Pseudo-Triangulations - a Survey

Details Pseudo-Triangulations - a Survey Pseudo-Triangulations - a Survey

2006-12-21

arxiv.org/abs/math/0612672v2

In "Surveys on Discrete and Computational Geometry: Twenty Years Later", Edited by J. E. Goodman, J. Pach, and R. Pollack, Con

Mathematics

Combinatorics

68 pages, 36 figures. To appear in "Proceedings of the Joint Summer Research Conference on Discrete and Computational Geometry

Scientific paper

A pseudo-triangle is a simple polygon with three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations appear as data structures in computational geometry, as planar bar-and-joint frameworks in rigidity theory and as projections of locally convex surfaces. This survey of current literature includes combinatorial properties and counting of special classes, rigidity theoretical results, representations as polytopes, straight-line drawings from abstract versions called combinatorial pseudo-triangulations, algorithms and applications of pseudo-triangulations.

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