filename : p313_sigg.pdf [not available yet] entry : incollection pages : 313--329 year : 2005 month : Feb title : Fast Third-Order Texture Filtering subtitle : author : Christian Sigg, Markus Hadwiger booktitle : GPU Gems {2} ISSN/ISBN : 0-321-33559-7 editor : Matt Pharr publisher : Addison Wesley keywords : high order filtering, graphics hardware, implicit surface rendering abstract : Current programmable graphics hardware makes it possible to implement general convolution filters in the fragment shader for high-quality texture filtering, such as cubic filters (Bjorke 2003). However, several shortcomings are usually associated with these approaches: the need to perform many texture lookups and the inability to antialias lookups with mipmaps, in particular. We address these issues in this chapter for filtering with a cubic B-spline kernel and its first and second derivatives in one, two, and three dimensions. The major performance bottleneck of higher-order filters is the high number of input texture samples that are required, which are usually obtained via repeated nearestneighbor sampling of the input texture. To reduce the number of input samples, we perform cubic filtering, building on linear texture fetches instead, which reduces the number of texture accesses considerably, especially for 2D and 3D filtering. Specifically, we are able to evaluate a tricubic filter with 64 summands using just eight trilinear texture fetches. Approaches that perform custom filtering in the fragment shader depend on knowledge of the input texture resolution, which usually prevents correct filtering of mipmappedtextures. We describe a general approach for adapting a higher-order filtering scheme to mipmapped textures. Often, high-quality derivative reconstruction is required in addition to value reconstruction, for example, in volume rendering. We extend our basic filtering method to reconstruction of continuous first-order and second-order derivatives. A powerful application of these filters is on-the-fly computation of implicit surface curvature with tricubic B-splines, which have been applied to offline high-quality volume rendering, including nonphotorealistic styles (Kindlmann et al. 2003).