Abstract: To reuse design knowledge in 3D CAD model, a CAD model retrieval method by using Lagrange multiplier method to solve attribute adjacency graph matching was presented. Firstly, 3D CAD models for search object and targeted search object were transformed to attribute adjacency graph using boundary representative information in 3D CAD models. Then, the vertex compatibility matrix and edge compatibility matrix between the attribute adjacency graph of the target and searched model were calculated, and the measurement of the two models similarity was created from the compatibility matrices, which served as the objective function for optimally selecting vertex mapping matrix M between the two models. At last, after relaxing objective function as equality constraints, Lagrange multiplier method was used to solve it. Experimental results showed that this method was able to support the 3D model retrieval and the similarity between the two models was ranked.

Key words: Lagrange multiplier method, model retrieval, attribute adjacency graph, computer aided design

摘要： 为了重用三维CAD模型中包含的设计知识，提出一种用拉格朗日乘子法求解属性邻接图匹配的三维CAD模型搜索方法。首先应用三维CAD模型中的边界表示信息，将搜索目标三维CAD模型与待搜索三维CAD模型转化为属性邻接图；然后计算搜索目标三维CAD模型与待搜索三维CAD模型属性邻接图之间的顶点和边的相似程度矩阵，并利用它建立两个三维CAD模型相似程度的度量作为选择不同顶点匹配矩阵M的优化目标函数；将目标函数松弛为等式约束后，采用拉格朗日乘子法进行求解。实验结果表明，该方法能够搜索到相似的三维CAD模型，并对模型的相似程度进行排序。

关键词: 拉格朗日乘子法, 模型搜索, 属性邻接图, 计算机辅助设计