Real-Time Polygonal-Light Shading with Linearly Transformed Cosines

实时多边形用线性变换余弦光影

Eric Heitz, Jonathan Dupuy, Stephen Hill and David Neubelt

ACM SIGGRAPH 2016

美国计算机协会 国际图形学大会 2016

Motivation 动力因素

Shading with area lights adds a great deal of realism to CG renders. However, it requires solving spherical equations that make it challenging for real-time rendering. In this project, we develop a new spherical distribution that allows us to shade physically based materials with polygonal lights in real-time.

阴影和区域光对CG增添了大量逼真渲染。然而，它需要解决的球面方程，使它具有挑战性的实时渲染。在这个项目中，我们开发了一个新的球形分布，使我们能够基于物理材质的实时多边形光。

Why is polygonal-light shading complicated? 为什么多边形光着色复杂？

Shading with polygonal lights requires integrating the BRDF over the polygonal domain covered by the light.

阴影与多边形光需要结合BRDF在光所涵盖的多边形区域。

 

Despite polygonal lights being theoretically one of the simplest lighting models, they are challenging in real-time rendering for two main reasons:

尽管多边形光在理论上是最简单的照明模式，他们在实时渲染具有挑战性的两个主要原因：

• Problem 1: Integrating parametric spherical distributions over spherical
  polygons is difficult in general, even with the simplest distributions.

• Problem 2: State-of-the-art physically based material models are not simple distributions; they have sophisticated shapes with anisotropic stretching and skewness that need to be represented for the material to appear realistic.

• 问题1：结合球形分布参数在球形多边形上一般是困难的，即使最简单的分布。

• 问题2：先进的基于物理的材质模型不是简单的分布；他们向异性拉伸和偏斜度的复杂的形状，需要材质呈现起来更真实。

Linearly Transformed Cosines 线性变换余弦

To overcome these problems, we introduce Linearly Transformed Cosines (LTCs), a new kind of spherical distribution that covers a wide variety of spherical shapes and can be analytically integrated over arbitrary polygons.

为了克服这些问题，我们引入线性变换余弦（LTCS），一种新型的球状分布，涵盖了各种各样的球形，并可以完全解析任意多边形。

Definition 释义

Our idea is to start from a simple clamped cosine distribution and apply a linear transformation to its direction vectors. This allows for controlling the properties of the shape of the distribution, such as roughness, anisotropy, and skewness.

我们的想法是从一个简单钳制的余弦分布，并应用一个线性变换到它的方向向量。这允许控制分布形状的属性，如粗糙度，各向异性和偏斜属性。

cosine (base shape)余弦(基于形状)

 

 Roughness（粗糙度）                                    Anisotropy（各向异性）                                  Skewness（偏斜）

BRDF approximation 近似BRDF

Thanks to the variety of spherical shapes they cover, Linearly Transformed Cosines can closely approximate physically based BRDFs. Below is an example of how a GGX BRDF (left) can be approximated with a LTC (right) for varying incident directions.

由于球面形状覆盖的多样性，线性变换余弦可以近似基于双向反射分布函数。下面是一个例子，说明一个GGX BRDF(左)可以近似用LTC(右)对不同入射方向。

 

Of course, the approximation is not perfect, but it efficiently recovers the main features of the BRDF for different roughness and incidence configurations.

当然，近视并不完美，但它为不同的粗糙度和关联配置有效地恢复BRDF的主要特点

Polygonal integration 多边形一体化

Thanks to their linear invariant properties, integrating a LTC over a polygon is equivalent to integrating the original clamped cosine distribution over the polygon transformed by the inverse linear transformation: it is just the irradiance (form factor) of the transformed polygon for which a closed form expression is available!

多亏了他们的线性不变特性，LTC多边形总和相等于逆线性变换转化多边形上的原始钳制余弦分布：这就是辐照度(形状因子)转化多边形可用的闭合表达式！

       LTC-polygon integral（多边形积分）                         ..equivalent to..（相等于）                      cosine-polygon integral（多边形余弦积分）

   

analytic solution! （解析解法）                       

Other properties 其他特性

With the same idea, we can use any spherical distribution as a base shape to create a new family of spherical distributions with parametric roughness, elliptic anisotropy and skewness. If the original distribution has an analytic expression, normalization, integration over spherical polygons, and importance sampling, then these properties are inherited by the linearly transformed distributions.

具有相同想法，我们可以使用任何球形分布为基础形状创建一个新的球形分布参数粗糙度、椭圆各向异性和偏度。如果原始分布的解析表达式、规范化、一体化球形多边形和重要性采样，则这些属性是继承线性变换分布。

 Downloads 下载

• paper
• slides
• supplemental: MATLAB
• supplemental: plots and validation
• supplemental: comparison against Technicolor’s technique
• Demo (executable + code)
• WebGL Demo
• BRDF fitting code