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An Anisoptropic Surface Remeshing Strategy Combining Higher Dimensional Embedding with Radial Basis Functions

Dassi, Franco, Patricio Farrell, Hang Si

Proceedings, 25th International Meshing Roundtable, Elsevier, Science Direct, September 26-30 2016

INTERNATIONAL
MESHING
ROUNTABLE

25th International Meshing Roundtable
Washington DC, U.S.A.
September 26-30, 2016

Franco Dassi, Weierstrass Institute for Applied Analysis and Stochastics, DE, franco.dassi@wias-berlin.de
Patricio Farrell, Weierstrass Institute for Applied Analysis and Stochastics, DE, patricio.farrell@wias-berlin.de
Hang Si, Weierstrass Institute for Applied Analysis and Stochastics, DE, hang.si@wias-berlin.de

Abstract
Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy.

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