Loxodromes on twisted surfaces in Lorentz–Minkowski 3-space

Abstract

In this paper, first, we give the general formulas according to first fundamental form of a surface for different types of loxodromes, meridians and surfaces in [Formula: see text]. After that, we obtain the differential equations of loxodromes on Type-I, Type-II and Type-III twisted surfaces in [Formula: see text] and also, we state a theorem which generalizes the differential equations of different types of loxodromes on the twisted surfaces for a special case. Finally, we provide several examples for visualizing our obtained results and draw our loxodromes and meridians on twisted surfaces with the aid of Mathematica.

Surface Applications of T-Bezier curves

“…Surface geometry is an application of curves for engineering and industrial designs such as, rotational surfaces (see [1], [2]), tensor product surfaces (see [16]), rational Bezier surfaces, B-spline surfaces (see [11]), NURBS surfaces and etc (see [17], [18]). These surfaces have been studied by geometers and engineers generally in Euclidean space, Minkowski space (see [21]), Galilean space, pseudo-Galilean space and etc (see [1][2][3][4][5][6][7][8], [10][11][12]). For example, Xi-An Hana, YiChen Maa, XiLi Huangc have used T-basis functions with two shape parameters in their paper which is the specific type of generalized trigonometric Bezier (i.e.…”