Planar minimally rigid graphs and pseudo-triangulations

Authors:
Ruth Haas;David Orden;Günter Rote;Francisco Santos;Brigitte Servatius;Hermann Servatius;Diane Souvaine;Ileana Streinu;Walter Whiteley
Affiliations:
Smith College, Northampton, MA;Universidad de Cantabria, Santander, Spain;Freie Universitat Berlin, Berlin, Germany;Universidad de Cantabria, Santander, Spain;Worcester Polytechnic Institute, Worcester, MA;Worcester Polytechnic Institute, Worcester, MA;Tufts University, Medford, MA;Smith College, Northhampton, MA;York University, Toronto, Canada
Venue:
Proceedings of the nineteenth annual symposium on Computational geometry
Year:
2003

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Abstract

Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (incident to an angle larger than p). In this paper we prove that the opposite statement is also true, namely that planar minimally rigid graphs always admit pointed embeddings, even under certain natural topological and combinatorial constraints. The proofs yield efficient embedding algorithms. They also provide---to the best of our knowledge---the first algorithmically effective result on graph embeddings with oriented matroid constraints other than convexity of faces.