中文摘要：

针对几何约束系统图分解中复合顶点的求解问题,提出复合顶点的图分解算法和等价自由变量的简化迭代求解算法.通过去除复合顶点部分边界约束对复合顶点进行图分解,对求解序列中的欠约束顶点添加等价自由变量、以等价自由变量的部分迭代求解、替代系统的整体数值求解,以提高求解效率和稳定性.该算法具有很强的通用性,并在实际应用中得到验证.

英文摘要：

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.