A study on Delaunay terminal edge method

Abstract

The Delaunay terminal edge algorithm for triangulation improvement proceeds by iterative Lepp selection of a point M which is midpoint of a Delaunay terminal edge in the mesh. The longest edge bisection of the associated terminal triangles (sharing the terminal edge) can be seen as a first step in the Delaunay insertion of M. The method was introduced as a generalization of non-Delaunay longest edge algorithms but formal termination proof had not been stated until now. In this paper termination is proved and several geometric aspects of the algorithm behavior are studied. © 2006 Springer.