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
Recommended Citation
Haas, Ruth; Orden, David; Rote, Günter; Santos, Francisco; Servatius, Herman; Souvaine, Diane; Streinu, Ileana; and Whiteley, Walter, "Planar Minimally Rigid Graphs and Pseudo-Triangulations" (2003). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/6
Comments
Peer reviewed accepted manuscript.