Numerical computing of isophote curves, general helices, and relatively normal-slant helices in Minkowski 3-space

Abstract

In this paper, we present a method for numerical computing of some characteristic kinds of non-null curves lying on a non-degenerate surface in Minkowski space (Formula presented.). Namely, we obtain the system of the first-order ordinary differential equations that correspond to general helix, relatively normal-slant helix, and isophote curve and integrate it under chosen initial conditions by applying the ode45 function of MATLAB and Runge-Kutta method. Depending on the kind of curve, we assume that parametric equation of the surface, an axis vector, value of the real cosine or hyperbolic cosine of the corresponding pseudo angle between axis vector and Darboux frame's vector, normal curvature, and geodesic torsion of the curve are given. Finally, we provide the related examples of numerically computed characteristic curves.