Ill talk about some generalizations of Voronoi diagrams, algorithms to compute them, and some applications in 3D modeling for computer fabrication. Ill present a general algorithm that computes the intersection between a (generalized) Voronoi diagram and a tetrahedralized mesh. This algorithm can be used by different numerical optimizations where the discretization of space is dynamically optimized, such as Voronoi meshing by Lloyd relaxation and implementing some particular numerical schemes (semi-discrete) for solving some Partial Differential Equations (Monge-Ampere).