2020 # On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3

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

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“…Recently equivalence conditions of control points and application to planar Bézier curves have been examined in [8] and [9].The Serret-Frenet frame and curvatures of Bézier curves are examined those in E 4 in [3]. Frenet apparatus of the cubic Bézier curves and involute of the cubic Bezier curve by using matrix representation have been examined in E 3 , in [11] and [12], respectively.…”

confidence: 99%

“…Recently equivalence conditions of control points and application to planar Bézier curves have been examined in [8] and [9].The Serret-Frenet frame and curvatures of Bézier curves are examined those in E 4 in [3]. Frenet apparatus of the cubic Bézier curves and involute of the cubic Bezier curve by using matrix representation have been examined in E 3 , in [11] and [12], respectively.…”

confidence: 99%

“…We have already examined the cubic Bézier curves and involutes in [11] and [12], respectively. The matrix form of the cubic Bézier curve with control points P 0 , P 1 , P 2 , and P 3 is…”

confidence: 99%

“…In [4], Frenet apparatus of the cubic Bézier curves has been examined in E 3 . We have already examine the cubic Bézier curves and involutes in [4] and [5], respectively. Before, 5 th order Bézier curve and its first, second, and third derivatives based on the control points are examined in [6,7].…”

confidence: 99%

“…Two curves are said to be parallel of one another if any curve normal to one is normal to the other. Kılıc ¸oglu and S ¸enyurt studied the involute of the cubic Bézier curve in Euclidean 3−space [2]. In [3], the evolute-involute curve couples of Bézier curves in Euclidean 3−space are investigated.…”

confidence: 99%