Symbolic Differentiation in GPU Shaders

Derivatives arise frequently in graphics and GPGPU applications. 1 To meet this need we have added symbolic differentiation as a built 2 in language feature in the HLSL shading language. The symbolic 3 derivative is computed at compile time so it is available in all types 4 of shaders (geometry, pixel, vertex, etc.). The algorithm for com5 puting the symbolic derivative is simple and has reasonable com6 pilation and run time overhead. We present two example shader 7 programs which show how to use the symbolic differentation fea8 ture to define procedural surfaces and textures, with automatic level 9 of detail and procedural texture antialiasing. 10