A new method for designing a developable surface utilizing the surface pencil through a given curve |
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Authors: | Hongyan Zhao Guojin Wang |
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Institution: | Department of Mathematics and State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China |
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Abstract: | This paper proposes a new method for designing a developable surface by constructing a surface pencil passing through a given curve,
which is quite in accord with the practice in industry design and manufacture. By utilizing the Frenet trihedron frame, we derive the
necessary and sufficient conditions to construct a developable surface through a given curve. Considering the requirements in shoemaking
and garment-manufacture industries, we also study the special case of specifying the given curve as a geodesic. The given geodesic can
be classified into three types corresponding to each type of developable surface. We also present the polynomial representation of the
developable surface. The algorithm is convenient and efficient for applications in engineering. |
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Keywords: | CAD/CAM Developable surface Geodesic Frenet frame |
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