The Experts below are selected from a list of 11595 Experts worldwide ranked by ideXlab platform
Mehmet Onder - One of the best experts on this subject based on the ideXlab platform.
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generalized normal Ruled Surface of a curve in the euclidean 3 space
arXiv: Differential Geometry, 2020Co-Authors: Onur Kaya, Mehmet OnderAbstract:In this study, we define the generalized normal Ruled Surface of a curve in the Euclidean 3-space $E^3$. We study the geometry of such Surfaces by calculating the Gaussian and mean curvatures to determine when the Surface is flat or minimal (equivalently, helicoid). We examine the conditions for the curves lying on this Surface to be asymptotic curves, geodesics or lines of curvature. Finally, we obtain the Frenet vectors of generalized normal Ruled Surface and get some relations with helices and slant Ruled Surfaces and we give some examples for the obtained results.
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Non-null slant Ruled Surfaces
AIMS Mathematics, 2019Co-Authors: Mehmet OnderAbstract:In this study, we define some new types of non-null Ruled Surfaces called slant Ruled Surfaces in the Minkowski 3-space $E_{1}^{3} $. We introduce some characterizations for a non-null Ruled Surface to be a slant Ruled Surface in $E_{1}^{3} $. Moreover, we obtain some corollaries which give the relationships between a non-null slant Ruled Surface and its striction line.
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position vector of a developable q slant Ruled Surface
The Korean Journal of Mathematics, 2018Co-Authors: Onur Kaya, Mehmet OnderAbstract:In this paper, we study the position vector of a developable $q$-slant Ruled Surface in the Euclidean 3-space $E^3$ in means of the Frenet frame of a $q$-slant Ruled Surface. First, we determinate the natural representations for the striction curve and ruling of a $q$-slant Ruled Surface. Then we obtain general parameterization of a developable $q$-slant Ruled Surface with respect to the conical curvature of the Surface. Finally, we introduce some examples for the obtained result.
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Non-null Slant Ruled Surfaces
2016Co-Authors: Mehmet OnderAbstract:In this study, we define some new types of non-null Ruled Surfaces called slant Ruled Surfaces in the Minkowski 3-space E_1^3. We introduce some characterizations for a non-null Ruled Surface to be a slant Ruled Surface in E_1^3. Moreover, we obtain some corollaries which give the relationships between a non-null slant Ruled Surface and its striction line in E_1^3.
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Timelike and Spacelike Slant Ruled Surfaces in the Minkowski 3-space
arXiv: Differential Geometry, 2016Co-Authors: Mehmet OnderAbstract:In this study, we define some new types of timelike and spacelike Ruled Surfaces, called slant Ruled Surfaces in the Minkowski 3-space E_1^3. We introduce some characterizations for a timelike or a spacelike Ruled Surface to be a slant Ruled Surface in E_1^3. Moreover, we obtain some corollaries which give the relationships between a slant Ruled Surface and its striction line in E_1^3.
Liyong Shen - One of the best experts on this subject based on the ideXlab platform.
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A symbolic-numeric approach for parametrizing Ruled Surfaces
Journal of Systems Science and Complexity, 2019Co-Authors: Sonia Pérez-díaz, Liyong ShenAbstract:This paper presents symbolic algorithms to determine whether a given Surface (implicitly or parametrically defined) is a rational Ruled Surface and find a proper parametrization of the Ruled Surface. However, in practical applications, one has to deal with numerical objects that are given approximately, probably because they proceed from an exact data that has been perturbed under some previous measuring process or manipulation. For these numerical objects, the authors adapt the symbolic algorithms presented by means of the use of numerical techniques. The authors develop numeric algorithms that allow to determine Ruled Surfaces “close” to an input (not necessarily Ruled) Surface, and the distance between the input and the output Surface is computed.
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Characterization of rational Ruled Surfaces
Journal of Symbolic Computation, 2014Co-Authors: Liyong Shen, Sonia Pérez-díazAbstract:The algebraic Ruled Surface is a typical modeling Surface in computer aided geometric design. In this paper, we present algorithms to determine whether a given implicit or parametric algebraic Surface is a rational Ruled Surface, and in the affirmative case, to compute a standard parametric representation for the Surface.
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proper reparametrization of rational Ruled Surface
Journal of Computer Science and Technology, 2008Co-Authors: Liyong Shen, Xiaoshan GaoAbstract:In this paper, we present a proper reparametrization algorithm for rational Ruled Surfaces. That is, for an improper rational parametrization of a Ruled Surface, we construct a proper rational parametrization for the same Surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.
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Proper Reparametrization of Rational Ruled Surface
2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics, 2007Co-Authors: Jia Li, Liyong ShenAbstract:Summary form only given. In this paper, we present a proper reparametrization algorithm for rational Ruled Surfaces. That is, for an improper rational parametrization of a Ruled Surface, we construct a proper rational parametrization for the same Surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.
Stefan Schaffler - One of the best experts on this subject based on the ideXlab platform.
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dual spherical spline a new representation of Ruled Surface optimization
International Conference on Control Automation Robotics and Vision, 2012Co-Authors: Yayun Zhou, Jorg Schulze, Stefan SchafflerAbstract:A Ruled Surface optimization model is proposed in the paper. It is set up especially to design a blade Surface as a Ruled Surface. In this model, the Ruled Surface is defined as a dual spherical spline and the control points of the dual spherical spline are served as optimization variables. As points on dual spherical splines correspond to infinite lines in Euclidean space, two directrix curves of a Ruled Surface are derived by intersecting the Ruled Surface with the fixed hub and shroud Surfaces. In this way, the proposed optimization model can reduce one third number of the variables compared with the conventional Ruled Surface parametrization methods, such as tensor product Surface. Besides, the optimized Ruled Surface defined as a dual spherical spline has direct link to the manufacturing process.
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blade geometry design with kinematic Ruled Surface approximation
ACM Symposium on Applied Computing, 2010Co-Authors: Yayun Zhou, Jorg Schulze, Stefan SchafflerAbstract:A blade geometry design method is proposed in this paper, which adopts a novel kinematic Ruled Surface approximation algorithm. The algorithm is applied to approximate a free-form blade Surface as a Ruled Surface in order to reduce the manufacturing cost. By applying Klein mapping and Study mapping, a Ruled Surface in Euclidean space is transformed to a curve on a Dual Unit Sphere (DUS). The kinematic Ruled Surface approximation algorithm is set up based on the novel definition of a spline on the DUS and the corresponding spline interpolation algorithm. This representation of Ruled Surface links directly to the manufacture procedure.
H. Hüseyin Uğurlu - One of the best experts on this subject based on the ideXlab platform.
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Dual Darboux Frame of a Spacelike Ruled Surface and Darboux Approach to Mannheim Offsets of Spacelike Ruled Surfaces
Natural Science and Discovery, 2015Co-Authors: Mehmet Onder, H. Hüseyin UğurluAbstract:In this paper, we define dual Darboux frame of a spacelike Ruled Surface. Then, we study Mannheim offsets of spacelike Ruled Surfaces in dual Lorentzian space by considering the E. Study Mapping. We represent spacelike Ruled Surfaces by dual Lorentzian unit spherical curves and define Mannheim offsets of the spacelike Ruled Surfaces by means of dual Darboux frame. We obtain relationships between the invariants of Mannheim spacelike offset Surfaces and offset angle, offset distance. Moreover, we obtain some conditions for Mannheim offsets of spacelike Ruled Surfaces to be developable.
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On the Developable Mannheim Offsets of Timelike Ruled Surfaces
Proceedings of the National Academy of Sciences India Section A: Physical Sciences, 2014Co-Authors: Mehmet Onder, H. Hüseyin UğurluAbstract:In this paper, using the classifications of timelike and spacelike Ruled Surfaces, we study the Mannheim offsets of timelike Ruled Surfaces in the Minkowski 3-space. First, we define the Mannheim offsets of a timelike Ruled Surface by considering the Lorentzian casual character of the offset Surface. We obtain that the Lorentzian casual character of the Mannheim offset of a timelike Ruled Surface may be timelike or spacelike. Furthermore, we give characterizations for developable Mannheim offsets of a timelike Ruled Surface.
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Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces
arXiv: Differential Geometry, 2011Co-Authors: Mehmet Onder, H. Hüseyin UğurluAbstract:In this paper, we introduce the dual geodesic trihedron (dual Darboux frame) of a timelike Ruled Surface. By the aid of the E. Study Mapping, we consider timelike Ruled Surfaces as dual hyperbolic spherical curves and define the Mannheim offsets of timelike Ruled Surfaces by means of dual Darboux frame. We obtain the relationships between invariants of Mannheim timelike Surface offsets. Furthermore, we give the conditions for these Surface offsets to be developable.
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On the Developable Mannheim Offsets of Timelike Ruled Surfaces
arXiv: Differential Geometry, 2009Co-Authors: Mehmet Onder, H. Hüseyin UğurluAbstract:In this paper, using the classifications of timelike and spacelike Ruled Surfaces, we study the Mannheim offsets of timelike Ruled Surfaces in Minkowski 3-space. Firstly, we define the Mannheim offsets of a timelike Ruled Surface by considering the Lorentzian casual character of the offset Surface. We obtain that the Mannheim offsets of a timelike Ruled Surface may be timelike or spacelike. Furthermore, we characterize the developable of Mannheim offset of a timelike Ruled Surface by the derivative of the conical curvature of the directing cone.
Yayun Zhou - One of the best experts on this subject based on the ideXlab platform.
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dual spherical spline a new representation of Ruled Surface optimization
International Conference on Control Automation Robotics and Vision, 2012Co-Authors: Yayun Zhou, Jorg Schulze, Stefan SchafflerAbstract:A Ruled Surface optimization model is proposed in the paper. It is set up especially to design a blade Surface as a Ruled Surface. In this model, the Ruled Surface is defined as a dual spherical spline and the control points of the dual spherical spline are served as optimization variables. As points on dual spherical splines correspond to infinite lines in Euclidean space, two directrix curves of a Ruled Surface are derived by intersecting the Ruled Surface with the fixed hub and shroud Surfaces. In this way, the proposed optimization model can reduce one third number of the variables compared with the conventional Ruled Surface parametrization methods, such as tensor product Surface. Besides, the optimized Ruled Surface defined as a dual spherical spline has direct link to the manufacturing process.
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blade geometry design with kinematic Ruled Surface approximation
ACM Symposium on Applied Computing, 2010Co-Authors: Yayun Zhou, Jorg Schulze, Stefan SchafflerAbstract:A blade geometry design method is proposed in this paper, which adopts a novel kinematic Ruled Surface approximation algorithm. The algorithm is applied to approximate a free-form blade Surface as a Ruled Surface in order to reduce the manufacturing cost. By applying Klein mapping and Study mapping, a Ruled Surface in Euclidean space is transformed to a curve on a Dual Unit Sphere (DUS). The kinematic Ruled Surface approximation algorithm is set up based on the novel definition of a spline on the DUS and the corresponding spline interpolation algorithm. This representation of Ruled Surface links directly to the manufacture procedure.
