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.

- Introduction
- Reconstruction of Limit Surface
- Mesh Generation
- Implementation Aspects
- Examples
- Conclusions
- Acknowledgments
- Bibliography
- Figures
- Tables

*Daniel Rypl
2005-12-03*