Lepp Terminal Centroid Method for Quality Triangulation: A Study on a New Algorithm

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◦.