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Parametric representation of a surface pencil with a common spatial geodesic

✍ Scribed by Guo-Jin Wang; Kai Tang; Chiew-Lan Tai

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
437 KB
Volume
36
Category
Article
ISSN
0010-4485

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✦ Synopsis

In this paper, we study the problem of constructing a family of surfaces from a given spatial geodesic curve. We derive a parametric representation for a surface pencil whose members share the same geodesic curve as an isoparametric curve. By utilizing the Frenet trihedron frame along the given geodesic, we express the surface pencil as a linear combination of the components of this local coordinate frame, and derive the necessary and sufficient conditions for the coefficients to satisfy both the geodesic and the isoparametric requirements. We illustrate and verify the method by finding exact surface pencil formulations for some simple surfaces, such as surfaces of revolution and ruled surfaces. Finally, we demonstrate the use of this method in a garment design application.

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