Evolution of Space Curves Using Type-3 Bishop Frame

Document Type: Research articles


Department of Mathematics Faculty of Science, Assiut University, Assiut, Egypt


In this paper, Firstly, we introduce a new version of Bishop frame using a common vector field as normal vector field of a regular curve and call this frame as type-3 Bishop frame. Geometric visualization for both Frenet frame and type-3 Bishop frame are plotted. Secondly, time evolution equation for type-3 Bishop frame and type three bishop curvatures are obtained and we plotted the evolving curve via the numerical integration of type-3 Bishop Serret Frenet equations. Finally, surfaces generated by evolving a regular space curve in $\mathbb{R}^3$ as it evolves over time with arbitrary velocities attached to type-3 Bishop frame are obtained. We plotted these surfaces via numerical integration of Gauss-Weingarten equations.


Article Title [Persian]


Abstract [Persian]