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°. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Rivara, M. C., & Calderon, C. (2008). Lepp terminal centroid method for quality triangulation: A study on a new algorithm. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4975 LNCS, pp. 215–230). Springer Verlag. https://doi.org/10.1007/978-3-540-79246-8_17
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