DeWall: A fast divide and conquer Delaunay triangulation algorithm in Ed

doi:10.1016/S0010-4485(97)00082-1

Computer-Aided Design

Volume 30, Issue 5, April 1998, Pages 333-341

https://doi.org/10.1016/S0010-4485(97)00082-1 Get rights and content

Abstract

The paper deals with Delaunay Triangulations (DT) in E^d space. This classic computational geometry problem is studied from the point of view of the efficiency, extendibility to any dimensionality, and ease of implementation. A new solution to DT is proposed, based on an original interpretation of the well-known Divide and Conquer paradigm. One of the main characteristics of this new algorithm is its generality: it can be simply extended to triangulate point sets in any dimension. The technique adopted is very efficient and presents a subquadratic behaviour in real applications in E³, although its computational complexity does not improve the theoretical bounds reported in the literature. An evaluation of the performance on a number of datasets is reported, together with a comparison with other DT algorithms.

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Citation Excerpt :
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DeWall: A fast divide and conquer Delaunay triangulation algorithm in Ed

Abstract

Computer-Aided Design

Voronoi diagrams—a survey of a fundamental geometric data structure

ACM Computing Survey

A comparison of sequential delaunay triangulation algorithms

Sur la sphere vide

Bull. Acad. Science USSR VII: Class. Sci. Mat. Nat.

Simulation of simpicity: a technique to cope with degenerate cases in geometric algorithms

ACM Transaction on Graphics

How good are convex hull algorithms?

Incremental topological flipping works for regula triangulaions

Randomized incremental construction of Delaunay and voronoy diagrams

DeWall: A fast divide and conquer Delaunay triangulation algorithm in E^d