几何约束求解的简化迭代算法  

A Simplified Iterative Algorithm to Solve Geometric Constraints

作　　者：石志良[1] 陈立平[1] 

机构地区：[1]华中科技大学国家CAD支撑软件工程技术研究中心,武汉430074

出　　处：《计算机辅助设计与图形学学报》2006年第6期787-792,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家重点基础研究发展规划项目(2003CB716207);国家自然科学基金(60503069)

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·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.

关 键 词：几何推理 几何约束 几何约束求解 图分解 等价自由变量 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]