A Simplified Iterative Algorithm to Solve Geometric Constraints

To improve efficiency and generality of solving non-constructible geometric constraints,a decomposing approach and a novel simplified iterative algorithm are presented.The proposed approaches work in two phases：a decomposing phase and a solving phase.The decomposing approach is based on graph theory to decompose the strongly connected components by cancelling some boundary constraints,while for underconstrained vertices,equivalence free variables are added.In solving phase,rather than undertaking simultaneously iteration of all variables,geometric constraints solving is accomplished by partial iteration of equivalence free variables alone.The presented method is effective and general,and has been successfully applied to a 2D parametric system.