A method and apparatus for performing the majority of texture map gradient calculations once per polygon so as to increase processing speed in a graphics system. Texture values are identified for each vertex of an input polygon and are interpolated over the polygon in perspective space in order to find the corresponding values at a given pixel within the polygon. The perspective values of the vertices are linearly interpolated across the polygon to determine the value at the given pixel. The texture gradients are then calculated by defining vectors perpendicular and parallel to the horizon of the plane containing the input polygon so that the resulting components may be calculated. The resulting value is the texture gradient, which may then be used to address a texture map to determine the pre-filtered texture value for that point. A hardware implementation performs the necessary calculations for each pixel in the input polygon. The invention so arranged removes artifacts in the texture mapped image at a low cost and at a high speed.