An Efficient Query Structure for Mesh Refinement

We are interested in the following mesh refinement problem: given an input set of points P in Rd , we would like to produce a good-quality triangulation by adding new points in P. Algorithms for mesh refinement are typically incremental: they compute the Delaunay triangulation of the input, and insert points one by one. However, retriangulating after each insertion can take linear time. In this work we develop a query structure that maintains the mesh without paying the full cost of retriangulating. Assuming that the meshing algorithm processes bad-quality elements in increasing order of their size, our structure allows inserting new points and computing a restriction of the Voronoi cell of a point, both in constant time.

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: Benoît Hudson, Duru Türkoglu
• Keywords: CCCG 2008, Computational Geometry, Delaunay Triangulation, Insert Points, Mesh Refinement