Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space

Authors

  • Wageeda Mohamed Mahmoud Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt
  • Mohamed Abdellatif Soliman Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
  • Samar Abdel Hafez Moukhtar Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt

DOI:

https://doi.org/10.15379/ijmst.v10i3.1864

Keywords:

Loft Surface; Isotropic Space; Quadratic Bezier Curve; Hermite Cubic Curve; Double Helix DNA Surface; Cusp Surface.

Abstract

This paper aims to design and generate a loft surface using three distinct curves (Hermitee cubic curve, straight line, and quadratic Bezier curve) and analyze its characteristics in isotropic space using type-2-Bishop. Moreover, the loft surface's 1st and 2nd - fundamental forms in the loft surface were investigated. In addition, their Gaussian, mean, and second Gaussian curvatures in I3 were computed using the first and second type-2-Bishop curvatures. Furthermore, the required and adequate conditions for the surface with type 2-Bishop curvatures that are developable, minimal, and Weingarten surfaces (W-surface) were furnished. Besides, based on our results, two applications were provided to create and design a loft surface in biology: a double helix DNA surface and a cusp surface and all the above properties (I, II, H, K, K11, developable, minimal, and W-surface) were studied.

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Published

2023-09-06

How to Cite

[1]
W. M. . Mahmoud, M. A. . Soliman, and S. A. H. . Moukhtar, “Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space”, ijmst, vol. 10, no. 3, pp. 1951-1968, Sep. 2023.