Complex Lagrange interpolation on a Jordan curve with cusps

In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line ℤ. Of these relations, we focus on a ternary one equipping the digital plane ℤ2 and the digital space ℤ3 with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.

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Quadratic spline interpolation on a Jordan curve

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.61.239 ◽

1985 ◽

Vol 61 (7) ◽

pp. 239-241 ◽

Cited By ~ 1

Author(s):

Aruna Chakrabarti

Keyword(s):

Jordan Curve ◽

Spline Interpolation ◽

Quadratic Spline

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Modelling human body motion using lagrange interpolation

2016 24th Signal Processing and Communication Application Conference (SIU) ◽

10.1109/siu.2016.7495785 ◽

2016 ◽

Author(s):

Egemen Halici ◽

Erkan Bostanci

Keyword(s):

Human Body ◽

Lagrange Interpolation ◽

Body Motion

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Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves

Numerische Mathematik ◽

10.1007/s00211-015-0762-1 ◽

2015 ◽

Vol 133 (4) ◽

pp. 685-705 ◽

Cited By ~ 15

Author(s):

Wolfgang Erb ◽

Christian Kaethner ◽

Mandy Ahlborg ◽

Thorsten M. Buzug

Keyword(s):

Lagrange Interpolation

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A Hierarchical Access Control Scheme Based on Lagrange Interpolation and ELGamal Algorithm with Numerical Experiments

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.385-386.1705 ◽

2013 ◽

Vol 385-386 ◽

pp. 1705-1707

Author(s):

Tzer Long Chen ◽

Yu Fang Chung ◽

Jian Mao Hong ◽

Jeng Hong Jhong ◽

Chin Sheng Chen ◽

...

Keyword(s):

Access Control ◽

Lagrange Interpolation ◽

Control Mechanism ◽

Key Generation ◽

Electronic Documents ◽

Control Scheme ◽

Video Systems ◽

Efficient Scheme ◽

On Line ◽

Access Control Mechanism

It is important to notice that the access control mechanism has been widely applied in various areas, such as on-line video systems, wireless network, and electronic documents. We propose an access control mechanism which is constructed based on two mathematical fundamentals: Lagrange interpolation and ElGamal algorithm. We conduct performance analysis to compare the efficiency of our proposed scheme with that of several related published schemes in both key generation phase and key derivation phase. Our new scheme is proven to be more efficient. It is shown, as expected, a more efficient scheme provides relatively less security and a more secure scheme is relatively less efficient for private keys of the same size.

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