We introduce a Monte Carlo importance sampling method for integrands composed of products and show its application to rendering where direct sampling of the product is often difficult. Our method is based on warp functions that operate on the primary samples in [0,1)n, where each warp approximates sampling a single factor of the product distribution. Our key insight is that individual factors are often well‐behaved and inexpensive to fit and sample in primary sample space, which leads to a practical, efficient sampling algorithm. Our sampling approach is unbiased, easy to implement, and compatible with multiple importance sampling. We show the results of applying our warps to projected solid angle sampling of spherical triangles, to sampling bilinear patch light sources, and to sampling glossy BSDFs and area light sources, with efficiency improvements of over 1.6× on real‐world scenes.

中文翻译：

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通过拟合和组合经线进行实际产品抽样

我们介绍了一种由乘积组成的被积函数的蒙特卡罗重要性采样方法，并展示了它在渲染中的应用，其中乘积的直接采样通常很困难。我们的方法基于对 [0,1)n 中的主要样本进行操作的扭曲函数，其中每个扭曲近似采样产品分布的单个因子。我们的主要见解是，单个因素通常表现良好且在主要样本空间中拟合和采样的成本较低，这导致了实用、高效的采样算法。我们的抽样方法是无偏的，易于实现，并且与多重重要性抽样兼容。我们展示了将我们的扭曲应用于球面三角形的投影立体角采样、采样双线性贴片光源以及采样光泽 BSDF 和区域光源的结果，