Document Type

Article

Publication Date

2003

Publication Title

Proceedings of the nineteenth annual symposium on Computational geometry

Abstract

Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than π). 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. These constraints are described by combinatorial pseudo-triangulations, first defined and studied in this paper. Also of interest are our two proof techniques, one based on Henneberg inductive constructions from combinatorial rigidity theory, the other on a generalization of Tutte’s barycentric embeddings to directed graphs.

Keywords

pseudo-triangulation, rigidity, graph drawing

First Page

154

Last Page

163

DOI

10.1145/777792.777817

ISSN

ISBN:1-58113-663-3

Comments

Peer reviewed post-print.

Included in

Mathematics Commons

Share

COinS