Method, system, and computer program product for implementing derivative operators with graphics hardware

A system for implementing derivative operators;

• comprising:
• means for receiving a data structure that represents the operation of one or more computer program statements that requires derivative information, and transforming the data structure into a first data tree having at least one substructure that is implemented with arithmetic operations;
• means for generating first and second copies of said at least one substructure;
• means for inserting the first and second copies into a second data tree corresponding to a transform rule;
• means for marking a node of the data structure that determines derivative information and traversing the first tree data structure to identify each node that determines a derivative value;
• and
• means for applying the second data tree to the node marked by said means for marking to obtain a transformed data structure, wherein the operations represented by the transformed data structure can be implemented with graphics hardware interface program statements.

A computer program product comprising a computer useable medium having computer program logic recorded thereon for enabling a processor to implementing derivative operations of a shading program language in graphics hardware, said computer program logic comprising:

• a receiving procedure that enables the processor to receive a data structure that represents the operation of one or more computer program statements, and transform the data structure into a first data tree having at least one substructure that is implemented with arithmetic operations, wherein at least one of the computer program statements requires derivative information;
• a generating procedure that enables the processor to generate first and second copies of said at least one substructure;
• an insertion procedure that enables the processor to insert the first and second copies into a second data tree corresponding to a transform rule;
• a marking procedure that enables the processor to mark a node of the data structure that determines derivative information by traversing the first tree data structure to identify one or more nodes that determine a derivative value;
• and
• a transformation procedure that enables the processor to apply the second data tree to the node marked by said marking procedure to obtain a transformed data structure having at least one substructure that is implemented with arithmetic operations, wherein the operations represented by the transformed data structure can be implemented with graphics hardware interface program statements.