Zamanımsı Asal Normalli Uzayımsı Bezier Eğrisinin Bazı Geometrik Özellikleri

Samanci, Hatice Kusak

doi:10.17776/csj.344353

Cited by 9 publications

(5 citation statements)

References 4 publications

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“…Corollary 2.8 ( [15]). Let b(t) be a spacelike Bézier curve with timelike normal and p j are control points.…”

Section: Article Informationmentioning

confidence: 99%

“…In [12], Ugail, Marquaez and Yılmaz handled the conditions of timelike and spacelike Bézier surfaces. The Serret-Frenet frames, curvatures and torsion of the timelike and spacelike Bézier curves were calculated at the end points in [13][14][15][16]. Our aim in this paper is to investigate the timelike and spacelike Bézier curve of degree m at all points.…”

Section: Introductionmentioning

confidence: 99%

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The Geometry of Bezier Curves in Minkowski 3−Space

Ceylan

2023

Universal Journal of Mathematics and Applications

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“…Corollary 2.8 ( [15]). Let b(t) be a spacelike Bézier curve with timelike normal and p j are control points.…”

Section: Article Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Geometry of Bezier Curves in Minkowski 3−Space

Ceylan

2023

Universal Journal of Mathematics and Applications

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“…Georgiev (2008) analyzed the Bezier curves in 3-D Minkowski space for the first time. Then, Kuşak Samancı (2018a, b, c, d) researched the Bezier, space-like rational Bezier, timelike rational Bezier, and the timelike uniform B-spline curves in Minkowski 3-space. Moreover,Kuşak Samancı et al .…”

Section: Introductionmentioning

confidence: 99%

The quasi-frame of the rational and polynomial Bezier curve by algorithm method in Euclidean space

Samanci

2023

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PurposeFrames play an important role in determining the geometric properties of the curves such as curvature and torsion. In particular, the determination of the point types of the curve, convexity or concavity is also possible with the frames. The Serret-Frenet frames are generally used in curve theory. However, the Serret-Frenet frame does not work when the second derivative is zero. In order to eliminate this problem, the quasi-frame was obtained. In this study, the quasi frames of the polynomial and rational Bezier curves are calculated by an algorithmic method. Thus, it will be possible to construct the frame even at singular points due to the second derivative of the curve. In this respect, the contribution of this study to computer-aided geometric design studies is quite high.Design/methodology/approachIn this study, the quasi frame which is an alternative for all intermediate points of the rational Bezier curves was generated by the algorithm method, and some variants of this frame were analyzed. Even at the points where the second derivative of such rational Bezier curves is zero, there is a curve frame.FindingsSeveral examples presented at the end of the paper regarding the quasi-frame of the rational Bezier curve, polynomial Bezier curve, linear, quadratic and cubic Bezier curves emphasize the efficacy and preciseness.Originality/valueThe quasi-frame of a rational Bezier curve is first computed. Owing to the quasi frame, it will have been found a solution for the nonsense rotation of the curve around the tangent.

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“…Numerous studies have been conducted on Bézier curves and surfaces, for example, Farin, 14 Farouki, 15 Hoschek, 16 Tiller and Hanson, 17 Potmann 18 Gray, 19 Chen et al, 20 Pottmann and Paukowitsch, 21 Krasauskas, 22 Reyes, 23 Mainar et al, 24 Jüttler and Wagner, 25 Q.J. Ge and Sirchia, 26 Mavroidis and Roth, 27 and Cholewa et al 28 Some other works 29–49 are given recently.…”

Section: Introductionmentioning

confidence: 99%

The new characterization of ruled surfaces corresponding dual Bézier curves

İncesu

2021

Math Methods in App Sciences

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Let be a Bézier curve in D3, that is, the control points of are the vectors in D3 = {u = (u1, u2, u3) : ui ∈ D,i = 1,2,3} which is the set of dual vectors whose each coordinate components are dual numbers defined as a+εa* : a,a* ∈ R,ε ≠ 0; ε2 = 0. So the spherical projection of is a spherical curve denoted by on the unit sphere in D3 and every point of corresponds to a directed line in real space R3 by Study transformation. In this study, the ruled surface X(t, ν) corresponding to this projection curve of dual Bézier curve is stated in terms of the parametric equation of the real and dual part of a given dual Bézier curve . Also, in this study, some fundamental characteristics such as the striction curve, the Gaussian curvature, and the distribution parameter of the ruled surface X(t, ν) corresponding to this projection curve of the dual Bézier curve are investigated. These concepts at any point are stated in terms of the control points of the given dual Bézier curve .

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Zamanımsı Asal Normalli Uzayımsı Bezier Eğrisinin Bazı Geometrik Özellikleri

Abstract: The aim of present paper is to introduce and investigate the spacelike Bezier curve with a timelike principal normal in Minkowski 3-space. The Serret-Frenet frame, curvatures and the derivation formulas of the curve at the starting and ending points are studied.

Cited by 9 publications

References 4 publications

The Geometry of Bezier Curves in Minkowski 3−Space

The Geometry of Bezier Curves in Minkowski 3−Space

The quasi-frame of the rational and polynomial Bezier curve by algorithm method in Euclidean space

The new characterization of ruled surfaces corresponding dual Bézier curves

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