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Curve Discretization

The curves are discretized by simply creating an edge for each segment of the binary tree structure associated with that curve. In case of relevant curves, this binary tree is directly built on that curve, in other cases, the binary tree is extracted from the tree structure of model entity being bounded by the curve. Since the binary tree has a very regular structure in the parametric space the curve discretization is likely to be very unsmooth. Therefore an optimization process has to be applied to improve the curve discretization. Apparently, application of plain Laplacian smoothing will result (after sufficient number of cycles of the smoothing) in equidistant node distribution over the curve, which is not acceptable. Therefore weighted Laplacian smoothing with weights based on required mesh size is used. This provides satisfactory results if non-boundary curve is considered. For boundary curves, this smoothing is still too ``free'' and will consequently spoil the shape of elements on surfaces and in regions bounded by this curve. To resolve this problem a selective smoothing was implemented. This weighted Laplacian smoothing is applied only to those nodes that are shared by segments with significantly different lengths. This solution seems to be a good compromise between the unsmoothed and standardly smoothed curve discretization.



Next: Surface Discretization Up: Mesh Generation Previous: Parametric Tree Construction

Daniel Rypl
2005-12-03