Quasi-Developable B-Spline Surface Design with Control Rulings |
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| Authors: | Zi-Xuan Hu Peng-Bo Bo Cai-Ming Zhang |
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| Affiliation: | 1.School of Computer Science and Technology, Harbin Institute of Technology, Weihai 264209, China;2.Shandong Co-Innovation Center of Future Intelligent Computing, Yantai 264005, China;3.Shandong Province Key Laboratory of Digital Media Technology, Shandong University of Finance and Economics, Jinan 250061, China |
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| Abstract: | We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as-developable-as-possible. Specifically, the terminal ruling lines are treated as hard constraints. Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control, our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely-designed rulings. We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications. The performance and the efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for path planning in 5-axis computer numerical control (CNC) flank milling. |
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| Keywords: | developable surface surface modeling B-spline surface numerical optimization |
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