Motorcycle graph enumeration from quadrilateral meshes for reverse engineering |
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Affiliation: | 1. Istanbul Technical University, Turkey;2. Chuo University, Japan;3. The University of Tokyo, Japan;1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;2. Department of Computer Science, The Technion Israel Institute of Technology, Haifa 32000, Israel;1. Technical University of Denmark, Denmark;2. Autodesk Research, Canada;1. RCAST, The University of Tokyo, 7-3-1, Hongo, Bunkyo, Tokyo 1538904, Japan;2. National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8563, Japan |
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Abstract: | Recently proposed quad-meshing techniques allow the generation of high-quality semi-regular quadrilateral meshes. This paper outlines the generation of quadrilateral segments using such meshes. Quadrilateral segments are advantageous in reverse engineering because they do not require surface trimming or surface parameterization. The motorcycle graph algorithm of Eppstein et al. produces the motorcycle graph of a given quadrilateral mesh consisting of quadrilateral segments. These graphs are preferable to base complexes, because the mesh can be represented with a smaller number of segments, as T-joints (where the intersection of two neighboring segments does not involve the whole edge or the vertex) are allowed in quadrilateral segmentation.The proposed approach in this study enumerates all motorcycle graphs of a given quadrilateral mesh and optimum graph for reverse engineering is then selected. Due to the high computational cost of enumerating all these graphs, the mesh is cut into several sub-meshes whose motorcycle graphs are enumerated separately. The optimum graph is then selected based on a cost function that produces low values for graphs whose edges trace a large number of highly curved regions in the model. By applying several successive enumeration steps for each sub-mesh, a motorcycle graph for the given mesh is found. We also outline a method for the extraction of feature curves (sets of highly curved edges) and their integration into the proposed algorithm. Quadrilateral segments generated using the proposed techniques are validated by B-spline surfaces. |
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Keywords: | Semi-regular quadrilateral mesh Motorcycle graph Mesh segmentation Reverse engineering |
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