In this paper, we have presented an efficient method for surface and subsequent volume remeshing. The method is based on the parametrization of a genus zero surface with a harmonic map. We have presented the discrete finite element harmonic map with appropriate boundary conditions. We have introduced a local 'cavity check' algorithm to enforce the discrete one-to-one mapping and showed that this approach leads to higher quality meshes than the convex combination map of Floater. A higher order approximation of the geometry based on curved PN triangles was introduced to smooth faceted STL (stereolithography) triangulations. Our procedure is easy to implement and very robust against low-quality input triangulations. Compared to smoothing-based approaches our technique does not result in any feature loss and naturally offers refinement options (boundary layer mesh, curvature, etc.). As it enables to remesh multiple CAD patches, the approach can be used to substantially reduce the time required to prepare CAD surface definition for surface mesh generation. The time required to generate the surface mesh is less than 100s per 106 elements. Furthermore, the generated elements have a high mean quality measure, which is a clear demonstration of the suitability of the meshes for finite element simulations. We are currently working on an optimal numerical homology algorithm that will automatically cut a initial surface onto different surfaces of genus zero with uniform geometrical aspect ratio. With this upcoming algorithm we hope to obtain a fully automatic method for high-quality remeshing of any topological surface without any geometrical constraint.
High-quality surface remeshing using harmonic maps
Hochqualitäts-Surface Remeshing mit Hilfe von Harmonic Maps
International Journal for Numerical Methods in Engineering ; 83 , 4 ; 403-425
2010
23 Seiten, 22 Bilder, 42 Quellen
Article (Journal)
English
British Library Conference Proceedings | 2010
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