Surface Representation

The proper surface representation is essential for the efficiency of the method. To make the algorithm applicable to a wide variety of surfaces with a reasonable level of complexity the family of tensor product polynomial surfaces (e.g., rational Bezier surface, B-spline surface, NURBS, etc.) is considered in the presented approach. This brings in several advantages. Since these surfaces are widely used in CAD and modeling systems, a natural and consistent interface (at least in terms of geometric description of the surface) between the modeler and the mesh generator is ensured. All these surfaces enable relatively simple evaluation of surface normal and gradients at discrete locations on the surface. And finally, the parametric space of these surfaces allows some procedures to be performed more efficiently.

In the present study, the geometry of the 3D surfaces is based on rational Bezier entities. The rational Bezier surface is bounded by four rational Bezier curves from which at most two (but not the two adjacent ones) may be collapsed into a single point. This allows to model degenerated surfaces often used as transition patches. Rational Bezier entities enable to exactly represent conics and quadrics by entities starting with the order of three (quadratic curves and biquadratic surfaces).

*Daniel Rypl
2005-12-03*