Author:
Wang Jun,Chen Miaochao,Wang Dongyin
Abstract
Developable surface is a simple and common surface in surface modeling. Geodesic, line of curvature, asymptotic curve, and D-type curve are important characteristic curves on the surfaces. This study gives a unified method for constructing developable surface pencils interpolating these four kinds of characteristic curves. Given a regular space curve R(r), we derive a new condition that a surface pencil P (r, t) interpolating R(r) is developable. The result shows that the condition completely depends on a univalent function λ and an angle θ. By choosing different λ and θ, we can not only control the shape of P (r, t), but also make R(r) become any kind of characteristic curve on P (r, t). Furthermore, we take natural and conjugate curve pairs as those characteristic curves to construct developable surface pairs. Finally, an example of a slant helix shows that the proposed unified method is more general than other methods, and has good interactivity and convenience.
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics,Materials Science (miscellaneous),Biophysics
Reference30 articles.
1. Geometry of the shoulder of a packaging machine;Boersma;SIAM Rev Soc Ind Appl Math,1995
2. Bending and creasing virtual paper;Kergosien;IEEE Comput Graph Appl,1994
3. Fitting a woven-cloth model to a curved surface: Mapping algorithms;Aono;Computer-Aided Des,1994
4. Classes of harmonic functions in 2d generalized poincaré geometry;Bercu;Filomat,2021
5. Logarithmically improved regularity criteria for supercritical quasi-geostrophic equations in orlicz-morrey spaces;Gala;Electron J Differential Equations,2016