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Lecture 18 Advance Topics in Rendering

Advanced Light Transport

Advanced Light Transport

  • Unbiased light transport methods
    • Bidirectional path tracing (BDPT)
    • Metropolis light transport (MLT)
  • Biased light transport methods
    • Photon mapping
    • Vertex connection and merging (VCM)
  • Instant radiosity (VPL / many light methods)

Biased vs. Unbiased Monte Carlo Estimators

  • An unbiased Monte Carlo technique does not have any systematic error
    • The expected value of an unbiased estimator will always be the correct value, no matter how many samples are used
    • 估计出的结果的期望永远都是我们要的真实值
  • Otherwise, biased
    • One special case, the expected value converges to the correct value as infinite #samples are used - consistent
    • 估计出的结果的期望和真实值不同
  • An easier understanding bias in rendering
    • Biased == blurry
    • Consistent == not blurry with infinite #samples

Bidirectional Path Tracing (BDPT)

  • Name: 双向路径追踪

  • Recall: a path connects the camera and the light （生成一些半路径）

    • Traces sub-paths from both the camera and the light
    • Connects the end points from both sub-paths

  • Pros

    • Suitable if the light transport is complex on the light’s side
    • unbiased
  • Cons
    • Difficult to implement
    • quite slow

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  • 双向路径追踪好的原因：因为对于这个场景而言，从摄像机出发做 Path Tracing 第一个打到的地方是 diffuse 的表面，这就导致了之后的路径不容易到达能量集中的区域
  • 而双向路径追踪适用于光线在光源处容易算的情况

Metropolis Light Transport (MLT)

  • 思想：使用统计学上的马克可夫链（根据当前的样本生成一个和它靠近的下一个样本）做采样工具
  • A Markov Chain Monte Carlo (MCMC) application
    • Jumping from the current sample to the next with some PDF
  • Very good at locally exploring difficult light paths
  • Key idea: Locally perturb an existing path to get a new path

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  • Pros
    • Works great with difficult light paths
    • 找到一条光线作为种子，可以在它周围找到其他的光线
    • unbiased
  • Cons
    • Difficult to estimate the convergence rate （收敛速率，也就是渲染速度难以分析）
    • Does not guarantee equal convergence rate per pixel
    • usually produces “dirty” results
    • usually not used to render animations

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Photon Mapping

  • A biased approach & A two-stage method
  • Very good at handling Specular-Diffuse-Specular (SDS) paths and generating caustics
    • caustics: 由于光线的聚焦产生的非常强的一些图案，例如水面的波纹

Approach (variations apply)

  • Stage 1 — photon tracing
    • Emitting photons from the light source, bouncing them around, then recording photons on diffuse surfaces（当光子打到 diffuse 的物体后停下）

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  • Stage 2 — photon collection (final gathering)
    • Shoot sub-paths from the camera, bouncing them around, until they hit diffuse surfaces （当 sub-paths 打到 diffuse 的物体后停下）
  • Calculation — local density estimation
    • Idea: areas with more photons should be brighter
    • For each shading point, find the nearest \(N\) photons. Take the surface area they over
    • 计算光子的密度

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Why biased?

  • Local Density estimation \(dN / dA \ne ΔN / ΔA\)
  • But in the sense of limit
    • More photons emitted \(\to\) the same \(N\) photons covers a smaller \(ΔA\) \(\to\) \(ΔA\) is closer to \(dA\) （So, biased but consistent!）
  • Why not do a “const range” search for density estimation?
    • More photons emitted \(\to\) in the same const range will have more photons \(\to\) \(ΔA\) is not closer to \(dA\) （So, biased and not consistent!）

Vertex Connection and Merging

  • 结合双向路径追踪和光子映射
  • Key idea
    • Let’s not waste the sub-paths in BDPT if their end points cannot be connected but can be merged
    • Use photon mapping to handle the merging of nearby “photons”

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Instant Radiosity (IR)

  • Sometimes also called many-light approaches
  • Key idea
    • Lit surfaces can be treated as light sources（已经被照亮的面也可以被认为是光源，生成 VPL 之后，使用直接光照就行）
  • Approach
    • Shoot light sub-paths and assume the end point of each sub-path is a Virtual Point Light (VPL)
    • Render the scene as usual using these VPLs

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  • Pros: fast and usually gives good results on diffuse scenes
  • Cons
    • Spikes will emerge when VPLs are close to shading points （在窄的缝隙和接缝出有问题）
    • Cannot handle glossy materials

Advanced Appearance Modeling

  • Non-surface models

    • Participating media
    • Hair / fur / fiber (BCSDF)
    • Granular material

  • Surface models

    • Translucent material (BSSRDF)
    • Cloth
    • Detailed material (non-statistical BRDF)
  • Procedural appearance

Non-Surface Models

Participating Media

  • Participating Media（散射介质）: Fog, Cloud, Hair(考虑光线和一根曲线的作用)
    • 不在表面上而是在空间中
  • At any point as light travels through a participating medium, it can be (partially) absorbed and scattered.

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  • Use Phase Function to describe the angular distribution of light scattering at any point x within participating media
    • 决定光线如何散射

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Participating Media: Rendering

  • Randomly choose a direction to bounce
  • Randomly choose a distance to go straight
  • At each ‘shading point’, connect to the light

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Hair Appearance

Kajiya-Kay Model
  • 只考虑反射

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Marschner Model
  • 考虑三种光线与头发圆柱的作用
    • R: 光线被头发表面反射
    • TT: 光线进入头发从头发另一侧折射出
    • TRT: 光线从头发底面被反射，从入射一侧折射出

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Fur Appearance — As Human Hair

  • Cannot represent diffusive and saturated appearance

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  • 动物的 medulla size 大
Double Cylinder Model

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Granular Material

  • 颗粒材质

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Surface Models

Translucent Material

  • translucent: 光线可以从一个地方进入物体，从另外一个面钻出
  • like: Jade, Jellyfish

Subsurface Scattering

  • Visual characteristics of many surfaces caused by light exiting at different points than it enters
  • 对 BRDF 的延申：从一个点进来，从另外一个其他点出去

Scattering Functions

  • BSSRDF: generalization of BRDF; exitant radiance at one point due to incident differential irradiance at another point:
\[ S\left(x_i, \omega_i, x_o, \omega_o\right) \]
  • Generalization of rendering equation: integrating over all points on the surface and all directions (!)
\[ L\left(x_o, \omega_o\right)=\int_A \int_{H^2} S\left(x_i, \omega_i, x_o, \omega_o\right) L_i\left(x_i, \omega_i\right) \cos \theta_i \mathrm{~d} \omega_i \mathrm{~d} A \]

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  • Approximate light diffusion by introducing two point sources.

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  • Example

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Cloth

  • A collection of twisted fibers!
  • Two levels of twist

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  • Woven or knitted

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  • Render as Surface
    • Given the weaving pattern, calculate the overall behavior
    • Render using a BRDF

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  • Render as Participating Media
    • Properties of individual fibers & their distribution \(\to\) scattering parameters
    • Render as a participating medium

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  • Render as Actual Fibers
    • Render every fiber explicitly!

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Detailed Appearance: Motivation

  • 真实世界中的物体是有瑕疵的，描述方法得到的方法过于完美，所以显得不真实
  • 可以在物体渲染时手动加入瑕疵

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Recap: Microfacet BRDF

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Difficult path sampling problem

  • 微表面反射的光线反射不到摄像机上

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Solution: BRDF over a pixel

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Recent Trend: Wave Optics

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Procedural Appearance

  • 定义三维的纹理：\(f(x,y,z)\) 查询得到纹理
  • define details without textures
    • Compute a noise function on the fly
    • 3D noise \(\to\) internal structure if cut or broken
Last update: July 30, 2023
Created: June 16, 2023