Gradient projection based optimization methods for untangling and optimization of 3 d meshes in implicit domains

Definition of complex domain as zero isosurface of scalar function resembling signed distance function is powerful and flexible mechanism of geometric modeling. Signed implicit functions can be constructed using surface triangulation, point clouds, set of planar cross-sections, “soup” consisting of disjoint edges and faces, and can be combined with analytical definitions and primitives using boolean operations. In order to construct tetrahedral meshes in implicit domains, special iterative technique for self-organization of points according to prescribed sizing function was developed in [1]. The points are distributed in such a way that sharp edges on the isosurface are approximated by Delaunay edges without special edge detection procedures. Thus meshes in volume and on the surface are constructed simultaneously.