Robustness and efficiency of geometric programs: The Predicate Construction Kit (PCK)

As an example of my approach, I give the formulas and PCK source-code for the 4 predicates used to compute the intersection between a 3d Voronoi diagram and a tetrahedral mesh, as well as symbolic perturbations that provably escapes the corner cases. This allows to robustly compute the intersection between a Voronoi diagram and a triangle mesh, or the intersection between a Voronoi diagram and a tetrahedral mesh. Such an algorithm may have several applications, including surface and volume meshing based on Lloyd relaxation.