On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$

Abstract

In this study we have examined, Bertrand mate of a cubic Bezier curve based on the control points with matrix form in E3. Frenet vector fields and also curvatures of Bertrand mate of the cubic Bezier curve are examined based on the Frenet apparatus of the first cubic Bezier curve in E3.

A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\'{e}zier Curve in Plane

“…In here, first 5 th order Bezier curve and its first, second and third derivatives have been examined based on the control points of 5 th order Bezier Curve in E 3 . Subsequently, in [15,16] involutes of cubic Bezier curves, in [17] and [18] the Bertrand and the Mannheim mate of a cubic Bézier curve by using matrix representation have been researched in E 3 . In [19], it has been researched the answer of the question "How to find a n th order Bezier curve if we know the first, second and third derivatives?…”

T-Bezier Eğrilerin Yüzey Uygulamaları

“…As an example, Bezier curves were used with minimal jerk energy (see [15]) and also studied for different spaces (see [14]). Furthermore, Many studies have been done on Bézier curves in different spaces, characterization and investigations have been made on different surfaces (see [19], [20], [23][24][25][26][27][28][29][30][31]). In addition, useful studies have been made in industrial field and examples have been made on the basis of curves (see [22]).…”

On approximation of helix by 3rd, 5th and 7th order Bezier curves in E3

“…E We have already examine in cubic Bezier curves and involutes in [7,9]. The Bertrand and the Mannheim mate of a cubic Bezier curve by using matrix representation have been researhed in 3 E [10,11], respectively. In [12], it has been examined the 5 th order Bezier curve and its derivatives.…”