Parametric representation of a surface pencil with a common spatial geodesic |
| |
Authors: | Guo-Jin Wang [Author Vitae] [Author Vitae] Chiew-Lan Tai [Author Vitae] |
| |
Affiliation: | a State Key Lab of CAD and CG, Department of Mathematics, Zhejiang University, Hangzhou 310027, China b Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China c Department of Computer Science, Hong Kong University of Science and Technology, Hong Kong, China |
| |
Abstract: | 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. |
| |
Keywords: | Surface pencil Geodesic Frenet frame Surface flattening |
本文献已被 ScienceDirect 等数据库收录! |
|