A Surface Pencil with Bertrand Curves as Joint Curvature Lines in Euclidean Three-Space
Open Access
Abstract
The main outcome of this work is the construction of a surface pencil with a similarity to Bertrand curves in Euclidean 3-space . Then, by exploiting the Serret–Frenet frame, we deduce the sufficient and necessary conditions for a surface pencil with Bertrand curves as joint curvature lines. Consequently, the expansion to the ruled surface pencil is also designed. As demonstrations of our essential findings, we illustrate some models to emphasize the process.
Keywords
This publication has 43 references indexed in Scilit:
- Parametric representation of a surface pencil with a common asymptotic curveComputer-Aided Design, 2012
- Parametric representation of a surface pencil with a common line of curvatureComputer-Aided Design, 2011
- Computing lines of curvature for implicit surfacesComputer Aided Geometric Design, 2009
- Extracting lines of curvature from noisy point cloudsComputer-Aided Design, 2009
- A generalization of surfaces family with common spatial geodesicApplied Mathematics and Computation, 2008
- Lines of curvature and umbilical points for implicit surfacesComputer Aided Geometric Design, 2007
- Parametric representation of a surface pencil with a common spatial geodesicComputer-Aided Design, 2004
- Umbilics and lines of curvature for shape interrogationComputer Aided Geometric Design, 1996
- Bertrand offsets of ruled and developable surfacesComputer-Aided Design, 1991
- An application of Bertrand curves and surfaces to CADCAMComputer-Aided Design, 1985