METHOD, SYSTEM, AND COMPUTER PROGRAM PRODUCT FOR IMPLEMENTING DERIVATIVE OPERATORS WITH GRAPHICS HARDWARE

Method, system, and computer program product for implementing derivative operators at an interactive rate in computer graphics systems. In an embodiment, a data structure representing the operation of one or more computer program statements is received by a compiler and transformed into a tree data structure. Nodes of the tree data structure that determine derivative information are marked, and a transform rule is applied to the marked nodes to transform the tree data structure into a data structure that can be implemented with graphics hardware interface program statements. In one embodiment of the invention, the compiler transforms shading language statements into graphics application programming interface statements that can be implemented with multiple passes through a graphics pipeline. It is a feature of the present invention that it can be implemented on a wide range of computer graphics systems.