一种设计分解的正确性证明(英文)

The Correctness Proof of a Decomposing Approach

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.