11. Global Illumination
11.1 The Rendering Equation
Reflectance Equation（反射方程）
The z-buffer computes it for rays cast from the eye into the scene
An important property of the rendering equation is that it is linear with respect to the emitted lighting.
Primitives are processed and rasterized independently, after which they are discarded. Results of the lighting calculations at point a cannot be accessed when performing calculations at point b.
Transparency, reflections, and shadows are examples of global illumination algorithms. They use information from other objects than the one being illuminated. These effects contribute greatly to increasing the realism in a rendered image, and provide cues that help the viewer to understand spatial relationships. At the same time, they are also complex to simulate and might require precomputations or rendering multiple passes that compute some intermediate information.
“glossy,” meaning shiny but not mirror-like
A basic z-buffer is L(D|S)E, or equivalently, LDE|LSE.
a (distant) specular or diffuse surface that was rendered into the environment map. So, there is an additional potential path: ((S|D)?S|D)E.
to simplify and to precompute
渲染方程里的使用到了raycasting表示，光栅化的z-buffer就是计算从相机出发的光线投射。渲染方程是线性的，入射加倍，着色也会加倍；材质对光线的响应是彼此独立的，所以多个光线的结果可以相加。光栅化中图元之间的处理和光栅化都是独立的，a点的光照计算结果，无法被b点的光照计算过程访问到，这也是全局光照在光栅化实现中的困境。
glossy，表示shiny但并不镜面的材质表面。
渲染方程可以表达为光路路径的正则表达式形式，environment map是（远处）的表面被渲染的结果，结合渲染引擎里envmap的生成方式，就是周围6个面的景色（直接光照），记录了光线路径的第二次弹射（渲染的时候，z-buffer可视的表面是第一次，envmap渲染的是第二次弹射），所以envmap是廉价且高效的全局光照方式。考虑envmap的光路表达是，
全局光照的实现和研究，主要有两个策略，简化和预计算。举个例子，简化：除开光线最后进入相机的那次弹射，其余的弹射都是diffuse的；预计算：使用离线方法把inter-object直接的信息预计算下来；lightmap是bake过程，同时使用了这两个策略。
11.2 General Global Illumination
粗糙度影响反射的清晰度，PathTracing中，一个像素，roughtness更大，导致的采样的范围更大，导致多个采样平均后，更模糊。 - roughness 小 → 方向集中 → 采样颜色相近 → 平均后清晰 - roughness 大 → 方向分散 → 采样颜色多样 → 平均后模糊 这个原理也是预过滤环境贴图（Pre-filtered Environment Map）的基础：
Roughness = 0.0 → 使用原始环境贴图（最清晰的mip level） Roughness = 0.3 → 使用略微模糊的mip level Roughness = 0.7 → 使用高度模糊的mip level Roughness = 1.0 → 使用完全模糊的mip level（接近环境的平均色）
Two common ways of solving the rendering equation are finite element methods and Monte Carlo methods.
11.2.1 Radiosity
11.5 Diffuse Global Illumination
11.5.3 Precomputed Transfer
Spherical Harmonic Lighting: The Gritty Details
Spherical Harmonics