Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

Also Proceedings of the Annual Symposium on Geometry ProcessingInternational audienceWe propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a vol- ume distortion criterion. The result is a point-to-point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoi Squared Distance Minimization (VSDM) combined with a higher-order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi-sharp features to be im- plicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We ap- ply our method to geometric modeling applications in computer-aided design and computer graphics, including mixed-element meshing, mesh optimization, subdivision volume fitting, and shell meshing