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Parametric representation of a surface pencil with a common line of curvature

✍ Scribed by Cai-Yun Li; Ren-Hong Wang; Chun-Gang Zhu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
986 KB
Volume
43
Category
Article
ISSN
0010-4485

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✦ Synopsis

Line of curvature on a surface plays an important role in practical applications. A curve on a surface is a line of curvature if its tangents are always in the direction of the principal curvature. By utilizing the Frenet frame, the surface pencil can be expressed as a linear combination of the components of the local frame. With this parametric representation, we derive the necessary and sufficient condition for the given curve to be the line of curvature on the surface. Moreover, the necessary and sufficient condition for the given curve to satisfy the line of curvature and the geodesic requirements is also analyzed.

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