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Lp Lloyd's Energy Minimization for Quadrilateral Surface Mesh Generation

Baudouin, Tristan Carrier, Jean-Francois Remacle, Emilie Marchandise, and Jonathan Lambrechts

20th International Meshing Roundtable, Springer-Verlag, pp.473-486, October 23-26 2011


20th International Meshing Roundtable
Paris, France
October 23-26, 2011

Institute of Mechanics, Materials and Civil Engineering, Universitie catholique de Louvain, Avenue Georges-Lemaitre 4, 1348 Louvain-la-Neuve, Belgium

Indirect methods recombine the elements of triangular meshes to pro- duce quadrilaterals. The resulting quadrilaterals are usually randomly oriented, which is not desirable. However, by aligning the vertices of the initial triangular mesh, precisely oriented quads can be produced. Levy's algorithm is a non-linear optimization procedure that can align points according to a locally de ned metric. It minimizes an energy functional based on the Lp distance in the local metric. The triangulation of a set of vertices smoothed with Levy's algorithm is mainly composed of right-angled triangles, which is ideal for quad recombination. An implementation of Levy's algorithm for the purpose of nite element computation has been developed. The implementation can create quads of desired size and orientation. The algorithm has been tested on two-dimensional geometries as well as parametrized curved surfaces. The results show an improvement of the quads alignment.

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