A computer-implemented method of performing anisotropic texture filtering for applying a texture at a sampling point in screen space, the method comprising: calculating texture-filter parameters for use in configuring a filter to perform filtering of the texture for the sampling point wherein the step of calculating the texture-filter parameters comprises: generating a first and a second pair of orthogonal screen-space basis vectors, the first and second pairs of screen-space basis vectors being rotated relative to each other; calculating first and second pairs of texture-space basis vectors that correspond to the first and second pairs of screen-space basis vectors transformed to texture space under a local affine approximation of a mapping between screen space and texture space; based on differences in magnitudes of the vectors for at least one of the pairs of texture-space basis vectors, determining an angular displacement between a selected pair of the first and second pairs of screen-space basis vectors and screen-space principal axes of the local approximation of the mapping that indicate the maximum and minimum scale factors of the mapping; and using the determined angular displacement and the selected pair of screen-space basis vectors to generate texture-space principal axes, the texture-space principal axes comprising a major axis associated with the maximum scale factor of the mapping and a minor axis associated with the minimum scale factor of the mapping; and calculating the texture-filter parameters using the major and minor axes for use in configuring a filter to perform filtering of the texture for the sampling point; and filtering the texture for the sampling point using a filtering kernel having a footprint in texture space determined by the calculated texture-filter parameters. calculating texture-filter parameters for use in configuring a filter to perform filtering of the texture for the sampling point wherein the step of calculating the texture-filter parameters comprises: generating a first and a second pair of orthogonal screen-space basis vectors, the first and second pairs of screen-space basis vectors being rotated relative to each other; calculating first and second pairs of texture-space basis vectors that correspond to the first and second pairs of screen-space basis vectors transformed to texture space under a local affine approximation of a mapping between screen space and texture space; based on differences in magnitudes of the vectors for at least one of the pairs of texture-space basis vectors, determining an angular displacement between a selected pair of the first and second pairs of screen-space basis vectors and screen-space principal axes of the local approximation of the mapping that indicate the maximum and minimum scale factors of the mapping; and using the determined angular displacement and the selected pair of screen-space basis vectors to generate texture-space principal axes, the texture-space principal axes comprising a major axis associated with the maximum scale factor of the mapping and a minor axis associated with the minimum scale factor of the mapping; and generating a first and a second pair of orthogonal screen-space basis vectors, the first and second pairs of screen-space basis vectors being rotated relative to each other; calculating first and second pairs of texture-space basis vectors that correspond to the first and second pairs of screen-space basis vectors transformed to texture space under a local affine approximation of a mapping between screen space and texture space; based on differences in magnitudes of the vectors for at least one of the pairs of texture-space basis vectors, determining an angular displacement between a selected pair of the first and second pairs of screen-space basis vectors and screen-space principal axes of the local approximation of the mapping that indicate the maximum and minimum scale factors of the mapping; and using the determined angular displacement and the selected pair of screen-space basis vectors to generate texture-space principal axes, the texture-space principal axes comprising a major axis associated with the maximum scale factor of the mapping and a minor axis associated with the minimum scale factor of the mapping; and calculating the texture-filter parameters using the major and minor axes for use in configuring a filter to perform filtering of the texture for the sampling point; and filtering the texture for the sampling point using a filtering kernel having a footprint in texture space determined by the calculated texture-filter parameters.