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Mesh Generation

The discretization is carried out in a hierarchical manner. Firstly, the model vertices are discretized. Then the curves are segmented using the mass curve of the required element density along that curve. And finally, the individual surfaces are triangulated. In the presented implementation, the surfaces are discretized by the advancing front technique constrained directly to the surface and modified to allow for surface curvature [4]. The generated mesh is then subjected to optimization in order to improve the quality of the final mesh. The Laplacian smoothing technique in combination with topological transformations (diagonal edge swapping) is adopted. This yields the optimized grid after only a few cycles of smoothing (typically up to six). Note that, contradictory to the smoothing carried out in 2D, the repositioning of a node is likely to shift the node out of the surface. Therefore, the point-to-surface projection has to be employed to satisfy the surface constraint.

Next: Implementation Up: Top Previous: Surface Representation

Daniel Rypl
2005-12-03