On affine rigidity

Authors

  • Steven J. Gortler Harvard University
  • Craig Gotsman Technion
  • Ligang Liu Zhejiang University
  • Dylan P. Thurston Barnard College, Columbia University

DOI:

https://doi.org/10.20382/jocg.v4i1a7

Abstract

We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding). Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1)-vertex-connected. We also show neighborhood affine rigidity of a graph implies universal rigidity of its squared graph.  Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.

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Author Biographies

Steven J. Gortler, Harvard University

Robert I. Goldman Professor of Computer Science

Craig Gotsman, Technion

ProfessorCenter for Graphics and Geometric Computing (CGGC)Computer Science Department

Ligang Liu, Zhejiang University

Associate Professor, CAGD&CG Group

State Key Lab of CAD&CG

Department of Mathematics, Zhejiang University

 

Dylan P. Thurston, Barnard College, Columbia University

Assistant Professor, Department of Mathemtics

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Published

2013-12-09

Issue

Vol. 4 No. 1 (2013)

Section

Articles

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