Eğitim Bilimleri Fakültesi / Faculty of Education
Permanent URI for this collectionhttps://hdl.handle.net/11727/2116
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Item On the Matrix Representation of Bezier Curves and Derivatives in E3(2023) Kilicoglu, Seyda; Senyurt, Suleyman; 0000-0003-1097-5541; GRY-4465-2022In 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.Item On the Differential Geometric Elements of the Involute D-Scroll in E3(2015) Senyurt, Suleyman; Kilicoglu, Seyda; GRY-4465-2022Deriving 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.Item On Approximation of Helix by 3(rd), 5(th) and 7(th) Order Bezier Curves in E-3(2022) Kilicoglu, SeydaApproximation of helices has been studied by using in many ways. In this study, it has been examined how a circular helix can be written as Bezier curve and written the 3(th) degree, 5(th) degree, and the 7(th) degree Maclaurin series expansions of helices for the polynomial forms. Hence, they can be written cubic, 5(th) order, and 7(th) order Bezier curves, based on the control points with matrix form we have already given in E-3. Further we have given the control points of the Bezier curve based on the coefficients of the Maclaurin series expansion of the circular helix.Item On Approximation Sine Wave with the 5(Th) and 7(Th) Order Bezier Paths in Plane(2022) Kilicoglu, SeydaThere are many studies to approximate to sine curve or sine wave. In this study, it has been examined the way how the sine wave can be written as any order Bezier curve. First, it has been written the 5(th) and the 7(th) degree Maclaurin series expansion of the parametric form of sine curve. Also, they are 5(th) and the 7(th) order Bezier paths, based on the control points with matrix form in E-2. Hence it has been given the control points of the 5(th) and the 7(th) order Bezier curve based on the coefficients of the 5(th) and the 7(th) degree Maclaurin series expansion of the sine curves in three steps. Further it has been given the coefficients based on the control points of the 5(th) and the 7(th) order Bezier curve too.Item An Examination on Helix as Involute, Bertrand Mate and Mannheim Partner of Any Curve Alpha in E-3(2017) Senyurt, Suleyman; Kilicoglu, SeydaIn 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.Item An Examination of Perpendicular Intersections of Bfrs And Mfrs In E-3(2018) Kilicoglu, Seyda; Senyurt, Suleyman; GRY-4465-2022We 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.Item On The Matrix Representation Of 5th Order Bezier Curve And Its Derivatives In E-3(2022) Kilicoglu, Seyda; Senyurt, SuleymanUsing 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.Item On the Involute of the Cubic Bezier Curve By Using Matrix Representation in E-3(2020) Kilicoglu, Seyda; Senyurt, SuleymanIn 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.Item ON THE SECOND ORDER INVOLUTE CURVES IN E-3(2017) Kilicoglu, Seyda; Senyurt, SuleymanIn 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.