一种设计分解的正确性证明(英文)  

The Correctness Proof of a Decomposing Approach

作　　者：袁波[1] 李彦涛[1] 孙家广[1] 

机构地区：[1]清华大学计算机科学与技术系,北京100084

出　　处：《软件学报》2001年第3期323-328,共6页Journal of Software

基　　金：国家自然科学基金&&

摘　　要：二维变量化设计系统可以用含有 n个未知数、m个方程的非线性方程组表示 .通过设计分解可以提高几何约束求解的效率和数值稳定性 .给出了一种基于图论的设计分解方法及其正确性证明 .该方法可以 (1)处理结构欠约束系统的分解 ;(2 )检测出冗余约束 .分解算法在有限步内终止 。Mathematically a 2D constrained design system can be modeled by m independent nonlinear equations with n design variables and the design process can be viewed as a process of solving a geometric constraint system. Design decomposition is a highly effective way to improve a geometric constraint solver to make it efficient and robust. This paper reports a graph based decomposing approach and gives the correctness proof of the approach: (1) this approach can deal with the decomposition of structurally under constrained systems, (2) this approach can detect structurally over constrained systems, (3) the approach can terminate within finite number of steps, and (4) the solving steps obtained through the decomposing approach are structurally consistent.

关 键 词：设计分解 几何约束求解 规约 三维变量设计系统 图论 CAD 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]