Higher Order Delaunay Triangulations

For a set P of points in the plane, we introduce a class of triangulations that is an extension of the Delaunay triangulation. Instead of requiring that for each triangle the circle through its vertices contains no points of P inside, we require that at most k points are inside the circle. Since there are many different higher-order Delaunay triangulations for a point set, other useful criteria for triangulations can be incorporated without sacrificing the well-shapedness too much. Applications include realistic terrain modeling and mesh generation. 2002 Elsevier Science B.V. All rights reserved.

• Type: Conference
• Year: 2000
• Where: ESA
• Authors: Joachim Gudmundsson, Mikael Hammar, Marc J. van Kreveld
• Keywords: Algorithms, Delaunay Triangulations, ESA 2000, Realistic Terrain Modeling, Useful Criteria