A 2-D geometric constraint solver using DOF-based graph reduction

Abstract

In this paper, we propose a new DOF-based graph reduction approach to geometric constraint solving. In the proposed approach, we incrementally solve a geometric constraint problem that is not ruler-and-compass constructible by incrementally identifying a set of constrained geometric entities with 3 DOF (degree of freedom) as a rigid body and determining the geometric entities in the rigid body using one of two solving procedures: algebraic procedure and numerical procedure, instead of solving it simultaneously using a numerical method. By solving a complex geometric constraint problem incrementally, the proposed method can maximize the efficiency and robustness of a geometric constraint solver.