Differential geometry properties of lines of curvature of parametric surfaces and their visualization

作者：Joo Han Kyul; Yazaki Tatsuya; Takezawa Masahito; Maekawa Takashi^*

来源：Graphical Models, 2014, 76(4): 224-238.

DOI：10.1016/j.gmod.2014.05.001

• Lines of curvature
• Curvature
• Torsion
• Plate development
• Line heating

We present algorithms for computing the differential geometry properties of lines of curvature of parametric surfaces. We derive a unit tangent vector, curvature vector, binormal vector, torsion, and algorithms to evaluate their higher-order derivatives of lines of curvature of parametric surfaces. Among these quantities, it is shown that the curvature and its first derivative of the lines of curvature lend a hand for the formation of curved plates in shipbuilding. We also visualize the twist of lines of curvature, which enables us to observe how much the osculating plane of the line of curvature turns about the tangent vector.

• 出版日期2014
• 单位MIT