Triangulation of 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
Abstract:
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.