Mathematically a 2Dconstrained design system can be modeled by mindependent nonlinear equa-tions with n design variables and the design process can be viewed as a process ofsolving a geometric constraintsystem.Design decomposition is a highly effective way to improve a geometric constraint solver to make it effi-cient and robust.This paper reports a graph based decomposing approach and gives the correctness proof oftheapproach:(1)this approach can dealwith the decomposition ofstructurally under-constrained systems,(2)thisapproach can detect structurally over-constrained systems,(3)the approach can terminate within finite numberofsteps,and(4)the solving steps obtained through the decomposing approach are structurally consistent.%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,其结果是结构相容的
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