Real-Time Ambient Occlusion(AO) Summary

• why can calculate AO separately
  • assumptions
  • deeper mind
• what is AO
  • definition
  • visibility function
  • interreflections
• Precomputed Ambient Occlusion
  • sampling
  • data storage
  • large-scale AO
• Dynamic Computation of Ambient Occlusion
  • 简化模型
  • SDF and cone tracing
  • voxel based
  • screen space accumulation
• Screen-Space Methods
  • screen-space ambient occlusion (SSAO)
  • volumetric based
  • horizon-based ambient occlusion (HBAO)
  • ground-truth ambient occlusion (GTAO)
• Directional Occlusion
  • AO不适用的场景
  • Solutions
    • 非平行光
    • glossy BRDF
    • screen space directional occlusion (SSDO)

why can calculate AO separately

AO的核心思想是把visibility计算和lighting计算分开，降低render equation计算的复杂度。

assumptions

• incident indirect lighting is constant
• diffuse materials

deeper mind

为什么把cos带上，实际是转换成在投影单位圆上的积分

what is AO

definition

• ambient occlusion a cosine-weighted percentage of the unoccluded hemisphere, 半球上的结合cos权重的归一化积分（因为带了cos所以归一化要除以 pi）。
• bent normal 考虑到遮挡关系，如果用a cosine-weighted average of unoccluded light directions作为shading的normal来使用，会得到更加准确的光照计算结果。

visibility function

对于室外，室内等不同场景，visibility function的定义决定了AO的质量和性能。

• ambient obscurance The value of ρ (l) is 0 at an intersection distance of 0 and 1 for any intersection distance greater than a specified distance d_max , or when there is no intersection at all. 就是在某个方向0-d_max范围内对应vis函数的值从1到0过渡。 这个虽然不是physically correct, 但效果已经还不错了，因为限制了d_max，所以性能上也会好很多，但是d_max的值需要人为设定。

interreflections

AO 和 GI 最大的一个不同就是考不考虑物体之间的相互反射。 如果有遮蔽，vis = 0，那就忽略了occluder的reflection，使得有些地方过黑。

• ambient obscurance 可以稍微缓解下这个问题
• 近似考虑interrelfections under diffuse illumination, the surface locations visible from a given location tend to have similar radiance.
• offline path tracing perform full, offline path tracing for a number of scenes, each lit by a uniformly white, infinitely distant environment map to obtain occlusion values. fit cubic polynomials to approximate the function f that maps from the ambient occlusion value k_A and subsurface albedo ρ_ss to the occlusion value k_A′, which is brightened by the interreflected light. 用三次多项式去拟合AO的函数。

Precomputed Ambient Occlusion

基本的思想是基于RT, 适用于静态物。

sampling

• Monte Carlo
• importance sampling the distribution of ray directions is cosine weighted.

data storage

• ambient occlusion field model how the ambient occlusion value changes with distance from the object with a reciprocal of a quadratic polynomial and its coefficients are stored in a cube map.
• ambient occlusion volume 三维贴图，存储ambient occlusion factors, and optionally the bent normal.

large-scale AO

a top-down view and process the resulting depth map to compute large-scale occlusion. 根据neighboring depth samples来计算AO.

Dynamic Computation of Ambient Occlusion

动态物的AO没办法实时用RT的方法去做，需要做一些简化来更快的近似计算出来。

简化模型

• modeling the surface as a collection of disk-shaped elements placed at the mesh vertices 之所以选择disk，是因为disk之间的遮挡关系计算是可控的。
• approximate the occluding geometry as a collection of spheres 个人感觉这两个方法商用起来都有点费劲，还不如直接拿静态物的occluder来用。

SDF and cone tracing

• 最终的occlusion factor = cone tracing过程中的最小立体角 / cone tracing的最初立体角
• a set of cones, covering the entire hemisphere
• global SDF & local SDF

voxel based

voxel GI 的时候顺带做。

screen space accumulation

对于每个object, 给出一个occlusion影响范围，在这个范围内计算物体对每个像素的occlusion影响，转换成 a proper spherical harmonic value is added to an offscreen buffer. After accumulating visibility for all the occluders, the values in the buffer are exponentiated to get the final.

Screen-Space Methods

screen-space ambient occlusion (SSAO)

如果已知normal，可以在半球上做结果更准确。 原算法忽略了cos项，觉得可以以cos的概率去随机选取采样点。

volumetric based

where X is a three-dimensional, spherical neighborhood around the point, 考虑周围三维空间的遮挡关系，利用三维的遮挡体积比例关系计算occlusion factor.

horizon-based ambient occlusion (HBAO)

基于的假设是，the data in the z-buffer represents a continuous heightfield, 连续了才能用角度近似。

本质上是用未被遮挡的立体角除以整个半球的立体角作为occlusion factor.

• W这个attenuation function可以是基于距离的衰减函数。
• t这个角度是该点的切平面和视线的切平面的夹角，那个黑色箭头是视线方向。
• 至于积分可以转换为离散采样等处理之后详细的再说说。

ground-truth ambient occlusion (GTAO)

• 为什么敢号称ground-truth HBAO忽略了(n dot L)项，并且还加了一项ad hoc attenuation. GTAO introduces the missing cosine factor, removes the attenuation function, and formulates the occlusion integral in the reference frame around the view vector.

• basic theory

  

  注意到HBAO的分母是2 pi，但GTAO是pi, 原因就差在一个cos项上。

Directional Occlusion

AO不适用的场景

会议下AO做的假设，就可以看出，AO不适用于

• large area light & punctual light
• glossy BRDF

Solutions

非平行光

light cone 和 visibility cone 求交

glossy BRDF

the approximate BRDF is defined as a sum of spherical Gaussians assume that the visibility function is constant across the entire support of each spherical Gaussian

screen space directional occlusion (SSDO)

采样各个点，如果遮蔽，计算遮蔽处的间接光照。 这样想的话 不是 AO * direct_lighting + DO 才是最终的光照结果。