Brian Guenter, John Rapp, and Mark Finch
Derivatives arise frequently in graphics and scientific computation applications. As GPU's become more widely used for scientific computation the need for derivatives can be expected to increase. To meet this need we have added symbolic differentiation as a built in language feature in the HLSL shading language. The symbolic derivative is computed at compile time so it is available in all types of shaders (geometry, pixel, vertex, etc.). The algorithm for computing the symbolic derivative is simple and has reasonable compilation and run time overhead.
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