Generating Generalized Cylinder with Geodesic Base Curve According to Darboux Frame

Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations

Abstract and Applied Analysis ◽

10.1155/2021/8624794 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Nidal Echabbi ◽

Amina Ouazzani Chahdi

Keyword(s):

Vector Field ◽

Ruled Surfaces ◽

Geodesic Curve ◽

Regular Surface ◽

Principal Line ◽

Asymptotic Line ◽

Darboux Vector ◽

Base Curve ◽

Darboux Frame ◽

Made In

In this work, we consider the Darboux frame T , V , U of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a V -direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.

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Reconstruction of B-spline skinning surface from generalized cylinder mesh

The Visual Computer ◽

10.1007/s00371-009-0374-9 ◽

2009 ◽

Vol 26 (1) ◽

pp. 31-40 ◽

Cited By ~ 1

Author(s):

Ken Yano ◽

Koichi Harada

Keyword(s):

B Spline ◽

Generalized Cylinder

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Contact Lens Base Curve Prediction from Videokeratography

Optometry and Vision Science ◽

10.1097/00006324-199806000-00028 ◽

1998 ◽

Vol 75 (6) ◽

pp. 445-449 ◽

Cited By ~ 8

Author(s):

JUDY S. CHAN ◽

ROBERT B. MANDELL ◽

LARISA JOHNSON ◽

COURTNEY REED ◽

ROBERT FUSARO

Keyword(s):

Contact Lens ◽

Base Curve

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Resistance of Plastic Ophthalmic Lenses: The Effect of Base Curve on Different Materials During Static Load Testing

Optometry and Vision Science ◽

10.1097/00006324-200107000-00015 ◽

2001 ◽

Vol 78 (7) ◽

pp. 518-524 ◽

Cited By ~ 3

Author(s):

MOHAMADOU LAMINE DIALLO ◽

PIERRE SIMONET ◽

BENOIT FRENETTE ◽

BERNARD SANSCHAGRIN

Keyword(s):

Static Load ◽

Load Testing ◽

Base Curve ◽

Static Load Testing

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Base curve analysis of progressive addition lenses

Ophthalmic and Physiological Optics ◽

10.1016/0275-5408(90)90190-a ◽

1990 ◽

Vol 10 (1) ◽

pp. 112 ◽

Cited By ~ 1

Author(s):

C Sullivan

Keyword(s):

Curve Analysis ◽

Base Curve ◽

Progressive Addition Lenses

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Harmonic evolutes of B-scrolls with constant mean curvature in Lorentz–Minkowski space

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819500762 ◽

2019 ◽

Vol 16 (05) ◽

pp. 1950076 ◽

Cited By ~ 1

Author(s):

Rafael López ◽

Željka Milin Šipuš ◽

Ljiljana Primorac Gajčić ◽

Ivana Protrka

Keyword(s):

Euclidean Space ◽

Minkowski Space ◽

Mean Curvature ◽

Constant Mean Curvature ◽

Ruled Surfaces ◽

Null Curve ◽

Base Curve

In this paper, we study harmonic evolutes of [Formula: see text]-scrolls, that is, of ruled surfaces in Lorentz–Minkowski space having no Euclidean counterparts. Contrary to Euclidean space where harmonic evolutes of surfaces are surfaces again, harmonic evolutes of [Formula: see text]-scrolls turn out to be curves. In particular, we show that the harmonic evolute of a [Formula: see text]-scroll of constant mean curvature together with its base curve forms a null Bertrand pair. This allows us to characterize [Formula: see text]-scrolls of constant mean curvature and reconstruct them from a given null curve which is their harmonic evolute.

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Conditional Fourier-Feynman Transforms with Drift on a Function Space

Journal of Function Spaces ◽

10.1155/2019/9483724 ◽

2019 ◽

Vol 2019 ◽

pp. 1-16

Author(s):

Dong Hyun Cho ◽

Suk Bong Park

Keyword(s):

Banach Algebra ◽

Function Space ◽

Fourier Transforms ◽

Convolution Product ◽

Borel Measures ◽

Conditional Expectations ◽

Change Of Scale ◽

Convolution Products ◽

Complex Borel Measures ◽

Generalized Cylinder

In this paper we derive change of scale formulas for conditional analytic Fourier-Feynman transforms and conditional convolution products of the functions which are the products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the complex Borel measures on L2[0,T] using two simple formulas for conditional expectations with a drift on an analogue of Wiener space. Then we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we establish various changes of scale formulas for the conditional transforms and the conditional convolution products.

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