Triangulation of Implicit Surfaces via Shell-Space Partition

A novel and robust method is presented for implicit surface triangulation problem. Particle system is used for sampling an implicit surface whose fission and death are guided by Gaussian curvature. This strategy leads to curvature adaptive samplings, so there are more small triangles in the high curvature region of constructed mesh. Triangular mesh can approximate the implicit surface better. More sample points are obtained by extending a proper distance along each normal vector. These new sample points are used as a sampling on surface of the shell space. Delaunay tetrahedron of these sample points fills in the shell space. Finally, triangles around zero set form a triangulation of the implicit surface. Compared with the existing methods, our method is more robust, and can achieve high quality model without post processing. Experiments are also conducted to demonstrate the efficiency of this new method.