Congruence Conditions for Nonplanar Developable Surfaces and Their Application to Surface Recognition

Lu, Hongqian; Todhunter, John S.; Sze, T. W.

doi:10.1006/ciun.1993.1042

Cited by 20 publications

(11 citation statements)

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“…In [16], the author constructed Frenet-Serret frame of a curve in the Galilean 4-space and obtained the mentioned curve's Frenet-Serret equations. Inextensible curve and surface flows also arise in the context of many problems in computer vision [6], [12] and computer animation [9], and even structural mechanics [17]. Papers in [5], [11], [13], [14] and [18] are obtained some new characterizations of the inextensible curve flows curves.…”

Section: Introductionmentioning

confidence: 99%

Second Binormal Motions of Inextensible Curves in 4-dimensional Galilean Space

Korkmaz

Bektaandş

2020

Applied Mathematics and Nonlinear Sciences

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Section: Introductionmentioning

confidence: 99%

Second Binormal Motions of Inextensible Curves in 4-dimensional Galilean Space

Korkmaz

Bektaandş

2020

Applied Mathematics and Nonlinear Sciences

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“…The evolution of curves and surfaces has important applications in many fields such ascomputer vision [1,2], computer animation [3], and image processing [4]. The motion of curves and surfaces in R 3 leads to nonlinear evolution equations, which are often integrable.…”

Section: Introductionmentioning

confidence: 99%

Generated Surfaces via Inextensible Flows of Curves inR3

Hussien

Mohamed

2016

Journal of Applied Mathematics

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We study the inextensible flows of curves in 3-dimensional Euclidean spaceR3. The main purpose of this paper is constructing and plotting the surfaces that are generated from the motion of inextensible curves inR3. Also, we study some geometric properties of those surfaces. We give some examples about the inextensible flows of curves inR3and we determine the curves from their intrinsic equations (curvature and torsion). Finally, we determine and plot the surfaces that are generated by the motion of those curves by using Mathematica 7.

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“…For example, both Chirikjian and Burdick [4] and Mochiyama et al [15] study the shape control of hyper-redundant, or snake-like, robots. Inextensible curve and surface flows also arise in the context of many problems in computer vision [10] and [14] and computer animation [5], and even structural mechanics [19].…”

Section: Introductionmentioning

confidence: 99%