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Surface Representation

As mentioned above, the high complexity of the mathematical description of various surfaces complicates seriously the meshing procedure with surface constraint. Therefore 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 surfaces1(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 for some procedures to be performed more efficiently than in 3D.

In the presented study, only the set of rational Bezier surfaces has been implemented. Each surface to be discretized 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 for modeling of degenerated surfaces often used as transition patches. This simple data structure, which can be easily extracted from modeler allowing to handle rational Bezier entities, may be extended in terms of additional curves (again, reducible to a single point) fixed to the surface, for example to specify the mesh density source or to constrain the triangulation.


... surfaces1
Note, the same class of surfaces is usually used in the indirect algorithms using the parametric space for actual grid generation.

Next: Advancing Front Technique on the Surface Up: Top Previous: Mesh Gradation Control

Daniel Rypl