Results 21 to 30 of about 824,488 (198)
Frenet Frames of Trigonometric B'ezier Curves
Turkish Journal of Mathematics and Computer Science, 2022 The geometry of curves and surfaces plays a very important role in computer-aided geometric design (CAGD). The goal of this paper is to construct the Frenet frames of trigonometric B\'ezier curves in Euclidean $ 2 $ and $ 3- $space. Especially, the curvatures of these curves are investigated at the beginning and the ending points.
Ayşe Yılmaz CEYLAN +2 more
openaire +1 more source
Frenet frame with respect to conformable derivative
Filomat, 2019 Conformable fractional derivative is introduced by the authors Khalil at al in 2014. In this study, we investigate the frenet frame with respect to conformable fractional derivative. Curvature and torsion of a conformable curve are defined and the geometric interpretation of these two functions is studied.
Gozutok, Ugur +2 more
openaire +4 more sources
Hypersurfaces With a Common Geodesic Curve in 4D Euclidean space E4
International Journal of Analysis and Applications, 2023 In this paper, we attain the problem of constructing hypersurfaces from a given geodesic curve in 4D Euclidean space E4. Using the Serret–Frenet frame of the given geodesic curve, we express the hypersurface as a linear combination of this frame and ...
Sahar H. Nazra
doaj +1 more source
Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$
Journal of New Theory, 2022 In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves.
Mehmet Bektaş +2 more
doaj +1 more source
Improving Frenet's Frame Using Bishop's Frame
Journal of Mathematics Research, 2013 The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The main drawback of the Bishop frame is that the principle normal vector N is not in it.
Carroll, Daniel +2 more
openaire +3 more sources
Characterizations of Tzitzeica Curves Using Conformable Frenet Frame
, 2023 Abstract Tzitzeica curve is a mathematical curve that has been used to describe the behavior of certain physical phenomena. It was first discovered by Romanian mathematician Gheorghe Tzitzeica and has since been used to model many phenomena, including the motion of a pendulum, the oscillations of a vibrating string, and the flow of electricity ...
Has, Aykut +2 more
openaire +2 more sources
Severi–Bouligand tangents, Frenet frames and Riesz spaces
Advances in Applied Mathematics, 2015 It was recently proved that a compact set $X\subseteq \mathbb R^2$ has an outgoing Severi-Bouligand tangent vector $u\not=0$ at $x\in X$ iff some principal ideal of the Riesz space $\mathcal R(X)$ of piecewise linear functions on $X$ is not an intersection of maximal ideals. "Outgoing" means $X\cap [x,x+u]=\{x\}$.
CABRER, LEONARDO MANUEL +1 more
openaire +4 more sources
A note on natural coordinates and frenet frames
Tsinghua Science and Technology, 2007 This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe
Xiaozhou Zhou, Keqin Zhu
openaire +1 more source
Spinor Darboux equations of curves in Euclidean 3-space [PDF]
Mathematica Moravica, 2015 In this paper, the spinor formulation of Darboux frame on an oriented surface is given. Also, the relation between spinor formulation of Frenet frame and Darboux frame is obtained.
Kisi Ilim, Tosun Murat
doaj
Generalized Spacelike Normal Curves in Minkowski Three-Space
Mathematics, 2022 Equiform geometry is considered an extension of other geometries. Furthermore, an equiform frame is a generalization of the Frenet frame. In this study, we begin by defining the term “equiform parameter (EQP)”, “equiform frame”, and “equiform formulas ...
Yusra Tashkandy +4 more
doaj +1 more source