Computer Graphics, from first principles从第一性原理出发

A linearized tour of the forward problem: given a described virtual world — geometry, materials, lights, a camera — compute the image a sensor there would measure. This is the exact inverse of the Computer Vision track, and the whole field turns out to be one equation pursued under a budget. 一次线性化的旅程，讲的是正向问题：给定一个被描述出来的虚拟世界——几何、材质、光源、一台相机——去计算放在那里的传感器会测到怎样的图像。这正是《计算机视觉》那门课的逆问题；而整个领域，最终都归结为“在预算约束下逼近同一个方程”。

The first-principles frame第一性原理框架

A renderer is a function from a scene to an image. The image is not arbitrary: it is what a virtual camera would measure if that scene were real and lit. So every graphics question reduces to four things, and the rest of the track just fills them in.

渲染器是一个从场景到图像的函数。这张图像并不是随便画出来的：它是——如果这个场景真的存在、真的被点亮——一台虚拟相机会测到的东西。于是所有图形学问题都归结为四件事，整门课不过是把它们逐一填满。

Why this order为什么是这个顺序

The order starts with the measurement, not with a GPU API. We first pin down what an image even is and the two ways to answer "what is visible" (rasterization vs ray tracing). Then we need the math to place things in space (transforms), and something to place (geometry). That gives the real-time path — turn triangles into pixels, interpolate, and fight aliasing. Only then do we earn the physics of light: the rendering equation, how surfaces respond (shading, PBR, materials), the correct global solution (ray and path tracing), and the real-time approximation of it. Motion, the color pipeline at the very end, and the GPU-as-a-system close the loop.

这个顺序从测量开始，而不是从某个 GPU API 开始。我们先弄清“图像到底是什么”，以及回答“什么是可见的”的两条路（光栅化 vs 光线追踪）。接着需要把物体摆进空间的数学（变换），以及可摆的东西（几何）。这就给出了实时路径——把三角形变成像素、做插值、和走样作斗争。到这一步，我们才有资格谈光的物理：渲染方程、表面如何回应光（着色、PBR、材质）、正确的全局解（光线追踪与路径追踪）及其实时近似。最后是运动、末端的色彩管线、以及“作为一套系统的 GPU”，把整条线收口。

The lessons课程目录

How to use this如何使用这门课

1. Read it linearly once. Path tracing assumes the rendering equation. The rendering equation assumes radiometry. Shading assumes visibility. Visibility assumes the transform chain. Skipping breaks the chain. 先按顺序完整读一遍。路径追踪以渲染方程为前提；渲染方程以辐射度量学为前提；着色以可见性为前提；可见性以变换链为前提。跳读会把这条链打断。
2. Always ask "which term of the rendering equation is this?" Every technique — a shadow map, a mipmap, a BRDF, a probe — is an approximation of one piece of that one integral, chosen to fit a budget. 时刻自问“这是渲染方程的哪一项？”每一种技术——阴影贴图、mipmap、BRDF、探针——都是那一个积分中某一块的近似，是为了塞进某个预算而选出来的。
3. Play with every widget. Aliasing, perspective-correct interpolation, importance sampling, and tone mapping are far easier to feel than to read. Each lesson ships exactly one. 把每个交互小控件都玩一遍。走样、透视校正插值、重要性采样、色调映射——这些用手感受远比读文字容易。每一课都恰好配一个。
4. Watch the linear-vs-encoded trap. Half the "why does it look wrong" bugs in graphics are a value that was in the wrong color space. Lesson 14 makes the rule explicit, but it lurks from lesson 05 onward. 盯紧“线性 vs 编码”这个坑。图形学里一半的“为什么看起来不对”都是某个值待在了错误的色彩空间里。第 14 课会把规则讲透，但它从第 05 课起就潜伏着。