Mesh Generation on 3D Surfaces
Reconstructed by Interpolating Subdivision

Daniel Rypl, Zdeněk Bittnar

Department of Structural Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic


An algorithm for triangulation of 3D surfaces is presented. A family of discrete surfaces represented by triangular mesh of arbitrary topology is considered. The limit surface over which the actual discretization takes place is recovered using the interpolating subdivision technique. The recovered surface is triangulated directly in the physical space using the advancing front technique. This avoids difficulties with the parameterization of the surface and its anisotropic triangulation in the parametric space. The mesh gradation is controlled by the octree data structure. Allowing only for one-level octree difference of octants sharing an edge, too steep size gradation is eliminated and therefore no special strategy for choosing an edge to be removed is to be employed. This leads to a favourable computational complexity of the mesh generation algorithm. The performance of the algorithm, in dependence on different aspects, is discussed and some modifications improving the performance are suggested.