Analytic Anti‐Aliasing of Linear Functions on Polytopes

This paper presents an analytic formulation for anti‐aliased sampling of 2D polygons and 3D polyhedra. Our framework allows the exact evaluation of the convolution integral with a linear function defined on the polytopes. The filter is a spherically symmetric polynomial of any order, supporting approximations to refined variants such as the Mitchell‐Netravali filter family. This enables high‐quality rasterization of triangles and tetrahedra with linearly interpolated vertex values to regular and non‐regular grids. A closed form solution of the convolution is presented and an efficient implementation on the GPU using DirectX and CUDA C is described.

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