通用几何约束系统统一建模研究

摘要

A united modeling method of generalized geometric constraint system is investigated on the basis of expressing geometric constraints and geometric elements by basic geometric constraints and Euler parameter, respectively. After ana-lyzing the decoupled property of orientation and position constraints related with spatial geometric elements, the basic bodies are summarized into ball, box and ball-box body to express spatial geometric elements, together with assembly con-straints expressed by a combination of basic constraints, which forms a particular hierarchy structure of geometric con-straint model. The geometric constraint system is coded as a directed geometric constraint graph which describes the rela-tion among the basic geometric elements. The model method can reflect the decoupled property of orientation and posi-tion constraints clearly. The smaller solving units and the efficient solving sequence can be obtained. This method has been implemented in prototype system WhutVAS.%在几何约束和几何实体的基本约束和欧拉参数表达的基础上，研究了通用几何约束系统的统一建模问题。通过对三维几何实体姿态约束和位置约束解耦性的分析，抽象出球实体、盒体和球盒体三种基本几何实体表达空间几何实体，并以基本约束的组合表达几何约束，形成几何约束模型特有的层次结构；并以有向图管理几何约束系统，可以清晰地反映姿态约束和位置约束的解耦性，实现约束系统的细粒度分解，得到规模更小的求解序列，实现高效求解。方法实现于原型系统WhutVAS中。