Triangulation of 3D surfaces reconstructed by interpolating subdivision

An algorithm for the discretization of parametric 3D surfaces has been extended to the family of discrete surfaces represented by a triangular mesh of arbitrary topology. The limit surface is reconstructed from the mesh using the modified Butterfly scheme which is an interpolating subdivision technique yielding a C1 surface. The recovered surface is discretized directly in the physical space by the advancing front technique, thereby parameterization of the surface is not required. The mesh gradation is controlled by the octree data structure that simultaneously serves as a localization tool for the intersection investigation. Considering the discrete nature of the surface, special attention is paid to the proper implementation of the point-to-surface projection algorithm in order to achieve robustness and reasonable efficiency of the algorithm. The performance of the proposed strategy is presented on a few examples.