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

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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.