Combining constructive and equational geometric constraint-solving techniques

Abstract

In the past few years, there has been a strong trend towards developing parametric, computer-aided design systems based on geometric constraint solving. An effective way to capture the design intent in these systems is to define relationships between geometric and technological variables. In general, geometric constraint solving including functional relationships requires a general approach and appropriate techniques to achieve the expected functional capabilities. This work reports on a hybrid method that combines two geometric constraint solving techniques: constructive and equational. The hybrid solver has the capability of managing functional relationships between dimension variables and variables representing conditions external to the geometric problem. The hybrid solver is described as a rewriting system and is shown to be correct.