Results 1 to 10 of about 2,644,458 (188)
SIAM Journal on Applied Mathematics, 2010 We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a function with values $+1$ on the inside and $-1$ on the outside of the curve.
Patrick Dondl +2 more
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A Survey of the Elastic Flow of Curves and Networks [PDF]
Milan Journal of Mathematics, 2020 We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject.
C. Mantegazza +2 more
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Elastic analysis of irregularly or sparsely sampled curves [PDF]
Biometrics, 2021 We provide statistical analysis methods for samples of curves in two or more dimensions, where the image, but not the parameterization of the curves, is of interest and suitable alignment/registration is thus necessary.
Lisa Steyer, Almond Stöcker, S. Greven
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An obstacle problem for elastic curves: Existence results [PDF]
Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications, 2018 We consider an obstacle problem for elastic curves with fixed ends. We attempt to extend the graph approach provided in [8]. More precisely, we investigate nonexistence of graph solutions for special obstacles and extend the class of admissible curves in
Marius Muller
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Environmental bias and elastic curves on surfaces [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 The behavior of an elastic curve bound to a surface will reflect the geometry of its environment. This may occur in an obvious way: the curve may deform freely along directions tangent to the surface, but not along the surface normal.
Jemal Guven +5 more
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A Property of Euler's Elastic Curve
Elemente der Mathematik, 2000 Euler and Legendre found formulas for certain products of elliptic integrals. Legendre's proof is sketched, and Euler's method is generalized to prove a more general formula which may be interpreted as a property of a curve generalizing Euler's elastic curve.
Victor H. Moll +3 more
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Elastic curves and phase transitions [PDF]
Mathematische Annalen, 2017 This paper is devoted to a classical variational problem for planar elastic curves of clamped endpoints, so-called Euler’s elastica problem. We investigate a straightening limit that means enlarging the distance of the endpoints, and obtain several new ...
Tatsuya Miura
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Approximation by planar elastic curves [PDF]
Advances in Computational Mathematics, 2015 We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for
D. Brander, J. Gravesen, T. B. Nørbjerg
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Shape Analysis of Elastic Curves in Euclidean Spaces [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011 This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric. In this SRV representation, the elastic metric simplifies to the IL2 metric, the reparameterization group acts ...
Anuj Srivastava +3 more
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On the elastic closed plane curves [PDF]
Kodai Mathematical Journal, 1985 Studying the variational problem for the functional \(E(C)=(1/2)\int_{C}k^ 2(s)ds\) (C a closed curve, s the arc length parameter of C, k(s) the curvature of C), under the condition \(\int_{C}ds=L=const.\), the author finds the following result: if E(C) is critical for a closed plane curve with \(L=const.\), then the curve C is either the plane circle \
Hiroshi Yanamoto
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