Spanning-tree modeling method for geometric constraint satisfaction problem

It is well known that parameterization is a powerful tool for creation and reuse of models. It allows us to construct models with predefined features, as well as to form new models by modification of parameters of already existing models. These opportunities are crucial for engineers and other CAD users, since they greatly reduce the total product operation time. There are two classical types of parametric design: the more traditional one is a hierarchical approach based on a history of model creation, and more powerful one is a variational design that expresses a model by a set of constraints. In this article we introduce a mathematical approach which combines the advantages of both methods and has no their drawbacks.