三维几何约束系统的等价性分析

针对过约束、完整约束和欠约束三维几何约束系统的求解问题,提出了等价性分析方法.该方法基于三维几何约束系统的内在等价性,充分挖掘几何领域知识,依据拆解约束闭环、缩减约束闭环和析出约束闭环等原则,采用等价约束替换来处理几何约束闭环问题,优化几何约束图的结构,实现几何约束系统的优化分解.最后用多个实例验证了该方法的正确性和有...

Equivalence Analysis of 3D Geometric Constraint Systems

This paper proposes a 3D geometric constraint solving method, based on equivalence analysis in graph theory, that can handle over-constrained, well-constrained, and under-constrained configurations naturally and efficiently. The basic idea is that there are equivalent geometric constraint systems with different geometric constraint graphs. If the geometric domain knowledge is exploited to transform a geometric constraint system into an equivalent one that has a better geometric constraint graph structure using equivalent constraint substitution, the decomposition of geometric constraint system can be optimized. Therefore, the proposed approach will not depend on the initial geometric constraint graph structure, but on the inherent characteristic of the geometric constraint system. This proposition can usually find the optimal decomposition of the geometric constraint system. Several typical examples have been given to illustrate the correctness and effectiveness of the proposed method.