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Quality Improvement of Surface Triangulations

Montenegro, R., J.M. Escobar, G. Montero and E. Rodriguez

Proceedings, 14th International Meshing Roundtable, Springer-Verlag, pp.469-484, September 11-14 2005

IMR
PROCEEDINGS

14th International Meshing Roundtable
San Diego, CA, USA
September 11-14, 2005

Institute for Intelligent Systems and Numerical Applications in Engineering, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain,
rafa@dma.ulpgc.es

Abstract
This paper presents a new procedure to improve the quality of triangular meshes defined on surfaces. The improvement is obtained by an iterative process in which each node of the mesh is moved to a new position that minimizes certain objective function. This objective function is derived from an algebraic quality measures of the local mesh (the set of triangles connected to the adjustable or free node). The optimization is done in the parametric mesh, where the presence of barriers in the objective function maintains the free node inside the feasible region. In this way, the original problem on the surface is transformed into a two-dimensional one on the parametric space. In our case, the parametric space is a plane, chosen in terms of the local mesh, in such a way that this mesh can be optimally projected performing a valid mesh, that is, without inverted elements. In order to show the efficiency of this smoothing procedure, its application is presented.

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