An approach for designing a developable surface through a given line of curvature

Developable surface and line of curvature play an important role in geometric design and surface analysis. This paper proposes a new method to construct a developable surface possessing a given curve as the line of curvature of it. We analyze the necessary and sufficient conditions when the resultin...

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Bibliographic Details
Published in:Computer aided design 2013-03, Vol.45 (3), p.621-627
Main Authors: Li, Cai-Yun, Wang, Ren-Hong, Zhu, Chun-Gang
Format: Article
Language:English
Subjects:
Computer aided design
Construction
Curvature
Cylinders
Design engineering
Developable surface
Frenet frame
Line of curvature
Mathematical analysis
Tangents
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Summary:Developable surface and line of curvature play an important role in geometric design and surface analysis. This paper proposes a new method to construct a developable surface possessing a given curve as the line of curvature of it. We analyze the necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface. Finally, we illustrate the convenience and efficiency of this method by some representative examples. ► We construct a developable surface possessing a given curve as the line of curvature. ► We derive the conditions when the developable surface is cylinder, cone or tangent surface. ► The function θ(s) can control the shape of the developable surface.
ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2012.11.001