Eğitim Bilimleri Fakültesi / Faculty of Education

Permanent URI for this collectionhttps://hdl.handle.net/11727/2116

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Author: search.filters.author.Kilicoglu, Seydasearch.filters.applied.f.rights: search.filters.rights.info:eu-repo/semantics/openAccess

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    On Approximation of Helix by 3(rd), 5(th) and 7(th) Order Bezier Curves in E-3
    (2022) Kilicoglu, Seyda
    Approximation 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.
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    On Approximation Sine Wave with the 5(Th) and 7(Th) Order Bezier Paths in Plane
    (2022) Kilicoglu, Seyda
    There 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.
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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 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 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.