A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t) and it is parametrized through Frenet frame of the spine curve C(t). If the radius function r(t) = r is a constant, then the canal surface is called a tube or tubular surface. In this work, we investigate tubular surface with Bishop frame ...

We consider a unit speed timelike curve α in Minkowski 4-space E41 and denote the Frenet frame of α by {T,N,B1,B2}. We say that α is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction U of E41. In this work we study those helices where the function 〈B2, U〉 is constant and we give different characterizations of such curves....

Frenet-Serret and Bishop rigid-body motions have many potential applications in robotics, graphics and computer aided design. In order to study these motions new characterisations in terms of their velocity twists are derived. This is extended to general motions based on any moving frame to a space curve. Further it is shown that any such general moving frame motion is the product of a Frenet-S...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

The scope of this paper is to look at some aspects the differential geometry Bezier curves in Minkowski space. For that purpose, we firstly introduce Frenet curve 3-space. Especially, investigate Serret-Frenet frame, curvature and torsion all points. Moreover, give apparatus these end

The aim of this paper is to demonstrate that the techniques of Computer Aided Geometric Design such as spatial rational curves and surfaces could be applied to Kinematics, Computer Animation and Robotics. For this purpose we represent a method which utilizes a special class of rational curves called Rational Frenet–Serret (RF) curves for robot trajectory planning. RF curves distinguished by the...

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...