A computer graphics system maps textures to displayed anti-aliased images with surfaces defined at oblique angles to the viewer. A circular pixel filter is projected onto a texture map to define an elliptical footprint in that texture map. The elliptical footprint has a major axis. Sample points are determined on a line in the footprint that closely approximates the major axis. These sample points are mapped to levels of detail and locations within a mip-map. Using a space-invariant filter, a texture value is computed for each sample point using data from one or more texture maps within the mip-map. These texture values for the sample points are post-filtered using a Gaussian filter function and summed to produce a final texture value. Blending the final texture with other characteristics of the pixel a produces the pixel data that are displayed on a display screen.