Temporal Normal Distribution Functions

Abstract

Specular aliasing can make seemingly simple scenes notoriously hard to render efficiently: small geometric features with high curvature and near specular reflectance result in tiny lighting features which are difficult to resolve at low sample counts per pixel. LEAN and LEADR mapping can be used to convert geometric surface detail to anisotropic surface roughness in a preprocess. In scenes including fluid simulation this problem is particularly apparent with fast moving elements such as spray particles, which are typically represented as participating media in movie rendering. Both approaches, however, are only valid in the far-field regime where the geometric detail is much smaller than a pixel, while the challenge of resolving highlights remains in the meso-scale. Fast motion and the relatively long shutter intervals, commonly used in movie production, lead to strong variation of the surface normals seen under a pixel over time aggravating the problem. Recent specular anti aliasing approaches preintegrate geometric curvature under the pixel footprint for one specific ray to achieve noise free images at low sample counts. We extend these to anisotropic surface roughness and to account for the temporal surface normal variation due to motion blur. We use temporal derivatives to approximate the distribution of the surface normal seen under a pixel over the course of the shutter interval. Furthermore, we discuss how this can afterwards be combined with the surface BSDF in a practical way.