混合式几何约束满足的研究

Research on Hybrid Geometric Constraint Satisfaction

几何约束系统可以分为陈述式和构造式两类 .为了使基于约束的设计更加符合使用要求 ,参数化 CAD系统需要综合满足两类约束 .文中研究了三维情况下陈述和构造统一的约束满足策略 ,通过引入形状自由度的概念 ,将形状变化和位置变化统一处理 .约束系统采用约束图来表示 ,各个子系统之间的层次结构利用约束层次树来表示 .采用剪枝和凝聚相结合的策略实现了欠约束和完备约束系统的分解 ,使用解析法和数值法对约束进行求解 .该策略已经在参数化 CAD系统 GEMS5 .0的二维和三维上实现 .

Geometric constraint systems can be divided into two categories: declarative and constructive systems. As far as simplicity and flexibility are concerned, parametric CAD systems should support constructive and declarative constraints synthetically. This paper describes a graph-based approach with a parametric design capability based on the combination of declarative and constructive constraints. The declarative and constructive constraint systems are organized hierarchically and we use hierarchy tree to represent them. We introduce the concept of shape degree of freedom so that shapes as well as locations of the geoms may vary to satisfy the constraints. Like most graph-based constraint solvers, the proposed method contains two phases: analysis phase and constraint evaluation phase. In the analysis phase, the clipping and reducing operations are used to decompose under-and fully-declarative constrained systems. Constructive constraint systems have natural solving sequences and there is no need for decomposition. After the analysis phase, the whole constraint system is translated into a tree structure such that the none-leaf nodes are cluster nodes and the leaf nodes are geometric elements. In the constraint evaluation phase, the inner constraints of each cluster are solved together by analytic or numerical algorithms, and then the results are propagated to the whole constraint system. The proposed strategy has been implemented both in 2D and 3D in a feature-based parametric CAD system, named GEMS 5.0.