论文标题
均匀平板和史密斯微杆上多个散射的无位置路径积分
A Position-Free Path Integral for Homogeneous Slabs and Multiple Scattering on Smith Microfacets
论文作者
论文摘要
我们考虑了史密斯微纤维上多次散射的问题。这个问题等于在同质平板中计算体积光传输。尽管平板的对称性允许大量简化，但对于大多数应用，完全分析的解决方案却很少，而且不够一般。标准的蒙特卡洛模拟虽然一般，但昂贵，并且导致必须处理的差异。 我们提出了第一个无偏见的，真正的无位置路径积分，用于评估同质平板的BSDF。我们使用碰撞距离的分析前整合以前作品的空间1D路径组成的空间1D路径组成部分。对所得路径积分的评估（现在仅包含方向）减少了简单的递归操纵指数分布。应用蒙特卡洛来解决减少的集成问题会导致差异降低。 我们的新算法使我们能够在史密斯微动子上散布多个差异，而差异的差异要小于先前的工作，并且对于导体而言，这样做没有任何偏见。此外，与标准的蒙特卡洛整合相比，我们的算法也可用于加速含有体积散射层的BSDF的渲染。
We consider the problem of multiple scattering on Smith microfacets. This problem is equivalent to computing volumetric light transport in a homogeneous slab. Although the symmetry of the slab allows for significant simplification, fully analytic solutions are scarce and not general enough for most applications. Standard Monte Carlo simulation, although general, is expensive and leads to variance that must be dealt with. We present the first unbiased, truly position-free path integral for evaluating the BSDF of a homogeneous slab. We collapse the spatially-1D path integral of previous works to a position-free form using an analytical preintegration of collision distances. Evaluation of the resulting path integral, which now contains only directions, reduces to simple recursive manipulation of exponential distributions. Applying Monte Carlo to solve the reduced integration problem leads to lower variance. Our new algorithm allows us to render multiple scattering on Smith microfacets with less variance than prior work, and, in the case of conductors, to do so without any bias. Additionally, our algorithm can also be used to accelerate the rendering of BSDFs containing volumetrically scattering layers, at reduced variance compared to standard Monte Carlo integration.
