Lloyd Relaxation using Analytical Voronoi Diagram in the L-infinity Norm and its Application to Quad Optimization

Research Notes, 21st International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 7-10 2012

IMR
PROCEEDINGS

21st International Meshing Roundtable
San Jose, CA
October 7-10, 2012

Universite de Liege, Aerospace and Mechanical Engineering Department, Chemin des Chevreuils, 1, 4000 Liege, Belgium
Email: {eric.bechet, thibaud.mouton}@ulg.ac.be

Summary
An incremental Delaunay triangulation algorithm to generate Voronoi diagrams within the L-infinity norm is presented. The main qualities are the preservation of the simplicity of the classical L2 version and its its intrinsic robustness It is then coupled to the well known Lloyd algorithm for computing Centroidal Voronoi Tesselations of point sets. This algorithm is then used to generate well shaped quadrilateral meshes.

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