A framework (G,p) is a straight line realization of a graph G=(V,E) in R 2, given by a map pV→R 2. We prove that if (G,p) is an infinitesimally rigid framework then there is an infinitesimally rigid framework (G,q) for which the points q(v), v∈V(G), are distinct points of the k×k grid, where k=⌈√|V|-1⌉+9. We also show that such a framework on G can be constructed in O(| V|3) time.
ASJC Scopus subject areas
- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics