This paper proposes a lightweight bidirectional scattering distribution function (BSDF) model for layered materials with anisotropic reflection and refraction properties. In our method, each layer of the materials can be described by a microfacet BSDF using an anisotropic normal distribution function (NDF). Furthermore, the NDFs of layers can be defined on tangent vector fields, which differ from layer to layer. Our method is based on a previous study in which isotropic BSDFs are approximated by projecting them onto base planes. However, the adequateness of this previous work has not been well investigated for anisotropic BSDFs. In this paper, we demonstrate that the projection is also applicable to anisotropic BSDFs and that the BSDFs are approximated by elliptical distributions using covariance matrices.

中文翻译：

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实时渲染具有各向异性正态分布的分层材料

本文针对具有各向异性反射和折射特性的层状材料，提出了一种轻量级的双向散射分布函数（BSDF）模型。在我们的方法中，可以使用各向异性正态分布函数（NDF）通过微面BSDF描述材料的每一层。此外，可以在切向矢量场上定义层的NDF，该向量在层与层之间是不同的。我们的方法基于先前的研究，在该研究中，通过将各向同性BSDF投影到基础平面上来近似它们。但是，对于各向异性的BSDF，以前的工作是否充分还没有得到很好的研究。在本文中，我们证明了该投影也适用于各向异性BSDF，并且使用协方差矩阵通过椭圆分布对BSDF进行了近似。