Proof of Correctness of the Digital Delaunay Triangulation
نویسنده
چکیده
We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations.
منابع مشابه
Formal Study of Plane Delaunay Triangulation
This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe triangulations, we rely on a combinatorial hypermap specification framework we have been developing for years. We embed hypermaps in the plane by attaching coor...
متن کاملDelaunay Triangulation Benchmarks
In this communication we propose an initial set of 2D Delaunay triangulation benchmarks for checking the correctness of algorithms and discovering possible flaws. A tool for verification of the generated triangulation is provided. The tool reports typical errors like the existence of unused points, missing edges, non-Delaunay triangles or degenerated triangles. While the tool has been primarily...
متن کاملFully Incremental 3D Delaunay Refinement Mesh Generation
The classical meshing problem is to construct a triangulation of a region that conforms to the boundary, is as coarse as possible, and is constructed from simplices having bounded aspect ratio. In this paper we present a fully incremental Delaunay re nement algorithm. The algorithm is an extension of one introduced by Ruppert. The algorithm is fully incremental in the sense that it does not nee...
متن کاملDelaunay triangulations , theory vs practice
Thirty years ago, at the early ages of computational geometry, the game of computational geometers was to design fancy algorithms with optimal theoretical complexities. The result was usually an algorithmic journal article, but not an implementation. In the same period, some people were actually coding geometric algorithms, but without regard for the asymptotic complexities, and without proof o...
متن کاملConstrained Delaunay Triangulations and Algorithms
Two-dimensional constrained Delaunay triangulations (of a planar straight-linegraph) introduced independently by Lee et al. [2] and Chew [1] are well studied struc-tures and can be constructed in optimal time. However, the generalization of suchobjects to three and higher dimensions is much less discussed in literature.In this talk, we first define a constrained Delaunay tri...
متن کامل