Skip to Main content Skip to Navigation
Conference papers

Enumerating Triangulations of Convex Polytopes

Abstract : A triangulation of a finite point set A in $\mathbb{R}^d$ is a geometric simplicial complex which covers the convex hull of $A$ and whose vertices are points of $A$. We study the graph of triangulations whose vertices represent the triangulations and whose edges represent geometric bistellar flips. The main result of this paper is that the graph of triangulations in three dimensions is connected when the points of $A$ are in convex position. We introduce a tree of triangulations and present an algorithm for enumerating triangulations in $O(log log n)$ time per triangulation.
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.inria.fr/hal-01182975
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 6, 2015 - 12:02:12 PM
Last modification on : Friday, December 18, 2020 - 5:30:03 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 10:11:57 AM

File

dmAA0107.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01182975, version 1

Collections

Citation

Sergei Bespamyatnikh. Enumerating Triangulations of Convex Polytopes. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. pp.111-122. ⟨hal-01182975⟩

Share

Metrics

Record views

217

Files downloads

654