Introduction to Timelike Uniform B-splineCurves in Minkowski-3 Space

Samanci, Hatice Kusak

doi:10.33187/jmsm.425068

Cited by 3 publications

(2 citation statements)

References 6 publications

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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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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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“…where ε B = B, B L = ±1 and ε T = T, T L = ±1, [5]. Some studies which are studied in the Minkowski 3-dimensional space can be found in [6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Siacci's Theorem for Frenet Curves in Minkowski 3-Space

Özen

2020

Mathematical Sciences and Applications E-Notes

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For motion of a material point along a space curve, due to Siacci [1], a resolution of the acceleration vector is well known. In this resolution, the acceleration vector is stated as the sum of two special oblique components in the osculating plane to the curve. In this paper, we have studied the Siacci's theorem for non-relativistic particles moving along the Frenet curves at very low speeds relative to the speed of light in Minkowski 3-space. Moreover, an illustrative example is given to show how the aforesaid theorem works. This theorem is a new contribution to the field and it may be useful for some specific applications in theoretical, mathematical and computational physics.

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The Serret-Frenet Frame of the Rational Bezier Curves in the Euclidean-3 Space by Algorithm Method

Samanci

2021

J. Sci. Arts

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Introduction to Timelike Uniform B-splineCurves in Minkowski-3 Space

Cited by 3 publications

References 6 publications

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

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

Siacci's Theorem for Frenet Curves in Minkowski 3-Space

The Serret-Frenet Frame of the Rational Bezier Curves in the Euclidean-3 Space by Algorithm Method

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