Parametric representation of a surface pencil with a common spatial geodesic

Wang, Guojin; Tang, Kai; Tai, Chiew-Lan

doi:10.1016/s0010-4485(03)00117-9

Cited by 117 publications

(84 citation statements)

References 24 publications

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“…As mentioned in [11], the marching-scale functions a(s; t); b(s; t) and c(s; t) can be decomposed into two factors:…”

Section: Surfaces With a Common Pseudo Null Geodesic Curve In E 3mentioning

confidence: 99%

“…In Euclidean 3-space, proposed a principle for constructing a surface pencil with a common isogeodesic curve and focused on the reverse problem by Wang, Tang, and Tai in [11]: given a space curve, how to characterize those surfaces that possess this curve as a common geodesic . They also derived a su¢ cient condition on marching-scale functions for which the curve is an isogeodesic curve on a given surface with the geodesic and isoparametric constraints.…”

Section: Introductionmentioning

confidence: 99%

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On surfaces with common pseudo null geodesic in Minkowski 3-space

Öztürk

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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C o m m u n . Fa c . S c i. U n iv . A n k . S é r. A 1 M a th . S ta t. Vo lu m e 6 6 , N u m b e r 1 , P a g e s 2 2 9 -2 4 1 (2 0 1 7 ) D O I: 1 0 .1 5 0 1 / C o m m u a 1 _ 0 0 0 0 0 0 0 7 9 2 IS S N 1 3 0 3 -5 9 9 1 ON SURFACES WITH COMMON PSEUDO NULL GEODESIC IN MINKOWSKI 3-SPACE UFUK OZTURKAbstract. The problem of constructing a family of parametric surfaces from a given pseudo null curve using the Frenet trihedron frame of the curve in the Minkowski 3-space is studied. The necessary and su¢ cient conditions for the given pseudo null curve to be a common geodesic of the parametric surface are derived. As a member of the family, considered a ruled surface with a pseudo null directrix, and some corollaries on the ruled surface are given. Also, some examples are given to show the family of surfaces with a common pseudo null geodesic.

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“…As mentioned in [11], the marching-scale functions a(s; t); b(s; t) and c(s; t) can be decomposed into two factors:…”

Section: Surfaces With a Common Pseudo Null Geodesic Curve In E 3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On surfaces with common pseudo null geodesic in Minkowski 3-space

Öztürk

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…For instance, Wang et al (2004) and Li et al (2011a) constructed parametric surfaces asking a given spatial curve to be a geodesic and a line of curvature, respectively. Furthermore, Kasap et al (2008) and Li et al (2013a) separately extended the parametric surfaces into a generalization of surface family interpolating a geodesic curve and a line of curvature.…”

Section: Introductionmentioning

confidence: 99%

Construction of B-spline surface from cubic B-spline asymptotic quadrilateral

Wang

Zhu

2017

JAMDSM

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Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents and curvatures of a cubic B-spline quadrilateral with six control points in each boundary, a family of asymptotic quadrilaterals are constructed after solving the identification conditions of the control points. An optimized one is obtained by minimizing the strain energy of the boundary curves. Then, the transverse tangent vectors along the boundaries of the B-spline surface can be obtained by the asymptotic conditions and the resulting B-spline surface is of bi-quintic degree. Two arrays of control points of the surface along the quadrilateral are obtained from combinations transverse tangent vectors and the boundaries which are elevated from the cubic B-spline curves. For the given inner control points, B-spline surface of bi-quintic degree interpolating the cubic B-spline asymptotic quadrilateral is constructed. The optimized surface is the one with the minimized thin plate spline energy. The method is verified by some representative examples including the boundary curves with lines and inflections. Such interpolation scheme for the construction of the tensor-product B-spline surfaces is compatible with the CAD systems.

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“…In [15], Wang et al introduced the concept of family of surfaces in the Euclidean 3-space. Then, Şaffak et al [12] defined the surfaces with a common asymptotic curve in the Minkowski 3-space.…”

Section: Introductionmentioning

confidence: 99%