Parametric representation of a surface pencil with a common line of curvature
Parametric representation of a surface pencil with a common line of curvature
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具有公共曲率线的表面铅笔的参数化表示
DOI：
10.1016/j.cad.2011.05.001
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发表时间：
2011-09-01
影响因子：
4.3
通讯作者：
Zhu, Chun-Gang
中科院分区：
文献类型：
--
作者：
Li, Cai-Yun;Wang, Ren-Hong;Zhu, Chun-Gang
曲面上的曲率线在实际应用中起着重要作用。如果曲面上的曲线的切线始终沿主曲率方向，则该曲线是曲率线。通过利用 Frenet 框架，表面铅笔可以表示为局部框架组件的线性组合。通过这种参数表示，我们推导出给定曲线成为曲面上的曲率线的充分必要条件。此外，还分析了给定曲线满足曲率线和测地线要求的充要条件。 (C) 2011 Elsevier Ltd. 保留所有权利。
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. (C) 2011 Elsevier Ltd. All rights reserved.