Results 1 to 10 of about 2,714,542 (302)
Analysis of shape data: From landmarks to elastic curves. [PDF]
Wiley Interdiscip Rev Comput Stat, 2020 Proliferation of high‐resolution imaging data in recent years has led to substantial improvements in the two popular approaches for analyzing shapes of data objects based on landmarks and/or continuous curves.
Bharath K, Kurtek S.
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Automatic Detection and Uncertainty Quantification of Landmarks on Elastic Curves. [PDF]
J Am Stat Assoc, 2019 A population quantity of interest in statistical shape analysis is the location of landmarks, which are points that aid in reconstructing and representing shapes of objects.
Strait J, Chkrebtii O, Kurtek S.
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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.
J. Guven +2 more
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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.
P. Dondl, Luca Mugnai, Matthias Röger
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Constrained Willmore Tori and Elastic Curves in 2-Dimensional Space Forms [PDF]
, 2013 In this paper we consider two special classes of constrained Willmore tori in the 3-sphere. The first class is given by the rotation of closed elastic curves in the upper half plane - viewed as the hyperbolic plane - around the x-axis.
Lynn Heller
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General rigidity principles for stable and minimal elastic curves [PDF]
Journal für die Reine und Angewandte Mathematik, 2023 For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers. Our results extend Maddocks’ and Sachkov’s rigidity principles for Euler’
Tatsuya Miura, Kensuke Yoshizawa
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Constrained elastic curves and surfaces with spherical curvature lines [PDF]
Indiana University Mathematics Journal, 2021 In this paper we consider surfaces with one or two families of spherical curvature lines. We show that every surface with a family of spherical curvature lines can locally be generated by a pair of initial data: a suitable curve of Lie sphere ...
Joseph Cho, M. Pember, Gudrun Szewieczek
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Variational analysis of inextensible elastic curves [PDF]
Proceedings of the Royal Society A, 2021 We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers’ method.
G. Bevilacqua, L. Lussardi, A. Marzocchi
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Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive ...
Samira Latifi +2 more
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Bifurcation of elastic curves with modulated stiffness [PDF]
European journal of applied mathematics, 2020 We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable.
K. Brazda +3 more
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