基于检索优化的三维特征建模方法研究

In this task, a 3D history-independent feature modeling method is researched. Topological faces are named by feature names. Topological edges and vertexes are named by their adjacent faces respectively. Virtual topological entities and sub-edges are introduced to solve the problem that topological entities disappear or can not construct geometry boundaries of the model. Feature dependent graph is extended, which makes it have hierarchical structures. In history-independent feature operations, the rules to determine the priorities of feature modification are proposed to reconstruct the model correctly. Ullmann algorithm is applied to model retrieval based on shape similarity and neighbor structure similarity. The reusable parts are retrieved from the existing model and are applied to the modeling process in which the method of constraint solving is utilized to improve the modeling efficiency. The definitions of dimensional rigid body kinematics are used for reference. Based on Euler parameter expressions of geometric entities, constraint expressions suitable to the history-independent modeling are given. Geometric constraints are transformed into algebraic expressions, and the process of solving algebraic equations is regarded as optimization problems. Particle swarm optimization algorithm is used to search solutions. Premature estimation mechanism is introduced to check the evolution of the swarm. Swarm fitness variance is computed to decide whether the particle swarm gets into the local extremum. When the algorithm gets into the local extremum, the chaos search strategy is used to activate particles and search the global best solution. The purpose of this task is to promote the efficiency of editing and modifying models.

本项目研究历程无关的三维特征建模方法。利用特征名来标识拓扑面，以邻接面为基础来命名边和点。引入虚拓扑元素与子边的概念来处理拓扑元素消失和不构成几何边界的问题。扩展特征依赖图，使其具有一定的层次结构。在历程无关特征操作中，提出确定特征修改优先级的相关规则，以实现模型的正确重构。以面的形状相似性和邻域结构相似性为基础，使用Ullmann算法进行模型检索。从已有模型中检索可重用部件，并将其用于约束求解，以提高造型效率。借鉴空间刚体运动学的基本定义，以几何实体的欧拉参数表示为基础，建立适用于历程无关建模的约束表达形式。将几何约束转化为代数表达式，将代数方程组的求解视为优化问题。利用粒子群优化算法进行搜索，引入早熟监视机制来观察种群的进化情况，计算种群适应度方差来判断搜索过程是否陷入局部最优。当陷入局部最优时，使用混沌搜索策略进行激活，指导粒子群寻找最优解，提高模型的可编辑性和可修改性。

历程无关建模是计算机辅助设计领域中的一个关键问题。历程无关建模技术将会极大地提高系统操作的灵活性和造型设计效率。本项目提出了一种基于局部历史的拓扑面编码方法，利用特征、操作步骤和操作历史来对拓扑面进行编码。将模型的变化归结为面的变化，对面继承、面相交和面合并操作中的拓扑面编码进行正确地处理，以维护模型的一致性。根据图元-参数图和特征依赖图来获取最小特征相关集，以确定模型操作所涉及的最小范围，降低建模的难度。在建模过程中，设计了确定特征优先级的相关算法，以生成满足用户设计意图的模型。利用边数差异来度量源模型面与目标模型面之间的形状相似度，引入面邻接对应关系矩阵来衡量两个模型面之间的结构相似性。利用贪心算法和蚁群算法来计算源模型与目标模型之间的整体相似性。将模型中的几何约束关系表示为一组代数方程组，利用代数方程组来构造目标函数。将几何约束求解问题转化为目标函数的优化问题。利用群智能算法来获取模型的最优解。实验结果表明：所提出的方法使模型检索和几何约束求解的效率有所提高。本项目的研究为历程无关建模工作提供了支持。