2020
DOI: 10.47000/tjmcs.704794
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Investigating a Quadratic Bezier Curve Due to N-C-W and N-Bishop Frames

Abstract: The purpose of our paper is to investigate N-Bishop frame of the quadratic Bezier curve which is one of the effective methods for computer-aided geometric design (CAGD). Then the N-Bishop curvatures and derivative formulas for quadratics Bezier curve are calculated and give some numeric examples.

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Cited by 8 publications
(9 citation statements)
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“…Proof. From Samanci and Incesu, 39 if the Gaussian curvature of a ruled surface X(u,v) R 3 is zero, then the ruled surface is developable ruled surface or flat ruled surface. So from 33, if the Gaussian curvature K(t,v) of the ruled surface X(t, ν) is zero, then…”
Section: Resultsmentioning
confidence: 99%
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“…Proof. From Samanci and Incesu, 39 if the Gaussian curvature of a ruled surface X(u,v) R 3 is zero, then the ruled surface is developable ruled surface or flat ruled surface. So from 33, if the Gaussian curvature K(t,v) of the ruled surface X(t, ν) is zero, then…”
Section: Resultsmentioning
confidence: 99%
“…According to this, α is not the striction curve of X ( t , ν ). So from this, the striction curve of X ( t , ν ) can be written as σ()t=ϖ()t+ϱ()tδ()t, where ϱ()t=〈〉,ϖ()tδ()t‖‖δ()t2. 39 Here, the magnitude of ‖ δ ′( t )‖ can be calculated as follows: ‖‖δ=‖‖ϒ×normalϒ×ϒnormalϒ3=1‖‖ϒ3ϒ×normalϒ×ϒϒ×normalϒ×ϒ, 1‖‖ϒ3〈〉,ϒϒ〈〉,normalϒ×ϒnormalϒ×ϒ=1‖‖ϒ3‖‖ϒ‖‖ϒ×normalϒ=‖‖ϒ×normalϒ‖‖ϒ2. …”
Section: Resultsmentioning
confidence: 99%
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“…Frenet apparatus of both the n th degree Bézier curves have been examined in E 3 , in [6]. The Bishop frame and the alternative frame have been associated with the Bézier curves in [7] and [8], respectively. The matrix forms of the cubic Bézier curve and its involute have been examined in [9] and [10], respectively.…”
Section: Introductionmentioning
confidence: 99%
“…In [10], the Bertrand pairs have also been examined by B-Spline curves. Last but not least, the Bézier curves have been associated to the alternative frame in [11].…”
Section: Introductionmentioning
confidence: 99%