Tetrahedral Interpolation on Regular Grids

Abstract

This work proposes the use of barycentric interpolation on enclosing simplices of sample points to infer a reconstructed function from discrete data. In particular, we compare the results of trilinear and tetrahedral interpolation over regular 3D grids of second order spherical harmonics (SH) light probes. In general, tetrahedral interpolation only requires four data samples per query in contrast to the 8 samples necessary for trilinear interpolation, at the expense of a more expensive weight computation. Our tetrahedral implementation subdivides the cubical cells into six tetrahedra and uses the barycentric coordinates of the query position as weights to blend the probe data. We show that barycentric coordinates can be calculated efficiently in shaders for our particular tetrahedral decomposition of the cube, resulting only in simple arithmetic and conditional move operations.