Abstract
We introduce a new Lepp-Delaunay algorithm for quality triangulation. For every bad triangle t with smallest angle less than a threshold angle θ, a Lepp-search is used to find an associated convex terminal quadrilateral formed by the union of two terminal triangles which share a local longest edge (terminal edge) in the mesh. The centroid of this terminal quad is computed and Delaunay inserted in the mesh. The algorithm improves the behavior of a previous Lepp-Delaunay terminal edge midpoint algorithm. The centroid method computes significantly smaller triangulation than the terminal edge midpoint variant, produces globally better triangulations, and terminates for higher threshold angle θ (up to 36°). We present geometrical results which explain the better performance of the centroid method. Also the centroid method behaves better than the off-center algorithm for θ bigger than 25°.
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Rivara, MC., Calderon, C. (2008). Lepp Terminal Centroid Method for Quality Triangulation: A Study on a New Algorithm. In: Chen, F., Jüttler, B. (eds) Advances in Geometric Modeling and Processing. GMP 2008. Lecture Notes in Computer Science, vol 4975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79246-8_17
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DOI: https://doi.org/10.1007/978-3-540-79246-8_17
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