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

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 1^st and 2^nd - 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.