SIGGRAPH 2014 Course: Physically Based Shading in Theory and Practice

https://blog.selfshadow.com/publications/s2014-shading-course/
course description
physically based shading is transforming the way we approach production rendering, and simplifying the lives of artists in the process. by adhering to physically based, energy-conserving models, one can easily create realistic materials that maintain their properties under a variety of lighting conditions. in contrasts, traditional ad hoc models have required extensive tweaking to achieve the same result. building upon previous incarnations of the course([1],[2],[3])
http://renderwonk.com/publications/s2010-shading-course/
https://blog.selfshadow.com/publications/s2012-shading-course/
https://blog.selfshadow.com/publications/s2013-shading-course/

we present further research and practical advice on the subject, from film and game production.

第一个：
Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs
http://jcgt.org/published/0003/02/03/

abstract
we provide a new presentation of the masking-shadowing functions (or geometric attenuation factors) in microfacet-based BRDFs and answer some common questions about their applications. our main motivation is to define a correct (geometrically indicated), physically based masking function for application in microfacet models, as well as the properties that function should exhibit. indeed, several different masking functions are often presented in the literature and making the right choice is not always obvious. we start by showing that physically based masking functions are constrained by the projected area of the visible microsurface onto the outgoing direction. we use this property to derive the distribution of visible normals from the microsurface, whose normalization factor is the masking function. we then show how the common form of microfacet-based BRDFs emerges from this distribution. as a consequence, the masking function is related to the correct normalization of microfacet-based BRDFs. however, while the correct masking function satisfies these normalization constrains, its explicit form is can only be determined for a given microsurface profile.

1. introduction
   microfacet theory was originally developed in the field of optical physics to study scattering on statistical surfaces[Beckmann and Spizzichino 1963]. in the graphics community, we use it to derive physically based bidirectional reflectance distribution functions (BRDFs)[cook and torrance 1982; oren and nayar 1994; walter et al. 2007], which are used widely in both real-time and production rendering. today, microfacet theory is a fundamental background topic in computer graphics. for instance, for the past two years, the SIGGRAPH course on physically based rendering began with an introduction to microfacet theory [McAuley et al. 2012; McAuley et al.2013], with the goal of providing the main intuitions derived from the underlying phyics. other considerations, such as flexibility for artistic direction and computational efficiency, are also discussed throughout that course. microfacets are an area of continuing development because the combination of different components in microfacet-based BRDFs offer a wide range of possibilities. so, the right choices for each of those components are frequently not obvious and in our experience, are a common source of confusion in the field.

2. derivation of the masking function
   in this section, we show how the projected area of the microsurface can be used to introduce a constraint on physically based masking functions, following Ashikhmin et al.[2000]. we start by defining the concept of projected area (2.1) and show why it is essential to the measure of radiance. then, we define the statistical framework of microfacet theory (2.2).

2.1 measuring radiance on a surface

Figure 1. The outgoing radiance of surface M is the average of the radiances from each point
of the surface, weighted by their projected-area fractions towards the outgoing direction.

radiance is the energy density traveling through an area from a solid angle. it is measured in watts per steradian per square meter (W/sr/m^2). The outgoing radiance L(ωo,M) of a given surface M in direction ωo, is the integral of the radiances L(ωo, pm) from each patch with center point pm on the surface, measured from outgoing direction ωo, and weighted by its projected area observed from that outgoing direction (as shown in Figure 1):

The area of each surface point projected in the outgoing direction is a view-dependent weighting factor and the integral S M projected area(pm)d pm, is the normalization coefficient of the projected-area fractions. Note that this normalization coefficient gives the entire expression radiance units; without it, the result would be missing the area units in the denominator.