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

Samanci, Hatice Kusak

doi:10.46939/j.sci.arts-21.3-a12

Cited by 2 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…dt where ΔP i;j ¼ P iþ1;j − P i;j is the difference between the intermediate points (Kus ¸ak Samancı, 2021).…”

Section: Bezier Curvementioning

confidence: 99%

See 1 more Smart Citation

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

Samanci

2023

View full text Add to dashboard Cite

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.

show abstract

“…dt where ΔP i;j ¼ P iþ1;j − P i;j is the difference between the intermediate points (Kus ¸ak Samancı, 2021).…”

Section: Bezier Curvementioning

confidence: 99%

“…Ceylan et al (2021) studied some geometric properties of the rational Bezier curves. Kus ¸ak Samancı (2021) computed the Serret-Frenet frame of the rational Bezier curves in 3-dimensional Euclidean space by the algorithm method.…”

Section: Introductionmentioning

confidence: 99%

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

Samanci

2023

View full text Add to dashboard Cite

show abstract

“…Additionally, numerical methods and energy functionals have been applied to obtain quasi-minimal surfaces [ 3 , 5 – 7 , 9 , 24 – 27 ]. Recent studies on the Serret-Frenet frame, such as the work by Samanci et al [ 28 ], have provided further insights into this topic. In the field of free field measurements under aided conditions, Razzaq et al [ 29 ] introduced a new loudness function that incorporates Bézier interpolation to improve accuracy.…”

Section: Introductionmentioning

confidence: 99%

Geometric analysis of non-degenerate shifted-knots Bézier surfaces in Minkowski space

Bashir,

Ahmad

2024

PLoS ONE

View full text Add to dashboard Cite

In this paper, we investigate the properties of timelike and spacelike shifted-knots Bézier surfaces in Minkowski space-E 1 3. These surfaces are commonly used in mathematical models for surface formation in computer science for computer-aided geometric design and computer graphics, as well as in other fields of mathematics. Our objective is to analyze the characteristics of timelike and spacelike shifted-knots Bézier surfaces in Minkowski space-E 1 3. To achieve this, we compute the fundamental coefficients of shifted-knots Bézier surfaces, including the Gauss-curvature, mean-curvature, and shape-operator of the surface. Furthermore, we present numerical examples of timelike and spacelike bi-quadratic (m = n = 2) and bi-cubic (m = n = 3) shifted-knots Bézier surfaces in Minkowski space-E 1 3 to demonstrate the applicability of the technique in Minkowski space.

show abstract

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

Cited by 2 publications

References 15 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

Geometric analysis of non-degenerate shifted-knots Bézier surfaces in Minkowski space

Contact Info

Product

Resources

About