To improve the efficiency and robustness of constraint solving algorithm

the paper presents a graph-constructive approach. In constructive phase

the algorithm can classify well-constrained

over constrained and under constrained configurations. By adaptively adding virtual constraints

the algorithm can handle all the above configurations

and can overcome the ill-condition constraint which occurs frequently in practice. Decomposition trees are used to reduce the scale of constraint solving problem

decompose it from global scope into many local sub-problems. By avoid solving large-scale equations

the algorithm can separately calculate the sub-problems geometrically with great improvement in efficiency and robustness. It also improves the efficiency for successive modification on constraints or geometric elements. Comparing to conventional algebra algorithms

symbolic algorithms

and rule-based algorithms

the algorithm is more practical and can be used in real-time constraint solving environment. It has been implemented in VC on Windows/NT platform

and been used as geometric constraint solving kernel of a feature based parametric modeling system GS-CAD

which is a commercial CAD system developed by Zhejiang University.