Geometric constraint solving via C-tree decomposition

Abstract

This paper has two parts. First, we propose a method which can be used to decompose a geometric constraint graph into a c-tree. With this decomposition, solving for a well-constrained problem is reduced to the solving for smaller rigid bodies if possible. Second, we give the analytical solutions to one of the basic merge patterns used to solve a c-tree: the 3A3D general Stewart platform, which is to determine the position of a rigid body relative to another rigid body when we know three angular and three distance constraints between the two rigid bodies.