Fast Third-Order Texture Filtering

Current programmable graphics hardware makes it possible to implement general convolution filters in fragment shaders for high-quality texture filtering, such as cubic filters (Bjorke 2004). 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.