Antialiasing of environment maps

Environment maps, like texture maps or any other maps consisting of discret ely stored data have to be properly filtered if they are being resampled in the process of rendering an image. For environment maps, this is especiall y important, as the sampling rate is subject to extreme changes due to the curvature of the reflecting surfaces. However for the same reason, the anti aliasing is especially difficult to perform, as the sampling rate has to be determined for each pixel. We introduce a method to perform this calculati on and determine the parameters for anisotropic filtering of the environmen t map, instead of the BRDF: we employ roughness pyramids to account for the properties of the reflecting surface. The principles that are used to perf orm this antialiasing can be applied for antialiasing reflected textures in general e.g. in ray tracing.