2010•PAMMRequires access

Aspects of the Facet‐Edge Data Structure for the Construction of Voronoi Cells

Christoph Weber, Stefan Loehnert, Peter Wriggers

Abstract

Abstract The construction of Voronoi diagrams has two main aspects: The construction algorithm and the data structure. For the construction of planar Voronoi diagrams e.g. the well known plane sweep algorithm can be applied. Another efficient method is the incremental construction of the Delaunay triangulation by using the quad‐edge data structure. Within this data structure the Delaunay triangulation is treated as a planar graph. Incremental construction implies that manipulations of the triangulation are allowed. Its Voronoi diagram is obtained simply by accessing the triangulation's dual graph. We extend this method to tree dimensions, by implementing a 3D Delaunay triangulation on the facet‐edge data structure. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

About this research paper

What this paper is about

Why it matters

OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Delaunay triangulation, Bowyer–Watson algorithm, Voronoi diagram, Pitteway triangulation, Constrained Delaunay triangulation, Centroidal Voronoi tessellation, Surface triangulation, Dual graph