Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space
Nadia Alluhaibi,
Rashad A. Abdel-Baky
Abstract:A principal curve on a surface plays a paramount role in reasonable implementations. A curve on a surface is a principal curve if its tangents are principal directions. Using the Serret–Frenet frame, the surface pencil couple can be expressed as linear combinations of the components of the local frames in Galilean 3-space G3. With these parametric representations, a family of surfaces using principal curves (curvature lines) are constructed, and the necessary and sufficient condition for the given Bertrand cou… Show more
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