Planar minimally rigid graphs and pseudo-triangulations

Abstract

Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with <i>pointed</i> vertices (incident to an angle larger than <i>p</i>). 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.

DOI: 10.1145/777792.777817

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@article{Haas2003PlanarMR, title={Planar minimally rigid graphs and pseudo-triangulations}, author={Ruth Haas and David Orden and G{\"{u}nter Rote and Francisco Santos and Brigitte Servatius and Herman Servatius and Diane L. Souvaine and Ileana Streinu and Walter Whiteley}, journal={Comput. Geom.}, year={2003}, volume={31}, pages={31-61} }