1-EXTENSIONS AND GLOBAL RIGIDITY OF GENERIC DIRECTION-LENGTH FRAMEWORKS

Abstract

The problem of deciding the unique realizability of a graph in a Euclidean space with distance and/or direction constraints on the edges of the graph has applications in CAD (Computer-Aided Design) and localization in sensor networks. One approach, which has been proved to be efficient in the similar problem for graphs with distance constraints, is to study operations to construct a uniquely realizable graph from a smaller one. In this paper, we extend a result of Jackson and Jordán on the unique realizability preservingness of the so-called “1-extension” in dimension 2 to all dimensions.