+		// 计算目标polygon的重心
+		Point3 target_centroid(0, 0, 0);
+		int target_n = static_cast<int>(obj->vertices_.size());
+		for (const auto &v : obj->vertices_) {
+			target_centroid += v;
+		}
+		target_centroid = target_centroid / static_cast<double>(target_n);
+
+		// 检测目标polygon是否与视锥体相交
+		bool intersects = false;
+
+		for (const Point3 &vertex : vertices_) { // 检查原点到当前polygon顶点的射线是否与目标polygon相交
+			Vec3 direction = vertex - viewport_origin_point;
+			if(direction.near_zero()) {
+				continue;
+			}
+			Ray ray(viewport_origin_point, direction);
+			Point3 hit;
+			// std::cout << "Checking hit: " << vertices_.size() << std::endl;
+			// 视锥体原点到viewport当前端点的连线与目标polugon相交
+			if(obj->intersect_ray(ray, hit)) {
+				// std::cout << "HIT!" << std::endl;
+				// 检测hit_point是否在viewport前面
+				double dist_to_hit = (hit - viewport_origin_point).length();
+				double dist_to_vertex = (vertex - viewport_origin_point).length();
+				if(dist_to_hit > dist_to_vertex - GEOMETRY_EPSILON) {
+					intersects = true;
+					break;
+				}
+			}
+		}
+
+		if (!intersects) { // 如果顶点都不在内部，检查从viewport_origin_point到目标顶点的射线是否与当前polygon相交
+			for (const Point3 &vertex : obj->vertices_) {
+				Vec3 dir = vertex - viewport_origin_point;
+				if (dir.near_zero())
+					continue;
+				dir.normalize();
+
+				Ray ray(viewport_origin_point, dir);
+				Point3 hit;
+				if (intersect_ray(ray, hit)) {
+					// 确保目标顶点在hit点之后（相对于viewport_origin_point）
+					double dist_to_hit = (hit - viewport_origin_point).length();
+					double dist_to_vertex = (vertex - viewport_origin_point).length();
+					if (dist_to_vertex > dist_to_hit - GEOMETRY_EPSILON) {
+						intersects = true;
+						break;
+					}
+				}
+			}
+		}
+
+		if (!intersects) { // 检查目标polygon的边是否穿过视锥体
+			for (int i = 0; i < target_n && !intersects; ++i) {
+				const Point3 &edge_start = obj->vertices_[i];
+				const Point3 &edge_end = obj->vertices_[(i + 1) % target_n];
+				Vec3 edge_dir = edge_end - edge_start;
+				double edge_len = edge_dir.length();
+				if (edge_len < GEOMETRY_EPSILON)
+					continue;
+				edge_dir = edge_dir / edge_len;
+
+				Ray edge_ray(edge_start, edge_dir);
+				Point3 plane_hit;
+				if (plane_.intersect_ray(edge_ray, plane_hit)) {
+					double t = (plane_hit - edge_start).dot(edge_dir);
+					if (t > GEOMETRY_EPSILON && t < edge_len - GEOMETRY_EPSILON) {
+						// 交点在边上，检查是否在当前polygon内
+						if (point_in(plane_hit)) {
+							intersects = true;
+						}
+					}
+				}
+			}
+		}
+
+		if (intersects) {
+			double dist = (target_centroid - viewport_origin_point).length();
+			intersected_polygons.push_back({ obj, dist, target_centroid });
+		}
+	}
+
+	std::cout << "Hitted" << intersected_polygons.size() << " polygons." << std::endl;
+
+	// 6. 按距离降序排序（远的先绘制，近的后绘制覆盖）
+	std::sort(intersected_polygons.begin(), intersected_polygons.end(),
+		[](const PolygonDistance &a, const PolygonDistance &b) {
+			return a.distance > b.distance;
+		});
+
+	int i = 0;
+	// 7. 遍历排序后的polygon数组，进行纹理映射
+	for (const auto &pd : intersected_polygons) {
+		Polygon *target_polygon = pd.polygon;
+
+		// 计算目标polygon每个顶点投影到当前平面的UV坐标
+		std::vector<std::pair<double, double>> projected_uvs;
+		bool projection_valid = true;
+
+		for (const Point3 &vertex : target_polygon->vertices_) {
+			Vec3 dir = vertex - viewport_origin_point;
+			if (dir.near_zero()) {
+				projection_valid = false;
+				break;
+			}
+			dir.normalize();
+
+			Ray ray(viewport_origin_point, dir);
+			Point3 intersection;
+			if (!plane_.intersect_ray(ray, intersection)) {
+				projection_valid = false;
+				break;
+			}
+
+			// 检查交点是否在viewport_origin_point和顶点之间的正确方向
+			Vec3 to_intersection = intersection - viewport_origin_point;
+			Vec3 to_vertex = vertex - viewport_origin_point;
+			if (to_intersection.dot(to_vertex) < GEOMETRY_EPSILON) {
+				projection_valid = false;
+				break;
+			}
+
+			// 计算交点的2D UV坐标
+			Vec3 rel = intersection - plane_origin;
+			double u = rel.dot(u_axis);
+			double v = rel.dot(v_axis);
+			projected_uvs.push_back({ u, v });
+		}
+
+		if (!projection_valid || projected_uvs.size() != target_polygon->vertices_.size()) {
+			continue;
+		}
+
+		// 获取反射后的viewport origin（用于递归调用）
+		Point3 reflected_origin;
+		if (!material_->reflect(target_polygon->plane_, viewport_origin_point, reflected_origin)) {
+			continue;
+		}
+
+		// 递归获取目标polygon的纹理
+		Texture target_texture = target_polygon->trace_texture(object_set, reflected_origin);
+		target_texture.save_texture(std::to_string(diguicishu) + "_" + std::to_string(i++) + ".ppm");
+
+		// 计算目标polygon顶点在其自身纹理中的UV坐标（最小包围盒原则）
+		Vec3 target_normal = target_polygon->plane_.normal.normalized();
+		Vec3 target_u_axis, target_v_axis;
+		if (std::abs(target_normal.x()) < 0.9) {
+			target_u_axis = target_normal.cross(Vec3(1, 0, 0)).normalized();
+		} else {
+			target_u_axis = target_normal.cross(Vec3(0, 1, 0)).normalized();
+		}
+		target_v_axis = target_normal.cross(target_u_axis).normalized();
+
+		Point3 target_plane_origin = target_polygon->vertices_[0];
+		double target_min_u = std::numeric_limits<double>::max();
+		double target_max_u = std::numeric_limits<double>::lowest();
+		double target_min_v = std::numeric_limits<double>::max();
+		double target_max_v = std::numeric_limits<double>::lowest();
+
+		std::vector<std::pair<double, double>> target_local_uvs;
+		for (const auto &vertex : target_polygon->vertices_) {
+			Vec3 rel = vertex - target_plane_origin;
+			double u = rel.dot(target_u_axis);
+			double v = rel.dot(target_v_axis);
+			target_local_uvs.push_back({ u, v });
+			target_min_u = std::min(target_min_u, u);
+			target_max_u = std::max(target_max_u, u);
+			target_min_v = std::min(target_min_v, v);
+			target_max_v = std::max(target_max_v, v);
+		}
+
+		double target_width = target_max_u - target_min_u;
+		double target_height = target_max_v - target_min_v;
+
+		if (target_width < GEOMETRY_EPSILON || target_height < GEOMETRY_EPSILON) {
+			continue;
+		}
+
+		// 将目标polygon的局部UV转换为纹理坐标（0到1范围，然后映射到像素）
+		std::vector<std::pair<double, double>> target_tex_coords;
+		for (const auto &uv : target_local_uvs) {
+			double tex_u = (uv.first - target_min_u) / target_width;
+			double tex_v = (uv.second - target_min_v) / target_height;
+			target_tex_coords.push_back({ tex_u, tex_v });
+		}
+
+		// 计算投影多边形的边界框
+		double proj_min_u = std::numeric_limits<double>::max();
+		double proj_max_u = std::numeric_limits<double>::lowest();
+		double proj_min_v = std::numeric_limits<double>::max();
+		double proj_max_v = std::numeric_limits<double>::lowest();
+		for (const auto &uv : projected_uvs) {
+			proj_min_u = std::min(proj_min_u, uv.first);
+			proj_max_u = std::max(proj_max_u, uv.first);
+			proj_min_v = std::min(proj_min_v, uv.second);
+			proj_max_v = std::max(proj_max_v, uv.second);
+		}
+
+		// 裁剪到当前polygon的UV范围
+		proj_min_u = std::max(proj_min_u, min_u_self);
+		proj_max_u = std::min(proj_max_u, max_u_self);
+		proj_min_v = std::max(proj_min_v, min_v_self);
+		proj_max_v = std::min(proj_max_v, max_v_self);
+
+		if (proj_min_u >= proj_max_u || proj_min_v >= proj_max_v) {
+			continue;
+		}
+
+		// 遍历结果纹理的每个像素，进行逆映射
+		for (int py = 0; py < result.height_; ++py) {
+			for (int px = 0; px < result.width_; ++px) {
+				// 将像素坐标转换为当前polygon平面的UV坐标
+				double uv_u = min_u_self + (static_cast<double>(px) + 0.5) / result.width_ * width_self;
+				double uv_v = min_v_self + (static_cast<double>(py) + 0.5) / result.height_ * height_self;
+
+				// 检查该点是否在投影多边形内（使用重心坐标或射线法）
+				// 使用射线法检测点是否在多边形内
+				bool inside_projected = false;
+				int num_projected = static_cast<int>(projected_uvs.size());
+				int crossings = 0;
+				for (int i = 0; i < num_projected; ++i) {
+					const auto &p1 = projected_uvs[i];
+					const auto &p2 = projected_uvs[(i + 1) % num_projected];
+
+					if ((p1.second <= uv_v && p2.second > uv_v) || (p2.second <= uv_v && p1.second > uv_v)) {
+						double t = (uv_v - p1.second) / (p2.second - p1.second);
+						double x_intersect = p1.first + t * (p2.first - p1.first);
+						if (uv_u < x_intersect) {
+							crossings++;
+						}
+					}
+				}
+				inside_projected = (crossings % 2) == 1;
+
+				if (!inside_projected) {
+					continue;
+				}
+
+				// 检查是否在当前polygon内
+				Point3 world_point = plane_origin + uv_u * u_axis + uv_v * v_axis;
+				if (!point_in(world_point)) {
+					continue;
+				}
+
+				// 使用重心坐标进行纹理映射（适用于任意凸多边形）
+				// 对于三角形，使用重心坐标；对于其他多边形，使用广义重心坐标
+
+				// 计算广义重心坐标（Mean Value Coordinates）
+				std::vector<double> weights(num_projected, 0.0);
+				double weight_sum = 0.0;
+				bool on_vertex = false;
+				int vertex_idx = -1;
+				bool on_edge = false;
+				int edge_idx = -1;
+				double edge_t = 0.0;
+
+				for (int i = 0; i < num_projected; ++i) {
+					double dx = projected_uvs[i].first - uv_u;
+					double dy = projected_uvs[i].second - uv_v;
+					double dist = std::sqrt(dx * dx + dy * dy);
+					if (dist < GEOMETRY_EPSILON) {
+						on_vertex = true;
+						vertex_idx = i;
+						break;
+					}
+				}
+
+				if (on_vertex) {
+					// 点在顶点上
+					double tex_x = target_tex_coords[vertex_idx].first * (target_texture.width_ - 1);
+					double tex_y = target_tex_coords[vertex_idx].second * (target_texture.height_ - 1);
+					int src_x = std::clamp(static_cast<int>(tex_x + 0.5), 0, target_texture.width_ - 1);
+					int src_y = std::clamp(static_cast<int>(tex_y + 0.5), 0, target_texture.height_ - 1);
+					result.pixel(px, py) = target_texture.pixel(src_x, src_y);
+					continue;
+				}
+
+				// 检查是否在边上
+				for (int i = 0; i < num_projected && !on_edge; ++i) {
+					const auto &p1 = projected_uvs[i];
+					const auto &p2 = projected_uvs[(i + 1) % num_projected];
+
+					double edge_dx = p2.first - p1.first;
+					double edge_dy = p2.second - p1.second;
+					double edge_len_sq = edge_dx * edge_dx + edge_dy * edge_dy;
+
+					if (edge_len_sq < GEOMETRY_EPSILON * GEOMETRY_EPSILON)
+						continue;
+
+					double t = ((uv_u - p1.first) * edge_dx + (uv_v - p1.second) * edge_dy) / edge_len_sq;
+					if (t < 0.0 || t > 1.0)
+						continue;
+
+					double closest_x = p1.first + t * edge_dx;
+					double closest_y = p1.second + t * edge_dy;
+					double dist_to_edge = std::sqrt((uv_u - closest_x) * (uv_u - closest_x) + (uv_v - closest_y) * (uv_v - closest_y));
+
+					if (dist_to_edge < GEOMETRY_EPSILON) {
+						on_edge = true;
+						edge_idx = i;
+						edge_t = t;
+					}
+				}
+
+				if (on_edge) {
+					// 点在边上，线性插值
+					int i1 = edge_idx;
+					int i2 = (edge_idx + 1) % num_projected;
+					double tex_u_interp = target_tex_coords[i1].first * (1.0 - edge_t) + target_tex_coords[i2].first * edge_t;
+					double tex_v_interp = target_tex_coords[i1].second * (1.0 - edge_t) + target_tex_coords[i2].second * edge_t;
+
+					double tex_x = tex_u_interp * (target_texture.width_ - 1);
+					double tex_y = tex_v_interp * (target_texture.height_ - 1);
+					int src_x = std::clamp(static_cast<int>(tex_x + 0.5), 0, target_texture.width_ - 1);
+					int src_y = std::clamp(static_cast<int>(tex_y + 0.5), 0, target_texture.height_ - 1);
+					result.pixel(px, py) = target_texture.pixel(src_x, src_y);
+					continue;
+				}
+
+				// 使用Mean Value Coordinates计算广义重心坐标
+				for (int i = 0; i < num_projected; ++i) {
+					int prev = (i - 1 + num_projected) % num_projected;
+					int next = (i + 1) % num_projected;
+
+					double dx_i = projected_uvs[i].first - uv_u;
+					double dy_i = projected_uvs[i].second - uv_v;
+					double r_i = std::sqrt(dx_i * dx_i + dy_i * dy_i);
+
+					double dx_prev = projected_uvs[prev].first - uv_u;
+					double dy_prev = projected_uvs[prev].second - uv_v;
+					double r_prev = std::sqrt(dx_prev * dx_prev + dy_prev * dy_prev);
+
+					double dx_next = projected_uvs[next].first - uv_u;
+					double dy_next = projected_uvs[next].second - uv_v;
+					double r_next = std::sqrt(dx_next * dx_next + dy_next * dy_next);
+
+					// 计算角度
+					auto compute_tan_half_angle = [](double dx1, double dy1, double r1,
+													  double dx2, double dy2, double r2) -> double {
+						double dot = dx1 * dx2 + dy1 * dy2;
+						double cross = dx1 * dy2 - dy1 * dx2;
+						double cos_angle = dot / (r1 * r2);
+						cos_angle = std::clamp(cos_angle, -1.0, 1.0);
+						double sin_angle = cross / (r1 * r2);
+						// tan(angle/2) = sin(angle) / (1 + cos(angle))
+						double denom = 1.0 + cos_angle;
+						if (std::abs(denom) < GEOMETRY_EPSILON) {
+							return (sin_angle >= 0) ? 1e10 : -1e10;
+						}
+						return sin_angle / denom;
+					};
+
+					double tan_alpha_prev = compute_tan_half_angle(dx_prev, dy_prev, r_prev, dx_i, dy_i, r_i);
+					double tan_alpha_next = compute_tan_half_angle(dx_i, dy_i, r_i, dx_next, dy_next, r_next);
+
+					weights[i] = (tan_alpha_prev + tan_alpha_next) / r_i;
+					weight_sum += weights[i];
+				}
+
+				if (std::abs(weight_sum) < GEOMETRY_EPSILON) {
+					continue;
+				}
+
+				// 归一化权重并计算插值纹理坐标
+				double interp_tex_u = 0.0;
+				double interp_tex_v = 0.0;
+				for (int i = 0; i < num_projected; ++i) {
+					double normalized_weight = weights[i] / weight_sum;
+					interp_tex_u += normalized_weight * target_tex_coords[i].first;
+					interp_tex_v += normalized_weight * target_tex_coords[i].second;
+				}
+
+				// 将归一化纹理坐标转换为像素坐标
+				double tex_x = interp_tex_u * (target_texture.width_ - 1);
+				double tex_y = interp_tex_v * (target_texture.height_ - 1);
+
+				// 双线性插值采样
+				int x0 = static_cast<int>(std::floor(tex_x));
+				int y0 = static_cast<int>(std::floor(tex_y));
+				int x1 = x0 + 1;
+				int y1 = y0 + 1;
+
+				x0 = std::clamp(x0, 0, target_texture.width_ - 1);
+				x1 = std::clamp(x1, 0, target_texture.width_ - 1);
+				y0 = std::clamp(y0, 0, target_texture.height_ - 1);
+				y1 = std::clamp(y1, 0, target_texture.height_ - 1);
+
+				double fx = tex_x - std::floor(tex_x);
+				double fy = tex_y - std::floor(tex_y);
+
+				Color3 c00 = target_texture.pixel(x0, y0);
+				Color3 c10 = target_texture.pixel(x1, y0);
+				Color3 c01 = target_texture.pixel(x0, y1);
+				Color3 c11 = target_texture.pixel(x1, y1);
+
+				Color3 sampled_color = c00 * (1.0 - fx) * (1.0 - fy) + c10 * fx * (1.0 - fy) + c01 * (1.0 - fx) * fy + c11 * fx * fy;
+
+				// 将采样的颜色写入结果纹理（金属反射直接覆盖）
+				result.pixel(px, py) = sampled_color;
+			}
+		}
+	}
+
+	return result;
+}
+
+}

src/texture.cpp

@@ -0,0 +1,397 @@
+#include <algorithm>
+#include <basic/math.h>
+#include <stdexcept>
+#include <string>
+#include <texture.h>
+
+namespace are {
+
+Texture::Texture(const std::string &image_path) {
+
+	FILE *fp = fopen(image_path.c_str(), "rb");
+	if (!fp) {
+		throw std::runtime_error("Failed to open texture file: " + image_path);
+	}
+
+	// Read PPM header
+	char format[3];
+	if (fscanf(fp, "%2s", format) != 1 || std::string(format) != "P6") {
+		fclose(fp);
+		throw std::runtime_error("Unsupported PPM format in file: " + image_path);
+	}
+	int width, height, max_val;
+	if (fscanf(fp, "%d %d %d", &width, &height, &max_val) != 3 || max_val != 255) {
+		fclose(fp);
+		throw std::runtime_error("Invalid PPM header in file: " + image_path);
+	}
+	fgetc(fp); // Consume the newline after max_val
+	width_ = width, height_ = height; // Set texture dimensions
+
+	// Allocate the memory for the pixel data.
+	// [WARN]: In order to ensure the cache hit rate(we tend to traverse the pixel array by line), the image_ array is allocated with declaration image_[height][width], it means you should access the array by image[y][x].
+	image_ = new Color3 *[height];
+	for (int i = 0; i < height; image_[i] = new Color3[width], ++i)
+		;
+
+	// Read pixel data
+	for (int y = 0; y < height; ++y) {
+		for (int x = 0; x < width; ++x) {
+			unsigned char r, g, b;
+			if (fread(&r, sizeof(unsigned char), 1, fp) != 1 || fread(&g, sizeof(unsigned char), 1, fp) != 1 || fread(&b, sizeof(unsigned char), 1, fp) != 1) {
+				fclose(fp);
+				throw std::runtime_error("Unexpected end of file while reading pixel data in file: " + image_path);
+			}
+			image_[y][x] = Color3(static_cast<double>(r) / 255.0,
+				static_cast<double>(g) / 255.0,
+				static_cast<double>(b) / 255.0);
+		}
+	}
+	fclose(fp);
+}
+
+Texture::Texture(int width, int height, const Color3 &fill_color) : width_(width), height_(height) {
+	if (width <= 0 || height <= 0) {
+		throw std::runtime_error("Texture width and height must be positive.");
+	}
+
+	// Allocate the memory for the pixel data.
+	// [WARN]: In order to ensure the cache hit rate(we tend to traverse the pixel array by line), the image_ array is allocated with declaration image_[height][width], it means you should access the array by image[y][x].
+	image_ = new Color3 *[height];
+	for (int i = 0; i < height; ++i) {
+		image_[i] = new Color3[width];
+		// Fill the image with the specified color.
+		for (int j = 0; j < width; image_[i][j] = fill_color, ++j)
+			;
+	}
+}
+
+Texture::~Texture() {
+	if (!image_) {
+		return;
+	}
+
+	for (int i = 0; i < height_; delete[] image_[i], ++i)
+		;
+}
+
+Color3 &Texture::pixel(int x, int y) {
+	if (!image_) {
+		throw std::runtime_error("Texture is not initialized.");
+	}
+
+	return image_[y][x];
+}
+
+void Texture::paste(const Texture &src_image,
+	const std::pair<int, int> &left_top,
+	const std::pair<int, int> &right_top,
+	const std::pair<int, int> &left_bottom,
+	const std::pair<int, int> &right_bottom) {
+	if (!image_) {
+		throw std::runtime_error("Texture is not initialized.");
+	}
+	if (src_image.width_ <= 0 || src_image.height_ <= 0) {
+		return;
+	}
+
+	struct Pt {
+		double x, y;
+	};
+
+	auto toPt = [](const std::pair<int, int> &p) -> Pt {
+		return Pt {
+			static_cast<double>(p.first),
+			static_cast<double>(p.second)
+		};
+	};
+
+	// Destination quad vertices (consistent order for polygon test)
+	// Note: Given points are LT, RT, LB, RB, but polygon order should be around the boundary.
+	// We'll use: LT -> RT -> RB -> LB (clockwise / counterclockwise both ok for ray casting).
+	Pt quad[4] = {
+		toPt(left_top),
+		toPt(right_top),
+		toPt(right_bottom),
+		toPt(left_bottom),
+	};
+
+	// Compute destination bounding box (in double), then clip to destination image bounds.
+	double min_x_d = std::min({ quad[0].x, quad[1].x, quad[2].x, quad[3].x });
+	double max_x_d = std::max({ quad[0].x, quad[1].x, quad[2].x, quad[3].x });
+	double min_y_d = std::min({ quad[0].y, quad[1].y, quad[2].y, quad[3].y });
+	double max_y_d = std::max({ quad[0].y, quad[1].y, quad[2].y, quad[3].y });
+
+	// If quad's bbox is completely outside destination, nothing to do (robustness).
+	if (max_x_d < 0.0 || max_y_d < 0.0 || min_x_d > static_cast<double>(width_ - 1) || min_y_d > static_cast<double>(height_ - 1)) {
+		return;
+	}
+
+	int x0 = std::max(0, static_cast<int>(std::floor(min_x_d)));
+	int x1 = std::min(width_ - 1, static_cast<int>(std::ceil(max_x_d)));
+	int y0 = std::max(0, static_cast<int>(std::floor(min_y_d)));
+	int y1 = std::min(height_ - 1, static_cast<int>(std::ceil(max_y_d)));
+
+	// Point in polygon test (ray casting, works for convex/concave simple polygons)
+	auto pointInPoly = [](double x, double y, const Pt *poly, int n) -> bool {
+		bool inside = false;
+		for (int i = 0, j = n - 1; i < n; j = i++) {
+			const double xi = poly[i].x, yi = poly[i].y;
+			const double xj = poly[j].x, yj = poly[j].y;
+
+			const bool intersect = ((yi > y) != (yj > y)) && (x < (xj - xi) * (y - yi) / ((yj - yi) == 0.0 ? 1e-30 : (yj - yi)) + xi);
+			inside ^= intersect; // if (intersect) inside = !inside;
+		}
+		return inside;
+	};
+
+	// Build homography from src rectangle corners to dest quad corners.
+	// Src corners in pixel coordinates:
+	// (0,0) -> left_top
+	// (w-1,0) -> right_top
+	// (0,h-1) -> left_bottom
+	// (w-1,h-1) -> right_bottom
+	const double sw = static_cast<double>(src_image.width_);
+	const double sh = static_cast<double>(src_image.height_);
+	const double sx0 = 0.0, sy0 = 0.0;
+	const double sx1 = sw - 1.0, sy1 = 0.0;
+	const double sx2 = 0.0, sy2 = sh - 1.0;
+	const double sx3 = sw - 1.0, sy3 = sh - 1.0;
+
+	const Pt dst0 = toPt(left_top);
+	const Pt dst1 = toPt(right_top);
+	const Pt dst2 = toPt(left_bottom);
+	const Pt dst3 = toPt(right_bottom);
+
+	// Solve A * h = b, where h = [h11 h12 h13 h21 h22 h23 h31 h32]^T, and h33 = 1
+	double A[8][9] = {}; // augmented matrix [A|b]
+
+	auto setEquations = [&](int row, double x, double y, double u, double v) {
+		// x' = (h11 x + h12 y + h13) / (h31 x + h32 y + 1)
+		// y' = (h21 x + h22 y + h23) / (h31 x + h32 y + 1)
+		//
+		// => h11 x + h12 y + h13 - u h31 x - u h32 y = u
+		// => h21 x + h22 y + h23 - v h31 x - v h32 y = v
+		//
+		// Row for x':
+		A[row + 0][0] = x;
+		A[row + 0][1] = y;
+		A[row + 0][2] = 1.0;
+		A[row + 0][3] = 0.0;
+		A[row + 0][4] = 0.0;
+		A[row + 0][5] = 0.0;
+		A[row + 0][6] = -u * x;
+		A[row + 0][7] = -u * y;
+		A[row + 0][8] = u;
+
+		// Row for y':
+		A[row + 1][0] = 0.0;
+		A[row + 1][1] = 0.0;
+		A[row + 1][2] = 0.0;
+		A[row + 1][3] = x;
+		A[row + 1][4] = y;
+		A[row + 1][5] = 1.0;
+		A[row + 1][6] = -v * x;
+		A[row + 1][7] = -v * y;
+		A[row + 1][8] = v;
+	};
+
+	setEquations(0, sx0, sy0, dst0.x, dst0.y);
+	setEquations(2, sx1, sy1, dst1.x, dst1.y);
+	setEquations(4, sx2, sy2, dst2.x, dst2.y);
+	setEquations(6, sx3, sy3, dst3.x, dst3.y);
+
+	// Gaussian elimination with partial pivoting to solve 8x8
+	auto solve8 = [&](double M[8][9], double out[8]) -> bool {
+		for (int col = 0; col < 8; ++col) {
+			// Find pivot
+			int pivot = col;
+			double best = std::fabs(M[col][col]);
+			for (int r = col + 1; r < 8; ++r) {
+				double v = std::fabs(M[r][col]);
+				if (v > best) {
+					best = v;
+					pivot = r;
+				}
+			}
+			if (best < GEOMETRY_EPSILON) {
+				return false;
+			}
+
+			// Swap rows
+			if (pivot != col) {
+				for (int c = col; c < 9; std::swap(M[col][c], M[pivot][c]), ++c)
+					;
+			}
+
+			// Normalize pivot row
+			double div = M[col][col];
+			for (int c = col; c < 9; M[col][c] /= div, ++c)
+				;
+
+			// Eliminate other rows
+			for (int r = 0; r < 8; ++r) {
+				if (r == col) {
+					continue;
+				}
+				double factor = M[r][col];
+				if (std::fabs(factor) < GEOMETRY_EPSILON) {
+					continue;
+				}
+				for (int c = col; c < 9; M[r][c] -= factor * M[col][c], ++c)
+					;
+			}
+		}
+
+		for (int i = 0; i < 8; out[i] = M[i][8], ++i)
+			;
+		return true;
+	};
+
+	double h[8] = {};
+	double A_copy[8][9];
+	for (int r = 0; r < 8; ++r) {
+		for (int c = 0; c < 9; ++c) {
+			A_copy[r][c] = A[r][c];
+		}
+	}
+
+	if (!solve8(A_copy, h)) {
+		// Degenerate mapping
+		return;
+	}
+
+	// Homography H (src -> dst)
+	double H[3][3] = {
+		{ h[0], h[1], h[2] },
+		{ h[3], h[4], h[5] },
+		{ h[6], h[7], 1.0 },
+	};
+
+	// Invert 3x3 matrix
+	auto invert3x3 = [](double M[3][3], double inv[3][3]) -> bool {
+		const double a = M[0][0], b = M[0][1], c = M[0][2];
+		const double d = M[1][0], e = M[1][1], f = M[1][2];
+		const double g = M[2][0], h = M[2][1], i = M[2][2];
+
+		const double A = (e * i - f * h);
+		const double B = -(d * i - f * g);
+		const double C = (d * h - e * g);
+		const double D = -(b * i - c * h);
+		const double E = (a * i - c * g);
+		const double F = -(a * h - b * g);
+		const double G = (b * f - c * e);
+		const double Hc = -(a * f - c * d);
+		const double I = (a * e - b * d);
+
+		const double det = a * A + b * B + c * C;
+		if (std::fabs(det) < GEOMETRY_EPSILON) {
+			return false;
+		}
+
+		const double inv_det = 1.0 / det;
+		inv[0][0] = A * inv_det;
+		inv[0][1] = D * inv_det;
+		inv[0][2] = G * inv_det;
+		inv[1][0] = B * inv_det;
+		inv[1][1] = E * inv_det;
+		inv[1][2] = Hc * inv_det;
+		inv[2][0] = C * inv_det;
+		inv[2][1] = F * inv_det;
+		inv[2][2] = I * inv_det;
+		return true;
+	};
+
+	double Hinv[3][3];
+	if (!invert3x3(H, Hinv)) {
+		return;
+	}
+
+	// Helper: sample src with bilinear interpolation
+	auto sampleBilinear = [&](double x, double y) -> Color3 {
+		// Clamp to valid range
+		x = std::clamp(x, 0.0, sw - 1.0);
+		y = std::clamp(y, 0.0, sh - 1.0);
+
+		int ix = static_cast<int>(std::floor(x));
+		int iy = static_cast<int>(std::floor(y));
+		int ix1 = std::min(ix + 1, src_image.width_ - 1);
+		int iy1 = std::min(iy + 1, src_image.height_ - 1);
+
+		double tx = x - static_cast<double>(ix);
+		double ty = y - static_cast<double>(iy);
+
+		const Color3 &c00 = src_image.image_[iy][ix];
+		const Color3 &c10 = src_image.image_[iy][ix1];
+		const Color3 &c01 = src_image.image_[iy1][ix];
+		const Color3 &c11 = src_image.image_[iy1][ix1];
+
+		// Assume Color3 supports + and * with scalar (common for Vec3/Color classes).
+		return c00 * ((1.0 - tx) * (1.0 - ty)) + c10 * (tx * (1.0 - ty)) + c01 * ((1.0 - tx) * ty) + c11 * (tx * ty);
+	};
+
+	// Iterate only in clipped bounding box, and only pixels inside quad
+	for (int y = y0; y <= y1; ++y) {
+		for (int x = x0; x <= x1; ++x) {
+			// Use pixel center for slightly better quality
+			const double X = static_cast<double>(x) + 0.5;
+			const double Y = static_cast<double>(y) + 0.5;
+
+			if (!pointInPoly(X, Y, quad, 4)) {
+				continue;
+			}
+
+			// Map destination -> source using Hinv
+			const double denom = Hinv[2][0] * X + Hinv[2][1] * Y + Hinv[2][2];
+			if (std::fabs(denom) < GEOMETRY_EPSILON) {
+				continue;
+			}
+
+			const double src_x = (Hinv[0][0] * X + Hinv[0][1] * Y + Hinv[0][2]) / denom;
+			const double src_y = (Hinv[1][0] * X + Hinv[1][1] * Y + Hinv[1][2]) / denom;
+
+			// Only paste if mapped point is inside source image
+			if (src_x < 0.0 || src_y < 0.0 || src_x > sw - 1.0 || src_y > sh - 1.0) {
+				continue;
+			}
+
+			image_[y][x] = sampleBilinear(src_x, src_y);
+		}
+	}
+}
+
+bool Texture::save_texture(const std::string &file_path) const {
+	if (!image_) {
+		throw std::runtime_error("Texture is not initialized.");
+	}
+
+	// Only support PPM format for simplicity.
+	if (file_path.size() < 4 || file_path.substr(file_path.size() - 4) != ".ppm") {
+		return false;
+	}
+
+	FILE *fp = fopen(file_path.c_str(), "wb");
+	if (!fp) {
+		return false;
+	}
+
+	// Write PPM header
+	fprintf(fp, "P6\n%d %d\n255\n", width_, height_);
+
+	// Write pixel data
+	for (int y = 0; y < height_; ++y) {
+		for (int x = 0; x < width_; ++x) {
+			const Color3 &color = image_[y][x];
+			unsigned char r = static_cast<unsigned char>(std::clamp(color.x() * 255.0, 0.0, 255.0));
+			unsigned char g = static_cast<unsigned char>(std::clamp(color.y() * 255.0, 0.0, 255.0));
+			unsigned char b = static_cast<unsigned char>(std::clamp(color.z() * 255.0, 0.0, 255.0));
+			fwrite(&r, sizeof(unsigned char), 1, fp);
+			fwrite(&g, sizeof(unsigned char), 1, fp);
+			fwrite(&b, sizeof(unsigned char), 1, fp);
+		}
+	}
+
+	fclose(fp);
+	return true;
+}
+
+}