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Minimal Variational Surfaces and Quality Triangular Meshes

Borouchaki, Houman, Pascal Lafon, Patrick Laug and Paul-Louis George

Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.217-225, October 2000


9th International Meshing Roundtable
October 2-5, 2000, New Orleans, Louisiana USA

Houman Borouchaki and Pascal Lafon
Universiti de Technologie de Troyes, GSM-LASMIS, France
Patrick Laug and Paul-Louis George
INRIA, Projet GAMMA, France

This paper describes a methodology to construct a quality triangular mesh of the domain from a given discretization of its boundary. We show that the size map related to such a mesh constitutes a minimal variational surface supported by a given contour. This surface can be constructed, from its boundary, using the finite element method or by the resolution of a simple discrete optimization problem. The quality mesh of the domain is then a mesh conforming to the size map given by this surface. A numerical example is given to demonstrate the method.

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