中文摘要：

对参数化设计问题提出了一种新的基于DOF（Degreesoffreedom）的定性建模与仿真方法。在几何约束求解的过程中，通常的定量数值化方法由于解空间的巨大而显得低效。通过定义基本约束簇类型和规则，新方法引入定性图对几何约束进行定性建模及模型求解．经过一系列基于DOF的定性图推理过程，几何约束的定性模型被规约为一个单节点后得出一系列的构造步骤。在这个推理阶段中得出的构造步骤被确定为以后精确定量计算的次序．结合了定性推理方法的高效性以及定量方法的精确性，初步实验表明新方法能够提高约束求解的效率。

英文摘要：

A new DOF-based qualitative modeling and simulation approach to parametric design was proposed. In the procedure for solving a geometric constraint problem, usual quantitative method is inefficiency because of huge solution space. By defining basic clustering types and rules, the new approach introduced qualitative graph modeling and simulation method to build and solve geometric constraint model. Through a series of DOF-based qualitative reduction processes to isolates R＆CC （ruler-and-compass constructible configurations） from R＆CNC （ruler-and-compass non-constructible configurations）, the graph representation of a geometric configuration was reduced into a single node. As the result of this graph reduction process, a sequence of construction steps was generated, which could be made use of by quantitative method. By associating the efficiency of the graph reduction and the quantitative method＇s precise, the proposed method could maximize the efficiency of a geometric constraint solver.