可分析的即時容積陰影演算法

Abstract

本論文透過數學分析的方式計算容積陰影的輻射傳送方程式(Radiative Transport Equation),經由這種輻射傳送方程式產生的結果和一般由數值方法計算的輻射傳送方程式所產生的結果相比,本論文所採用的方式產生之結果較具有物理意義,並且本論文在影子的空間中提出新的取樣方法,和簡化過的可分析輻射傳送方程式,再將場景分為沒有介質的場景和有介質的場景,針對有介質的場景作縮減取樣,計算有介質場景的輻射強度,最後利用雙邊濾鏡(Bilateral Filter)將兩個場景結合,和其他方法相比,本論文的演算法不需要前置處理,而且在非等向性的介質環境中,可以達到互動式的效能,在等向性的介質環境,可以達到即時的效能

In this thesis, we propose an analytical approach to compute the radiative transport equation of volumetric shadows. Our approach can achieve a more realistic result than using numerical methods. In this approach, a new sampling method is applied to the shadow region, which can reduce the computation for the analytical radiative transport equation. A scene can be considered as consisting of two parts, with and without participating media respectively. We only need to downsample the past with participating media, and calculate its radiance by using the simplified analytical radiative transport equation. Finally, we combine these two parts by using a bilateral filter. Compare to other techniques, our algorithm relies neither on pre-computation nor on storage. For a scene with anisotropic participating media, we can achieve interactive frame rate. For a scene with isotropic participating media, its performance can be real-time.