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Triangulation of 3D Surfaces:
From Parametric to Discrete Surfaces

Daniel Rypl, Zdenek Bittnar

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


An algorithm for 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 interpolation subdivision technique yielding a  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, a special attention has to be 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.

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Daniel Rypl