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第二十一节：动态全局光照和 Lumen

Global Illumination (GI)

全局光照

The Rendering Equation

渲染方程

James Kajiya,”The Rendering Equation.” SIGGRAPH 1986. Energy equilibrium:

$L_o(x,\omega_o)=L_e(x,\omega_o)+\int_{H^2}f_r(x,\omega_o,\omega_i)L_i(x,\omega_i)\cos\theta_id\omega_i$

outgoing = emitted + reflected

Radiance and Irradiance 辐射和辐照度

这个方程揭示了渲染的规律。

Global Illumination: Billions of Light Source

全球照明：数十亿光源

然而，要计算渲染方程的积分可不容易，现实生活中的反射有无数次。

Global Illumination is Matter for Gaming

全局照明对游戏很重要

游戏中要加上一个全局照明以近似周围环境反射而来的光照效果。

Monte CarloIntegration

蒙特卡洛一体化

How to solve an integral, when it's too hard to solve it analytically?

当一个积分很难解析求解时，如何求解它？

Approximate integral with the average of randomly sample values

随机样本值平均值的近似积分

Monte Carlo Ray Tracing (Offline)

蒙特卡罗射线追踪（离线）

使用蒙特卡洛算法求解渲染方程中的积分。

Sampling is the Key

采样是关键

Noise decreases as the number of samples per pixel increases. The top left shows 1sample per pixel, and doubles from left to right each square.

噪声随着每像素采样数的增加而降低。左上角显示每个像素 1 个样本，每个方格从左到右加倍。

Sampling : Uniform Sampling

取样：均匀取样

$\begin{aligned} \int_a^bf(x)\mathrm{~d}x& \begin{aligned}&=\lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^{n}f(x_i)(b-a)\end{aligned} \\ &=\lim_{n\to\infty}\frac1n\sum_{i=1}^n\frac{f(x_i)}{\frac1{b-a}} \end{aligned}$

We are doing uniform random sample, so we have factor $\frac{1}{b-a}$ here

我们正在进行均匀随机采样，因此这里有因子 $\frac{1}{b-a}$

Probability Distribution Function

概率分布函数

$\int_a^bf(x)\mathrm{d}x\sim F_n(X)=\frac1n\sum_{k=1}^n\frac{f(X_k)}{PDF(X_k)}$

Probability Distribution Function

概率分布函数

Describes the relative likehood for this random variable to take on a given value

描述此随机变量取给定值的相对可能性
Higher means more possible to be chosen

更高意味着更有可能被选择

Importance Sampling

重要性采样

The PDF can be arbitrary, but which is the best?

PDF 可以是任意的，但哪个是最好的？

Importance Sampling : Best PDF for Rendering?

重要性采样：最佳的 PDF 渲染？

Rendering equation:

渲染方程式：

$L_o\left(p,\omega_o\right)=\int_{\Omega^+}L_i\left(p,\omega_i\right)f_r\left(p,\omega_i,\omega_o\right)\left(n\cdot\omega_i\right)\mathrm{d}\omega_i$
Monte Carlo Integration:

蒙特卡洛积分：

$L_o\left(p,\omega_o\right)\approx\frac{1}{N}\sum_{i=1}^{N}\frac{L_i\left(p,\omega_i\right)f_r\left(p,\omega_i,\omega_o\right)\left(n\cdot\omega_i\right)}{p\left(\omega_i\right)}$
What's our f(x)?

$L_i(p,\omega_i)f_r(p,\omega_i,\omega_o)(n\cdot\omega_i)$
What's our pdf?
- Uniform: $p(\omega_i)=\frac1{2\pi}$
- Other pdf? (cosine-weight, GGX)（余弦权重，GGX）

Importance Sampling : PDF is Matter

重要性采样：PDF 很重要

重要性采样比均匀采样渲染出的效果更好。

Importance Sampling: Cosine and GGX PDF

重要性采样：余弦和 GGX PDF

换一种 PDF 会产生不同的渲染效果。

Reflective Shadow Maps (RSM, 2005)

Let’s inject light in. (Photon Mapping?)

反射阴影贴图（RSM，2005）

让我们注入光线。（光子映射？）

Each pixel on the shadow map is a indirect light source

阴影贴图上的每个像素都是间接光源

How the RSM pixel $X_p$ illuminates position $x$ ?

RSM 像素 $X_p$ 如何照亮位置 $X$ ？

$E_p(x,n)=\phi_p\frac{\max\{0,\langle n_p|x-x_p\rangle\}\max\{0,\langle n|x_p-x\rangle\}}{\|x-x_p\|^4}$

The indirect irradiance at a surface point $x$ can be approximated by summing up the illumination due to all pixel lights.

表面点 $x$ 处的间接辐照度可以通过将所有像素光的照度相加来近似。
Do not consider occlusion.

不要考虑遮挡。

$E(x,n)=\sum_{\text{pixels}p}E_p(x,n)$

Cone Tracing with RSM

使用 RSM 进行锥体追踪

Gathering Indirect Illumination

收集间接照明
- random sampling RSM pixels
  
  随机采样 RSM 像素
- precompute such a sampling pattern and reuse it for all indirect light computations
  
  预先计算这样的采样模式，并将其重新用于所有间接光计算
  - 400samples were sufficient
    
    400 个样本就足够了
  - use Poisson sampling to obtain a more even sample distribution
    
    使用泊松采样获得更均匀的样本分布

Sampling pattern example. The sample density decreases and the sample weights (visualized by the disk radius) increases with the distance to the center.

采样模式示例。随着到中心的距离的增加，样品密度降低，样品重量（通过圆盘半径显示）增加。

Acceleration with Low-Res Indirect Illumination

低分辨率间接照明加速

Compute the indirect illumination for a low resolution image

计算低分辨率图像的间接照明
For each pixel on full resolution:

对于全分辨率的每个像素：
- get its four surrounding low-res samples
  
  获取其四个周围的低分辨率样本
- validate by comparing normal and world space position
  
  通过比较正常空间位置和世界空间位置进行验证
- bi-linear interpolation
  
  双线性插值
Recompute the left (red pixels)

重新计算左侧（红色像素）

Gears of War 4, Uncharted 4, The Last of US, etc.

《战争机器 4》、《神秘海域 4》、“最后的美国”等

Thanks, RSM

Cool Ideas

很酷的想法

Easy to be implemented

易于实施
Photon Injection with RSM

RSM 的光子注入
Cone sampling in mipmap

mipmap 中的圆锥采样
Low-res Indirect illumination with error check

低分辨率间接照明，带错误检查

Cons

缺点

Single bounce

单次反弹
No visibility check for indirect illumination

间接照明不进行能见度检查

Light Propagation Volumes (LPV)

光传播体积（LPV）

First introduced in CryEngine 3（SIGGRAPH 2009）

首次引入 CryEngine 3（SIGGRAPH 2009）

Key Idea

核心思想
- Use a 3D grid to propagate radiance from directly illuminated surfaces to anywhere else
  
  使用 3D 网格将辐射从直接照射的表面传播到其他任何地方

Steps

步骤

Generation of radiance point set scene representation

辐射点集场景表示的生成
Injection of point cloud of virtual light sources into radiance volume

将虚拟光源的点云注入辐射体积

Volumetric radiance propagation

体积辐射传播
Scene lighting with final light propagation volume

具有最终光传播量的场景照明

Reflective shadow map generation → Radiance injection → Radiance propagation → Scene lighting

反射阴影贴图生成→辐射注入→辐射传播→场景照明

“Freeze” the Radiance in Voxel

“冻结”体素中的光芒

Light Injection

光注入

Pre-subdivide the scene into a 3D grid

将场景预细分为 3D 网格
For each grid cell, find enclosed virtual light sources

对于每个网格单元，找到封闭的虚拟光源
Sum up their directional radiance distribution

总结它们的方向辐射分布
Project to first 2 orders of SHs (4 in total)

前 2 个 SH 订单的项目（共 4 个）

Radiance Propagation

辐射传播

For each grid cell, collect the radiance received from each of its 6 faces

对于每个网格单元，收集从其 6 个面中的每一个面接收到的辐射
Sum up, and again use SH to represent

总结一下，再次用 SH 表示
Repeat this propagation several times till the volume becomes stable

重复此传播几次，直到体积稳定

Light with “Limit Speed”？

“限速”灯

Sparse Voxel Octree for Real-time Global Illumination (SVOGI)

稀疏体素八叉树用于实时全局照明（SVOGI）

Voxelization Pass

体素化通行证

Collect Surface Voxels

收集表面体素

Inject Irradiance into voxels from light

从光线向体素中注入辐照度
Filter irradiance inside the octree

八叉树内部的过滤辐照度

Shading with Cone Tracing in Voxel Tree

体素树中的圆锥体跟踪着色

Pass 2 from the camera

从相机中传 2

Emit some cones based on diffuse + specular BRDF

基于漫反射 + 镜面反射 BRDF 发射一些锥体
Query in octree based on the (growing) size of the cone

基于圆锥体（增长）大小的八叉树查询

Voxelization Based Global Illumination (VXGI)

基于体素化的全局照明（VXGI）

Store the voxel data in clipmaps

将体素数据存储在 clipmap 中
- Multi-resolution texture
  
  多分辨率纹理
- Regions near the center have higher spatial resolution
  
  中心附近的区域具有更高的空间分辨率
- Seems to map naturally to cone tracing needs
  
  似乎很自然地映射到锥体跟踪需求
A clipmap is easier to build than SVO

clipmap 比 SVO 更容易构建
- No nodes, pointers etc., handled by hardware
  
  没有由硬件处理的节点、指针等
A clipmap is easier to read from

Clipmap 更容易阅读
Clipmap size is (64…256)^3 with 3…5 levels of detail

Clipmap 大小为（64…256）^3，具有 3…5 个细节级别
- 16…32 bytes per voxel => 12 MB … 2.5 GB of video memory required
  
  每个体素 16…32 字节=>12 MB…需要 2.5 GB 的视频内存

Voxel Update and Toroidal Addressing

体素更新和环形寻址

A fixed point in space always maps to the same address in the clipmap

空间中的固定点总是映射到剪贴图中的同一地址
The background shows texture addresses: frac(worldPos.xy / clipmapSize.xy)

背景显示纹理地址：frac(worldPos.xy / clipmapSize.xy)

Voxelization for Opacity

不透明度的体素化

We have a triangle and a voxel

我们有一个三角形和一个体素
Select the projection plane that yields the biggest projection area

选择产生最大投影面积的投影平面
Rasterize the triangle using MSAA to compute one coverage mask per pixel

使用 MSAA 对三角形进行光栅化，以计算每个像素的一个覆盖掩模
Take the MSAA samples and reproject them onto other planes

采集 MSAA 样本并将其重新投影到其他平面上
Repeat that process for all covered samples

对所有覆盖的样本重复该过程
Thicken the result by blurring all the reprojected samples

通过模糊所有重新投影的样本来增加结果

Voxelization: Directional Coverage

体素化：定向覆盖

Light Injection

光注入

Calculate emittance of voxels that contain surfaces lit by direct lights

计算包含由直射光照亮的表面的体素的发射度
Take information from reflective shadow maps (RSM)

从反射阴影图（RSM）中获取信息

Shading with Cone Tracing

使用圆锥体追踪进行着色

generate several cones based on BRDF

基于 BRDF 生成多个锥体

Accumulate Voxel Radiance and Opacity along the Path

沿路径累积体素辐射度和不透明度

$C_{\mathrm{dst}}\leftarrow C_{\mathrm{dst}}+(1-\alpha_{\mathrm{dst}})C_{\mathrm{src}}\\\alpha_\mathrm{dst}\leftarrow\alpha_\mathrm{dst}+(1-\alpha_\mathrm{dst})\alpha_\mathrm{src}$

Problems in VXGI

VXGI 中的问题

Incorrect Occlusion (opacity)

遮挡不正确（不透明）

naively combine the opacity with alpha blending.

天真地将不透明与阿尔法混合结合起来。

Light Leaking

漏光

when occlusion wall is much smaller than voxel size

当闭塞壁远小于体素尺寸时

Screen Space Global Illumination (SSGI)

屏幕空间全局照明（SSGI）

Advances in Real-Time Rendering- SIGGRAPH 2015 (realtimerendering.com)

General Idea

总体思路

Reuse screen-space data

重复使用屏幕空间数据

Radiance Sampling in Screen Space

屏幕空间中的辐射采样

For each fragment:

对于每个片段：

Step 1: compute many reflection rays

步骤 1：计算许多反射光线
Step 2: march along ray direction (in depth gbuffer)

步骤 2：沿射线方向行进（在深度 gbuffer 中）
Step 3: use color of hit pointas indirect lighting

步骤 3：使用目标点的颜色作为间接照明

Linear Raymarching

线性射线推进

General Steps

一般步骤
- Step forward at a fixed step size
  
  以固定步长向前迈进
- At each step, check depth value
  
  每一步，检查深度值
Features

特征
- Fast
  
  快速
- May skip thin objects
  
  可能跳过薄物体

Hierachical Tracing

层次追踪

Generate min-depth mipmap (pyramid)

生成最小深度 mipmap（金字塔）
Stackless ray walk of min-depth mipmap

最小深度 mipmap 的无堆叠射线行走

level = 0;
while(level > -1)
{
	stepcurrentcell();
    if (above z plane) level++;
    if (below z plane) level--;
}

Ray Reuse among Neighbor Pixels

相邻像素间的光线复用

Store hitpoint data

存储命中点数据
Assume visibility is the same between neighbors

假设邻居之间的能见度相同
Regard ray to neighbor's hitpointas valid

将邻居的 hitpoint 视为有效

Cone Tracing with Mipmap Filtering

基于 Mipmap 滤波的圆锥跟踪

Estimate footprintof a coneat hit point

估算锥形撞击点的足迹

roughness

粗糙度
distance to hit

击中距离

Sample the color mipmap

对彩色 mipmap 进行采样

mip level is determined by footprint

mip 级别由足迹决定

Pre-filter color mipmap (pyramid)

预过滤彩色 mipmap（金字塔）

SSGI Summary

SSGI 总结

Pros:

优点：
- Fast for glossy and specular reflections
  
  快速实现光泽和镜面反射
- Good quality
  
  质量好
- No occlusion issues
  
  无遮挡问题
Cons:

缺点：
- Missing information outside screen
  
  屏幕外信息缺失
- Affects of incorrect visibility of neighbor ray reuse
  
  相邻射线重用可见性不正确的影响

Unique Advantages of SSGI

SSGI 的独特优势

Easy to handle close contact shadow

易于处理近距离接触阴影
Precise hit point calculation

精确的命中点计算
Decouple from scene complexity

与场景复杂性解耦
Handle dynamic objects

处理动态对象

Lumen

Lumen 是一个实时全局光照系统，由 Epic Games 开发，用于其虚幻引擎（Unreal Engine）。它旨在提高游戏和其他实时应用中的光照效果的真实感。Lumen 可以动态地计算光线的传播、反射和折射，无需事先烘焙光照贴图，因此能更好地适应场景的变化，比如光线源的移动或物体的位置改变。它通过实时计算来模拟复杂的光照效果，比如间接光和反射，使得视觉效果更加自然和沉浸。

Ray Traces are slow

光线追踪很慢

Can only afford 1/2 ray per pixel

每像素只能提供 1/2 射线
But quality GI needs hundreds

但高质量的 GI 需要数百个

Sampling is hard

取样很困难

Previous real-time work: Irradiance Fields

以前的实时工作：辐照度场

Problems:

问题：
- Leaking and over-occlusion
  
  渗漏和过度堵塞
- Probe placement
  
  探头放置
- Slow lighting update
  
  照明更新缓慢
- Distinctive flat look
  
  独特的扁平外观

Previous real-time work: Screen Space Denoiser

以前的实时工作：屏幕空间去噪器

Problems:

问题：
- Too noisy in many difficult indoor cases
  
  在许多困难的室内环境中噪音太大
- Noise is not constant.
  
  噪音不是恒定的。

Low-res filtered scene space probes lit full pixels

低分辨率滤波场景空间探测器照亮了全像素

Phase 1 : Fast Ray Trace in Any Hardware

阶段 1：任何硬件中的快速光线追踪

Signed Distance Field (SDF)

签名距离字段（SDF）

What is SDF

The distance to the nearest surface at every point

每个点到最近曲面的距离
Inside regions store negative distance (signed)

内部区域存储负距离（带符号）
Distance = 0 is the surface

距离 = 0 是曲面

Per-Mesh SDF

每网格 SDF

Store SDF of the whole scene is expensive

整个场景的商店 SDF 都很贵

Generated for each mesh

为每个网格生成

Resolution based on mesh size

基于网格大小的分辨率
Embree point query

Embree 积分查询
Trace rays and count triangle back faces for sign ( more than 25% hit back is negative)

追踪光线并计算标志的三角形背面（超过 25% 的回射为负）

Original Mesh

原始网格
Resolution is too low, important features are lost

分辨率太低，重要功能丢失
Resolution has been increased, important features represented

分辨率已提高，重要功能已呈现

SDF for Thin meshes

用于薄网格的 SDF

Half voxel expand to fix leaking

半体素扩展以修复泄漏
Lost contact shadows due to surface bias

表面偏移导致接触阴影丢失
- Over occlusion better than leaking
  
  过度堵塞比泄漏好

Ray Tracing with SDF

使用 SDF 进行光线追踪

Ray intersection skips through empty space based on distance to surface

射线交点根据到曲面的距离跳过空白空间

Safe and fast

安全快捷
Each time at $p$ , just travel $SDF(p)$ distance

每次在 $p$ 时，只需行进 $SDF(p)$ 距离

Cone Tracing with SDF (ie. Soft Shadow)

使用 SDF 进行圆锥体跟踪（即软阴影）

Sparse Mesh SDF

稀疏网格 SDF

Divides the Mesh SDF into bricks

将网格 SDF 划分为块

Define a max_encode_distance

定义 max_encode 距离
- Invalid if ∀ sdf(brick) > max_encode_distance
  
  如果 ∀sdf(brick) > max_encode_distance，则无效
IndirectionTable store the index of each brick

IndirectionTable 存储每块砖的索引

Mesh SDF LoD

网状 SDF LoD

Every frame GPU gathers requests

每一帧 GPU 都会收集请求
CPU download requests and streams pages in/out

CPU 下载请求和流式页面输入/输出
3mips are generated

生成 3 个 MIP
- Lowest resolution always loaded and the other 2streamed
  
  始终加载最低分辨率，其他 2 个分辨率为流式传输

Sparse Mesh SDF

稀疏网格 SDF

Ray Tracing Cost in Real Scene

真实场景中的光线追踪成本

Trace camera rays and visualize the number of steps

追踪相机光线并可视化步数

Many Objects along Each Ray

每条射线上有许多物体

Number of hit objects along each ray

沿每条射线的命中物体数量

Global SDF

全球 SDF

Global SDF is inaccurate near surface

全球 SDF 在地表附近不准确
Sample object SDFs near start of cone, global SDF for the rest

在圆锥体起点附近采样对象 SDF，其余部分为全局 SDF

Ray Tracing with Global SDF

使用全局 SDF 进行光线追踪

Massively reduces tracing cost on overlapping objects

大幅降低重叠对象的跟踪成本

Cache Global SDF around Camera

在相机周围缓存全局 SDF

4 clipmaps centered around camera

4 张以相机为中心的剪贴画
Clipmaps are scrolled with movement

Clipmap 随着移动而滚动
Distant clipmaps updated less frequently

远处的 clipmap 更新频率较低
Also sparsely stored (~16x memory saving)

存储也很稀疏（约节省 16 倍内存）

Phase 2 : Radiance Injection and Caching

阶段 2：辐射注入和缓存

Mesh card –orthogonal camera on 6-Axis Aligned directions

网格卡——6 轴对齐方向上的正交相机

C++

class FLumenCard
{
	FLumenCardOBB LocalOBB;
    FLumenCardOBB WorldOBB;
    uint8 AxisAliqnedDirectionIndex;
}

Generate Surface Cache

生成 Surface 缓存

Two Passes

两个步骤

Pass 1：Card capture

步骤 1：卡捕获

Fix texel budget per frame (512 x 512)

固定每帧的纹理像素预算（512 x 512）
Sort by distance to camera and GPU feedback

按距离相机和 GPU 反馈排序
Capture resultion depends on card projection on screen

捕获结果取决于屏幕上的卡片投影

Pass 2：Copy cards to surface cache and compress

步骤 2：将卡片复制到表面缓存并压缩

4096 x 4096 Surface Cache Atlas

贴图	颜色通道	纹理压缩	缓存大小
Albedo	RGB8	BC7	16mb
Opacity	R8	BC4	8mb
Depth	R16	-	32mb
Normal	Hemisphere RG8	BC4	16mb
Emissive	RGB Float16	BCGH	16mb

compress from 320mb to 88mb

从 320mb 压缩到 88mb

C++

static FLumenSurfaceLayerConfig Configs[(uint32)ELumenSurfaceCacheLayer::MAX]
{
    {TEXT("Depth"), PF_G16, PF_Unknown, PF_Unknown, FVector(1.af,0.0f,0.0f)},
    {TEXT("Albedo"), PF_R8G8B8A8,PF_BC7, PF_R32G32B32A32_UINT, FVector(0.0f,0.0f,0.0f)},
    {TEXT("Opacity"), PF_G8, PF_BC4, PF_R32G32B32A32_UINT, FVector(1.0f,0.0f,0.0f)},
    {TEXT("Normal"), PF_R8G8, PF_BC5, PF_R32G32A32_UINT, FVector(0.0f,0.0f,0.0f)},
    {TEXT("Emissive"), PF_BC4, PF_FloatR11G11B10, PF_BC6H, PF_R32G32B32A32_UINT, FVector(0.0f,0.0f,0.0f)}
};

View Dependent Per-Object Card Resolution

查看每对象卡分辨率

128 x 128 physical pages in a 4096 x 4096 atlas

4096 x 4096 图集中的 128 x 128 个物理页面

Card capture res >= 128 x 128

卡捕获分辨率 >= 128 x 128

Split into multiple 128 x 128 physical pages

拆分为多个 128 x 128 物理页面

Card capture res < 128 x 128

卡捕获分辨率 < 128 x 128

Sub-allocate from a 128 x 128 physical page

从 128 x 128 物理页面进行子分配

How can we "freeze" lighting on Surface Cache

我们如何在 Surface Cache 上“冻结”照明

How to compute lighting on hit?

如何计算命中时的光照？

Is the pixel under the shadow

像素是否位于阴影之下
How can we handle multi-bounce

我们如何处理多次反弹

Lighting Cache Pipeline

照明缓存管道

Direct Lighting

直接照明

Divide 128 x 128 page into 8 x 8 tiles

将 128 x 128 页划分为 8 x 8 个图块
Cull lights with 8 x 8 tile

8 x 8 瓷砖装饰灯
Select first 8 lights per tile

为每块瓷砖选择前 8 盏灯
1bit shadow mask

1bit 荫罩

One tile can be lited by multilights, the result will be accumlated

一块瓷砖可以被多盏灯照亮，结果会累加

Global SDF can't sample surface cache

全局 SDF 无法对曲面缓存进行采样

no per mesh information, only hit position and normal

无网格信息，仅命中位置和正常

Use voxel lighting to sample

使用体素照明进行采样

Voxel Clipmapfor Radiance Caching of the Whole Scene

体素剪贴画用于整个场景的辐射缓存

4 level clipmaps of 64x64x64 voxels

64 x 64 x 64 体素的 4 级剪贴图

Radiance per 6 directions per voxel

每个体素每 6 个方向的辐射
Sample and interpolate 3 directions by normal

通过法线对 3 个方向进行采样和插值
Clipmap0 cover 50m^3, voxel size is 0.78m

Clipmap0 覆盖 50m^3，体素大小为 0.78m
Store in 3D texture

存储在 3D 纹理中

Clipmapupdate frequency rules

剪贴图更新频率规则

	Clipmap 0	Clipmap 1	Clipmap 2	Clipmap 3
Start_Frame	0	1	3	7
Update_interval	2	4	8	8

Build Voxel Faces by Short Ray cast

通过短光线投射构建体素人脸

Trace mesh DF on 6 directions per voxel

在每个体素的 6 个方向上跟踪网格 DF
Hit mesh id and hit distance

命中网格 id 和命中距离
RayStart = VoxelCenter – AxisDir * VoxelRaidus
RayEnd = VoxelCenter + AxisDir * VoxelRaidus

store hit infro intovisibilty buffer uint32 [Hit distance| Hit object id]

将命中信息存储到可见性缓冲区 uint32 [命中距离|命中对象 id]

Filter Most Object Out by 4x4x4 Tiles

通过 4x4x4 瓷砖过滤掉大部分对象

Inject light into clipmap

将光线注入 clipmap

Clear all voxel lighting in entire Clipmap

清除整个 Clipmap 中的所有体素照明
Compact all valid VisBuffer in Clipmap

压缩 Clipmap 中的所有有效 VisBuffer
Sampling FinalLighting from VisBufferand inject lighting

从 VisBuffer 中采样 FinalLighting 并注入照明

Indirect Lighting

间接照明

Place 2 x 2 probes on each tile -each probe cover 4 x 4 texels

在每个瓷砖上放置 2 x 2 个探头，每个探头覆盖 4 x 4 纹理像素
Trace 16 rays from hemisphere per probe

每个探测器追踪 16 条来自半球的射线
Jitter probe placement and ray directions

抖动探头位置和射线方向

Spatial filtering between probes

探头之间的空间滤波
Convert to TwoBandSH (store in half4)

转换为 TwoBandSH（存储在 half4）

Per-Pixel Indirect Lighting with 4 Probe Interpolation

采用 4 探头插值的每像素间接照明

Integrate on pixel -bilinear interpolation of 4 neighbor probes

4 个相邻探针的像素双线性插值集成

Combine Lighting

组合照明

FinalLighting = (DirectLighting + IndirectLighting) * Diffuse_Lambert(Albedo) + Emissive;

Ligting Update Strategy

Ligting 更新策略

Fix budget

固定预算

1024 x 1024 texels for direct lighting

1024 x 1024 像素用于直接照明
512 x 512 texels for indirect lighting

512 x 512 像素用于间接照明
Select pages to update based on Priority = LastUsed-LastUpdated

根据优先级 = 上次使用上次更新选择要更新的页面

Priority queue using bucket sort

使用桶排序的优先级队列

128 buckets

128 桶
Update buckets with priority until reaching budget

优先更新存储桶，直到达到预算

Phase 3: Build a lot of Probes with Different Kinds

第三阶段：构建大量不同类型的探测器

Screen Space Probe

屏幕空间探测器

Octahedral atlas with border

带边框的八面体图集

Typically 8 x 8 per probe

通常每个探头 8 x 8
Uniformly distributed world space directions

均匀分布的世界空间方向
Neighbors have matching directions

邻居有匹配的方向

Radiance and HitDistance in 2d atlas

二维图谱中的辐射度和 HitDistance

Octahedron mapping

八面体映射

C++

float2 unitVectorTo0ctahedron(float3 N)
{
    N.xy /= dot(1, abs(N));
    if(N.z<= 0)
    {
    	x_factor = N.x >= 0 ? 1.0 : -1.0;
        y_factor = N.y >= 0 ? 1.0 : -1.0;
        N.xy = (1 - abs(N.yx)) * float2(x_factor, y_factor);
    return float2(N.xy);
}

Screen Probe Placement

屏幕探头放置

Adaptive placement with Hierarchical Refinement

具有层次细化的自适应布局
Iteratively place where interpolation fails

迭代地放置插值失败的位置

Plane distance weighting of Probe Interpolation

探针插值的平面距离加权

Detect Non-Interpolatable Cases

检测不可插值的案例

C++

float4 PlaneDistances;
PlaneDistances.x = abs(dot(float4(Position00, -1), ScenePlane));
PlaneDistances.y = abs(dot(float4(Position10, -1), ScenePlane));
PlaneDistances.z = abs(dot(float4(Position01, -1), ScenePlane));
PlaneDistances.w = abs(dot(float4(Position11, -1), ScenePlane));
 
float4 RelativeDepthDifference = PlaneDistances / SceneDepth;
 
Depthweights = CornerDepths > 0 ? exp2(-10000. 0f * (RelativeDepthDifference * RelativeDepthDifference)) : 0;
 
InterpolationWeights = float4(
    (1-BilinearWeights.y) * (1-BilinearWeights.x),
    (1-BilinearWeights.y) * BilinearWeights.x,
    BilinearWeights.y * (1 - BilinearWeights.x),
    BilinearWeights.y * BilinearWeights.x);
InterpolationWeights *= DepthWeights;
 
float Epsilon = .01f;
ScreenProbeSample.Weights /= max(dot(ScreenProbeSample.Weights, 1), Epsilon);
float LightingIsValid = (dot(ScreenProbeSample.Weights, .1) < 1.0f - Epsilon) ? 0.0f : 1.0f.

Screen Probe Atlas

屏幕探针图谱

Atlas have upper limit for real-time

Atlas 有实时上限
Place adaptive probes at the bottom of the atlas

将自适应探头放置在图谱底部

Screen Probe Jitter

屏幕探头抖动

Place probedirectly on pixels

将探测器直接放置在像素上
Temporally jitter placement and direction

时间抖动位置和方向
Use Hammersley points in [0, 15]

在 [0,15] 中使用 Hammersley 积分

Importance Sampling

重要性采样

But too much noise at ½ ray per pixel

但每像素 ½ 射线的噪声太大

Better sampling -importance sample incoming lighting and BRDF

更好的采样-重要样本输入照明和 BRDF

$\lim_{N\to\infty}\frac1N\sum_{k=1}^N\frac{L_i(l)f_s(l\to v)\cos(\theta l)}{P_k}$

We would like to distribute rays proportional to the integrand

我们希望光线的分布与被积函数成正比

How can we estimate these?

我们如何估算这些？

Approximate Radiance Importance from Last Frame Probes

最后一帧探测器的近似辐射重要性

Incoming Radiance:

入射辐射：

Reproject to last frame and average the four neighboring Screen Probes Radiance

重新投影到最后一帧，并对四个相邻的屏幕探头辐射进行平均
No need to do an expensive search, as rays already indexed in octahedral atlas

无需进行昂贵的搜索，因为光线已经在八面体图集中索引
Fallback to World Space Probe Radiance ifneighboring probes are occluded

如果相邻探测器被遮挡，则回退到世界空间探测器辐射

Accumulate Normal Distribution Nearby

附近累积正态分布

BRDF:

For a probe that’s placed on a flat wall, about half of its spherehaving a zero BRDF

对于放置在平坦墙壁上的探头，其球体的大约一半具有零 BRDF
Accumulate from pixels that will use this Screen Probe

从将使用此屏幕探测器的像素中累积

Nearby Normal Accumulation

附近正常堆积

Gathter 64 neighbor pixels around current probe's pixel in a 32 x 32 pixelrange

在 32 x 32 像素范围内收集当前探头像素周围的 64 个相邻像素
Acceptpixel if its depth weight > 0.1

如果像素的深度权重 > 0.1，则接受像素
Accumulate these pixels' world normal into SH

将这些像素的世界法线累积到 SH 中

Structured Importance Sampling

结构化重要性抽样

Assigns a small number of samples to hierarchically structured areas of the Probability Density Function (PDF)

将少量样本分配给概率密度函数的分层结构区域（PDF）
Achieves good global stratification

实现良好的全球分层
Sample placement requires offline algorithm

样本放置需要离线算法

Maps perfectly to Octahedral mip quadtree!

完美映射到八面体 mip 四叉树！

Fix Budget Importance Sampling based on Lighting and BRDF

基于照明和 BRDF 的固定预算重要性抽样

Start with uniformly distributed probe ray directions

从均匀分布的探头射线方向开始
Fixed probe tracing ray count = 64

固定探头跟踪射线计数 = 64
Calculate BRDF PDF * Lighting PDF for each Octahedral texel

计算每个八面体纹理的 BRDF * Lighting PDF
Sort rays by PDF from low to high

按 PDF 从低到高对光线进行排序
For every 3 rays with PDF below cull threshold, supersample the matching highest PDF ray

对于 PDF 低于剔除阈值的每 3 条射线，对匹配的最高 PDF 射线进行超采样

{% div subfields %}

{% div subfield %}

{% enddiv %}

{% div subfield %}

{% enddiv %}

右边是使用 BRDF 和 Lighting PDF 的效果。

Denoising and Spatial Probe Filtering

去噪和空间探测滤波

Denoise: Spatial filtering for Probe

去噪：探头的空间滤波

Large spatial filter for cheap

大空间滤波器，成本低

Each probe cover 16 x 16 pixels, 3 x 3 filtering kernelin probe space equals 48 x 48 inscreen space

每个探头覆盖 16 x 16 像素，探头空间中的 3 x 3 滤波核等于屏幕空间中的 48 x 48

Can ignore normal differences between spatial neighbors

可以忽略空间邻居之间的正常差异

Only depth weighting

仅深度加权

C++

float GetFilterPositionWeight(floatProbeDepth, float sceneDepth)
{
    float DepthDifference = abs(ProbeDepth - SceneDepth);
    float RelativeDepthDifference = DepthDifference / sceneDepth;
    return ProbeDepth >= 0 ? exp2(-spatialFilterPositionweightscale * (RelativeDepthDifference * RelativeDepthDifference)) : 0;
}

Denoise: Gather Radiance from neighbors

降噪：从邻居那里收集辐射

Gather radiance from matching Octahedral cell in neighbor probes

在相邻探针中收集匹配八面体细胞的辐射

Error weighting:

错误加权：

Angle error from reprojected neighbor ray hits (less than 10 degree)

重新投影的相邻光线照射的角度误差（小于 10 度）
Filters distant lighting, preserves local shadowing

过滤远距离照明，保留局部阴影

Clamp Distance Mismatching

夹紧距离不匹配

Angle error biases toward distant light = leaking

角度误差偏向远光 = 泄漏

Distant light has no parallax and never gets rejected

远光没有视差，永远不会被拒绝

Solution: clamp neighbor hit distance to our own before reprojection

解决方案：在重新投影之前，将邻居的击中距离限制在我们自己的距离

World Space Probes and Ray Connecting

世界空间探测器和射线连接

World Space Radiance Cache

世界空间辐射缓存

Problem: distant lighting

问题：远距离照明

Noise from small bright feature increases with distance

小亮特征的噪声随着距离的增加而增加
Long incoherent traces are slow

长的非相干痕迹很慢
Distant lighting is changing slowly -opportunity to cache

远距离照明变化缓慢——缓存机会
Redundant operations for nearby Screen Probes

附近屏幕探头的冗余操作

Solution: separate sampling for distant Radiance

解决方案：对远距离辐射进行单独采样

World space Radiance Caching for distant lighting

用于远距离照明的世界空间辐射缓存
Stable error since world space -easy to hide

自世界空间以来的稳定错误-易于隐藏

Placement

4 level clipmaps around camera

相机周围的 4 级 clipmap
default resolution is 48^3

默认分辨率为 48^3
clipmap0size is 50m^3

clipmap0 的大小为 50m^3

Radiance

32 x 32 atlas a per probe

每 32 x 32 的区域放置一个探头

Connecting rays

连接射线

How to connect Screen Probe ray and World Probe ray

如何连接 Screen Probe ray 和 World Probe ray

World Probe ray must skip the interpolation footprint

World Probe 射线必须跳过插值足迹

Screen Probe ray must cover interpolation footprint + skipped distance

屏幕探测光线必须覆盖插值足迹 + 跳过距离

Problem: leaking!

问题：泄漏！
World probe radiance should have been occluded

世界探测器的辐射应该被遮挡了
- But wasn’t due to incorrect parallax
  
  但不是因为视差不正确

Solution: simple sphere parallax

解决方案：简单球面视差
Reproject Screen Probe ray intersection with World Probe sphere

重新投影屏幕探头射线与 World Probe 球体的交点

Placement and caching

放置和缓存

Mark any position that we will interpolate from later in clipmap indirections

标记我们稍后将在 clipmap 间接中插入的任何位置
For each marked world probe:

对于每个标记的世界探测器：
- Reuse traces from last frame, or allocate new probe index
  
  重用上一帧的跟踪，或分配新的探测索引
- Re-trace a subset of cache hits to propagate lighting changes
  
  重新跟踪缓存命中的子集以传播照明变化

Place Peobes → Reuse existing probe traces → Generate rays → Trace → Probe space filtering

放置探针 → 重复使用现有的探针痕迹 → 生成射线 → 痕迹 → 探针空间过滤

Without World Space Probes

没有世界空间探针

Screen Radiance Cache for the first 2meters

前 2 米的屏幕辐射缓存
World Radiance Cache for any lighting further than that.

World Radiance Cache 适用于任何超出此范围的照明。