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Examples

To demonstrate the ability of the developed mesh generation technique several example meshes are presented in this section. The first example, the uniform mesh of a hemisphere, has been chosen to compare the overall quality of the mesh for different decompositions of the hemisphere into Bezier bicubic patches. Three cases have been investigated. In the first one, the hemisphere is approximated with a single patch with two strong singularities as it is displayed in Figure 8. The final mesh is presented in Figure 9, while the mesh in the parametric space is in Figure 10, demonstrating the power of modified advancing front technique for generation of anisotropic meshes with extreme stretches. Shaded triangles mark the subregions used to eliminate evaluation of infinite stretches around singular points. The parametric space with outlined principal directions and associated stretches is presented in Figure 11. The triangulation resulting from the approximation by a single patch without any purely singular point (Fig. 12) is displayed in Figure 13. The associated mesh in the parametric space is visualized in Figure 14, the principal stretches in Figure 15. The third case deals with the hemisphere decomposed into four identical patches cut off from the hemisphere by four octants (Fig. 16). Each of the patches has a singular point which corresponds to the top of the hemisphere. The final mesh of the hemisphere and the intermediate mesh of one of the patches in the parametric space are depicted in Figures 17 and 18, the latter one demonstrating again the generation of enormously stretched triangles. The positioning of mesh control points in the nodes of a quadtree in the parametric space may me distinct from the figure of principal directions and stretches (Fig. 19). There are no significant differences in the mesh quality for the individual decompositions of the hemisphere into patches. The second example describes a graded mesh on a hyperbolic paraboloid approximated (only roughly) with a single patch without any singularity (Fig. 20). Both meshes, the final mesh and the mesh in the parametric space, are visualized in Figures 21 and 22. In the final example, a surface close to a twisted rectangle with a hole in the middle has been triangulated (Fig. 23). The surface has not been decomposed into more patches, as it could be expected, only a single one has been used. The opening has been simply specified in the parametric space that has been subsequently meshed as a domain containing one void subregion, as it is presented in Figure 25. The resulting mesh is depicted in Figure 24.



Next: Summary Up: Top Previous: Local Smoothing

Daniel Rypl
2005-12-03