Submitted Contributions

Applied Computational Geometry Towards Geometric Engineering

Volume 1148 of the series Lecture Notes in Computer Science pp 203-222


Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator

  • Jonathan Richard ShewchukAffiliated withSchool of Computer Science, Carnegie Mellon University

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Triangle is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunay refinement algorithm for quality mesh generation. Several implementation issues are discussed, including the choice of triangulation algorithms and data structures, the effect of several variants of the Delaunay refinement algorithm on mesh quality, and the use of adaptive exact arithmetic to ensure robustness with minimal sacrifice of speed. The problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is shown to be impossible for some PSLGs, contradicting the claim that a variant of the Delaunay refinement algorithm solves this problem.