Regular triangulations of dynamic sets of points

Marc Vigo, Núria Pla, Josep Cotrina
2002 Computer Aided Geometric Design  
The Delaunay triangulations of a set of points are a class of triangulations which play an important role in a variety of different disciplines of science. Regular triangulations are a generalization of Delaunay triangulations that maintain both their relationship with convex hulls and with Voronoi diagrams. In regular triangulations, a real value, its weight, is assigned to each point. In this paper a simple data structure is presented that allows regular triangulations of sets of points to be
more » ... dynamically updated, that is, new points can be incrementally inserted in the set and old points can be deleted from it. The algorithms we propose for insertion and deletion are based on a geometrical interpretation of the history data structure in one more dimension and use lifted flips as the unique topological operation. This results in rather simple and efficient algorithms. The algorithms have been implemented and experimental results are given.
doi:10.1016/s0167-8396(01)00082-6 fatcat:u7rukq77uzegdf6g3xn2btn3qe