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New Mathematical Tools and Techniques for the Refinementand/or Improvement of Unstructured Triangulations

Rivara, Maria-Cecilia

5th International Meshing Roundtable, Sandia National Laboratories, pp.77-86, October 1996


In this paper I introduce a new mathematical tool for dealing with the refinement and/or the improvement of unstructured triangulations: the Longest- Side Propagation Path associated with each triangle to be either refined and/or improved in the mesh. This is defined as the (Finite) ordered list of successive neighbor triangles having longest-side greater than or equal to the longest side of the preceding triangle in the path. I use this idea to introduce a new Backward Longest-Side Refinement Algorithm that produces the same triangulation as the original algorithm in a more efficient, direct and easy-to-implement way. Based on this idea, I introduce and discuss a new Backward (Longest Side) Refinement Algorithm for Delaunay triangulations, suitable to deal (in a reliable, robust and effective way) with the three important related aspects of the (triangular) mesh generation problem: mesh refinement, mesh improvement, and automatic generation of good-quality surface and volume triangulation of general geometries including small details.

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