Development of methods of determining shape similarities for plane curves and surfaces using geometrical information

在CAD/CAM、计算机图形学和机器人视觉等许多工程领域中，三维物体的处理和操作尤为重要。三维物体的几何相似性识别是工艺规划、自动机器人眼机构的构建、设计模型和产品信息检索等领域的需要。本文提出了平面曲线和三维曲面物体的几何相似性判定算法。平面曲线与曲面的相似性比较本文描述了由细分技术生成的两条平面曲线和两个曲面之间的形状相似性的有效判定方法。这些方法的基本思想是基于两个形状的控制点匹配。使用对应点之间的距离来计算数值相似性。各种例子进行测试，以确认该方法的实用性。结果表明，相似度的数值计算结果与我们的直观结果相吻合。2.基于特征部分的三维物体相似度比较此外，本文还提出了一种基于特征部分的三维物体相似度的确定方法。该方法包括以下三个步骤。（1）利用模式匹配技术提取实体模型的形状特征，并由形状特征集生成依赖图。（2）通过对两个依赖图的比较，检测出公共子图，并对图的整体结构进行相似性估计。（3）在图形结构相似的情况下，确定对应特征部分的形状相似性。

In many engineering fields such as CAD/CAM, computer graphics and robot vision, processing and manipulating 3D objects is especially important. Recognition of geometrical similarities of 3D objects is required for process planning, constructing eye mechanism of automated robots, information retrieval of design models and products, etc. In this research, algorithms for deciding the geometrical similarities of plane curves and 3D objects with curved surfaces are proposed.1. Similarity comparison for plane curves and curved surfacesWe describe methods for efficiently deciding the shape similarity between two plane curves and between two surfaces, which are generated by the subdivision technique. The basic idea of those methods is based on matching the control points of two shapes. The numerical similarity is calculated using the distance between corresponding points. Various examples are tested to confirm the usefulness of the method. The results show that the similarities determined numerically match with our intuition.2.Similarity comparison of 3D objects based on feature partsIn addition, this report presents a method for determining the similarity of 3D objects, based on feature parts. The method consists of following three procedures. (1)The form features of a solid model are extracted by using the pattern matching technique, and the dependency graph is generated from the set of form features. (2)The common sub-graphs are detected in comparison with two dependency graphs, and the similarity of overall graph structures is estimated. (3)The shape similarity of the corresponding feature parts is determined, if the graph structures are similar.A similarity retrieval system of 3D objects has been also constructed experimentally.