METHOD AND SYSTEM FOR EVALUATING DERIVATIVES IN SCREEN SPACE USING PERSPECTIVE CORRECTED BARYCENTRIC COORDINATES

Method and system for evaluating derivatives in screen space using perspective corrected barycentric coordinates. A preferred embodiment provides a method for computing the LOD at individual pixels directly without relying on approximations. In this embodiment, screen coordinates of a pixel and derivatives of the texture coordinates at the vertices of the triangle enclosing the pixel are determined. Derivatives of texture coordinates at the pixel with respect to screen space are evaluated by interpolation of the derivatives of the texture coordinates at the vertices using barycentric coordinates of the pixel. Then, using the derivatives of the texture coordinates and without relying on neighboring pixels' texture coordinates, the LOD at the pixel is computed, such that the LOD as computed is unbiased in any particular direction. Significantly, such direct computation allows exact LOD values to be easily computed and eliminates the artifacts that are inherent in prior art implementations. This embodiment also enables a higher level of parallel processing by eliminating the prerequisite of computing texture coordinates before computing LOD, thereby enhancing system performance. Another embodiment provides a method for computing derivatives of a function with respect to screen space, where the function can be interpolated in eye space by perspective corrected barycentric coordinates for a point in screen space. The method of this embodiment can be used to evaluate any nth-order derivative where n is a positive integer.