Browsing by Author "Senyurt, Suleyman"

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    An Examination of Perpendicular Intersections of Bfrs And Mfrs In E-3
    (2018) Kilicoglu, Seyda; Senyurt, Suleyman; GRY-4465-2022
    We already have defined and found the parametric equations of Frenet ruled surfaces which are called Bertrandian Frenet Ruled Surfaces (BFRS) and Mannheim Frenet Ruled Surfaces (MFRS) of a curve a, in terms of the Frenet apparatus. In this paper, we find a matrix which gives us all sixteen positions of normal vector fields of eight BFRS and MFRS in terms of the Frenet apparatus. Further using the orthogonality conditions of the eight normal vector fields, we give perpendicular intersection curves of the eight BFRS and MFRS.
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    An Examination on Helix as Involute, Bertrand Mate and Mannheim Partner of Any Curve Alpha in E-3
    (2017) Senyurt, Suleyman; Kilicoglu, Seyda
    In this study we consider three offset curves of a curve a such as the involute curve alpha*, Bertrand mate alpha(1) and Mannheim partner alpha(2). We examined and find the conditions of Frenet apparatus of any curve alpha which has the involute curve a*, Bertrand mate alpha* and Mannheim partner alpha(2) are the general helix.
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    On the Differential Geometric Elements of the Involute D-Scroll in E3
    (2015) Senyurt, Suleyman; Kilicoglu, Seyda; GRY-4465-2022
    Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], D-scroll, which is known as the rectifying developable surface, of any curve and the involute D-scroll of the curve alpha are alreadyDefined, E-3. In this paper, we consider these special ruled surfaces D-scroll and involute D-scroll, associated to a space curve with curvature k(1) not equal 0 and involute beta. We will examine theDifferential geometric elements (such as, Weingarten map S, curvatures K and H) of the involute D-scroll and D-scroll relative to each other. Further we will examined the fundamental forms too.
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    On the Involute of the Cubic Bezier Curve By Using Matrix Representation in E-3
    (2020) Kilicoglu, Seyda; Senyurt, Suleyman
    In this study we have examined, involute of the cubic Bezier curve based on the control points with matrix form in E-3. 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 E-3.
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    On The Matrix Representation Of 5th Order Bezier Curve And Its Derivatives In E-3
    (2022) Kilicoglu, Seyda; Senyurt, Suleyman
    Using the matrix representation form, the first, second, third, fourth, and fifth derivatives of 5th order Bezier curves are examined based on the control points in E-3. In addition to this, each derivative of 5th order Bezier curves is given by their control points. Further, a simple way has been given to find the control points of a Bezier curves and its derivatives by using matrix notations. An example has also been provided and the corresponding figures which are drawn by Geogebra v5 have been presented in the end.
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    On the Matrix Representation of Bezier Curves and Derivatives in E3
    (2023) Kilicoglu, Seyda; Senyurt, Suleyman; 0000-0003-1097-5541; GRY-4465-2022
    In this study we have examined, the coefficient matrix of a cubic, 4th order and nth order Bezier curves using combinations as the elements to get a pattern. Also their first, second, third derivativies are examined based on the control points, in matrix represation in E3. Further as a simple way has been given to find the equation of a Bezier curves and its derivatives using matrix product, based on the control points.
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    ON THE SECOND ORDER INVOLUTE CURVES IN E-3
    (2017) Kilicoglu, Seyda; Senyurt, Suleyman
    In this study we worked on the involute of involute curve of curve alpha. We called them the second order involute of curve alpha in E-3. All Frenet apparatus of the second order involute of curve alpha are examined in terms of Frenet apparatus of the curve alpha. Further we show that; Frenet vector fields of the second order involute curve alpha(2) can be written based on the principal normal vector field of curve alpha. Besides, we illustrate examples of our results.