geometric constraint solving via c-tree decomposition
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.
geometric constraint solving generalized stewart platform decomposition tree assembly parametric cad general construction sequence