利用球面輻射基底函數對BRDF及環境光源之重要性取樣

Abstract

我們藉由球面輻射基底函數（SRBF）的特性，針對高動態範圍（HDR）環境光源以及經由測量所得的雙向反射分佈函數（BRDF）這兩種函數的乘積，提出一種新的重要性取樣技術。在前處理時，我們透過非線性最佳化的演算法，將高動態範圍環境光源貼圖以及雙向反射分佈函數轉換成球面輻射基底函數的表示形式。在執行顯像運算時，我們先計算出兩個球面輻射基底函數的乘積，然後根據球面輻射基底函數的表示形式，提出有效率的重要性取樣方法，其產生出來的取樣分佈可以契合球面輻射基底函數所描述的資料分佈。此方法可以在全域光源照射的環境下，有效率地繪製包含多種複雜材質以及高動態範圍環境光源的場景。

We propose a new technique for importance sampling products of the complex high-dynamic range lighting environment and the measured BRDF data using Spherical Radial Basis Functions (SRBFs). In the pre-process, we transform the complex HDR environment map and the measured BRDF data into the scattered SRBF representation by using the non-uniform and non-negative SRBF fitting algorithm. In the run time rendering process, we first evaluate the product of the two SRBFs. As this product is evaluated, we present an efficient sampling algorithm on the unit sphere, and the generated point distribution can match the SRBF representation. As a consequence, our method can efficiently render images with multiple measured BRDFs and HDR environment maps under global illumination.