### 重点梳理

The microfacet normals have an underlying probability density function $p(\bold h)$.

We believe that in most cases the shape of p(h) function itself has a much greater impact on the appearance than the shadowing. This suggests the key idea in this paper: the shadowing term should be made as simple as possible while remaining physically plausible.

As can be seen from Equation 10, at the very least shadowing should take care of the divergence at grazing angles where the denominator terms disappear: $(k_1 \cdot n)(k_2 \cdot n) → 0$.

In most of this paper we will use the uncorrelated form of the shadowing term written as a product of the two independent factors for each of the two directions:

### 对假设条件的讨论

Note that surface description in the language of p(h) is less detailed than that of using height correlation functions.

The two surfaces in Figure 3 may still have the same distribution p(h) and there is no way for us to distinguish between the two cases. Similarly, we will not be able to distinguish, for example, between “positive” and “negative” cylinders of Poulin and Fournier [16] but from their images it is clear that the differences in appearance due to microfacet visibility issues and not to the distribution of microfacets are minor in this case.

### 方法应用

1. 原文中的重要应用

2. 布料材质上的应用之一 Production Friendly Microfacet Sheen BRDF5

We follow up on the approach of using cylindrical microfibers [Ashikmin et al. 2000] as the main source of scattering.

In their virtual gonioreflectometer, Westin et al. [27], model velvet microstructure as a forest of narrow cylinders (fibers) with the orientation of each cylinder perturbed randomly. While it is difficult to write an exact p(h) corresponding to such “surface” for the reasons outlined in Section 2, a simple intuitive form of this function written as an “inverse Gaussian” heightfield is enough to capture the main character of the distribution.

Westin 19926 通过射线追踪进行的渲染结果如下图.

1. [1] Michael Ashikhmin, Simon Premoze, Peter Shirley. 2000. A Microfacet-based BRDF Generator.

2. [2] Gregory Ward. 1992. Measuring and Modeling Anisotropic Reflection.

3. [3] Jan Koenderink, Sylvia Pont. 2003. The Secret of Velvety Skin.

4. [4] Eric Heitz. 2014. Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs.

5. [5] Alejandro Estevez, Christopher Kulla. 2017. Production Friendly Microfacet Sheen BRDF.

6. [6] Stephen Westin, James Arvo, Kenneth Torrance. 1992. Predicting Reflectance Functions From Complex Surfaces.

7. [7] Pierre Poulin, Alain Fournier. 1990. A Model for Anisotropic Reflection.