基于柔性约束关系的二维几何系统的建模及求解

采用约束图 (无向图 )来表达几何系统的柔性约束关系模型 ,通过面向对象技术用类封装系统几何基元并通过无向图的扩展邻接多重表来构建该系统模型 ;对不同约束的具体处理方法可归纳并规范为处理规则 ,规则也采用规则图 (无向图 )的形式来表达 ,对于每一个规则 ,设一个标识。我们建立两种典型类型的规则图 ,对应于两种类型的规则图分别建立两个函数 ,在函数体中根据规则的标识将规则映射为方程(组 ) ,通过数值算法得到方程 (组 )的解 ;在约束模型推理求解过程中 ,根据人工智能技术中深度优先搜索算法并结合几何元素的自由度分析 ,搜索到可依次求解未知元素的约束子图 ,对于约束子图我们同样设一标识 ,约束子图和规则图通过标识相匹配 ,根据规则图的类型 ,调用对应于该类型规则的函数即可求解出约束子图中的未知元素

A Method for Establishing and Solving 2D Geometrical System Model Bas ed on Flexible Constraint Relation

The constraint graph(undirected graph) is used t o represent the flexible relations in a geometry model.Using the OOP technique ,we can encapsulate the geometrical primitives by classes.An extended construc tion of the adjacent multilist of the undirected graph is used to build and stor e the geometry model.The constraint acting rule graph is used to represent a co nstraint processing rule and the rule graph is also the undirected graph.For ea ch rule graph,we set an identifier.The rule graphs are classified into two cat egories and a corresponding function is created for each category.Based on the identifier,the rule is translated into equations and the system of equations is solved using numerical method.Based on the analysis of the degree of freedom o f the geometrical primitive and depth-first algorithm,the constraint graph is decomposed into a series of subgraph in the constraint solving.Subgraphs are ma tched with the rule graph through the identifier and can be solved using the cor responding rule function.