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Published in:
2008 | OriginalPaper | Chapter
Lepp Terminal Centroid Method for Quality Triangulation: A Study on a New Algorithm
Authors : Maria-Cecilia Rivara, Carlo Calderon
Published in: Advances in Geometric Modeling and Processing
Publisher: Springer Berlin Heidelberg
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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°.