A Spatial Constraint Problem

Three-dimensional geometric constraint solving is a rapidly developing eld, with applications in areas such as kinematics, molecular modeling, surveying, and geometric theorem proving. While two-dimensional constraint solving has been studied extensively, there remain many open questions in the arena of three-dimensional problems. In this paper, we continue the development of our previous work on con guring a set of points and planes in three-space so that the con guration satis es a given system of constraints. The constraint system considered consists of six geometric elements and pairwise constraints between triples of the elements. We rst review the basic techniques developed in our earlier work germaine to the current problem and explain how the problem we consider in this paper occurs. We then demonstrate how to solve the case of a geometric constraint system with four points and two planes.