几何约束求解技术是参数化特征造型系统的核心技术之一，是研究在设计者给定的各种条件下，自动生成符合要求的设计对象的技术，其实只是一个约束满足问题。基于约束满足模型的CAD技术是智能CAD研究的一个重要方向。以国家863项目“基于线框、曲线、实体、特征表示的产品造型与设计系统”和国家“九五”科技攻关项目“机械CAD/CAM系统开发及产品化”的研究为背景，本文对以几何约束求解问题为核心的变量化设计技术进行了研究。几何约束分解是结合约束求解技术的关键。一个几何约束系统本质上可以看作是一个非线性方程组，对几何约束系统进行分解可提高求解的效率与稳定性。几何约束分解又成为设计分解，基于几何约束分解策略的几何约束求解过程有两个阶段构成：构造求解序列和按照序列求解。本文在总结国内外研究成果基础山研究了几何约束问题，提住了一种基于剪枝一归约算法的几何约束分解策略。该算法在约束图表示的基础上引进了两种操作：剪枝操作和规约操作。通过交替运用两种操作，可有效处理完备约束、欠约束和过约束情况下的几何约束分解问题。主要工作包括：对几何约束分解技术进行了研究，在构图造法的基础上提出了一种基于剪枝椆嬖妓惴ǖ募负卧际纸獠呗浴６约糁规约算法进行了分析，给除了算法的正确证明。引入约束优先和几何元素优先级，以指导几何约束系统的分解过程。针对草图变量化设计的特点提出了活动约束系统的概念，通过分析几何约束系统的约束结构，构造一个规模较小的活动约束系统，以进一步减小带球几何约束系统的规模。在几何约束系统求解技术的研究基础上，开发了一个支持变量设计的二维几何约束求解器并应用于参数化特程造型系统GEM5.0的草图设计中。

Geometric constraint solving is one of the key techniques for a parametric feature-based modeling system. The aim of geometric constraint solving is to automatically generate a design object meeting all sorts of geometric constrains and requirements specified by designers. Geometric constraint solving can be looked as a constraint satisfaction problem, and the constraint satisfaction based computer aided design is an important research area of intelligent CAD . as part of research supported by the Chinese national 863 project "Wireframe, surface, solid and feature based product modeling and design system" and the Chinese National 9 th five-year plan project "mechanical CAD/CAM system and commercial applications" this dissertation studies the geometric constraint solving problem, which is the core of variational design approaches. Geometric constraint decomposition is the key task of geometric constraint solving. Substantially a geometric constraint system can be treated as a set of nonlinear equations. Geometric constraint decomposition is also called design decomposition. The constraint solving process based on the geometric constraint decomposition consists of two phases: decomposing phase and execution phase. This algorithm introduces two operation on the clipping reducing algorithm. This algorithm introduces two operations on the basis of constraint graph: clipping and reducing. By applying these two operation on a constraint graph alternately, this approach can deal with the decomposition of well, over and under constrained design system effectively. The mainly work includes:1studied the geometric constraint solving technology.2 analyzed the clipping reducing algorithm and gave the correctness proof of the algorithm. 3introduced the priorities of geometric onstraints and geometric elements to direct the geometric constraint decomposition to make the solving results meet the designers' intent as much as possible. 4 presented the concept of the active constructed of a geometric constraint system ,a small active constraint system is constructed to further decrease the scale of a geometric solving problem.5 developed a 2d geometric constraint constraint solver and applied it to the variational sketch design in the parametric feature based modeling system GEMS5.0.