Non-Simplicial Delaunay Meshing via Approximation by Radical Partitions

We consider the construction of a polyhedral Delaunay partition as limit sequence power diagrams (radical partitions). The dual Voronoi diagram is obtained weighted partitions. problem reduced to two convex polyhedra, inscribed and superscribed around circular paraboloid, pairs general polyhedra. primal polyhedra should converge polyhedron converges polyhedron. are interested in case when vertices can move or merge together, i.e., no new faces allowed for These rules define transformation set initial spheres into using radius variation sphere movement elimination. Existence theorems still unavailable but we suggest functional measuring deviation from one paraboloid. It discrete Dirichlet function which linear interpolant vertical distance functional's absolute minimizer attained on constant field, meaning that be by simple translation. This formulation surface not quadratic since unknowns polyhedron, hence, unique. concentrate experimental confirmation approach viability put aside mesh quality problems. zero value gradient proposed defines manifold describing evolution spheres. Hence, Delaunay-Voronoi meshes optimized constraint.