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/closedAccess

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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 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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    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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    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.