Results 1 to 10 of about 97,540 (161)
Weak elastic energy of irregular curves
Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2023 A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Ourp-energy is defined through a relaxation process, where a suitablep-rotation of inscribed polygons is adopted. The discretep-rotation we choose has a geometric flavour: a polygon is viewed as an approximation to a smooth curve, and ...
Domenico Mucci, Alberto Saracco
exaly +5 more sources
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 IL(2) metric, the reparameterization group acts by isometries, and the space of unit length curves becomes the unit sphere.
Anuj Srivastava +2 more
exaly +4 more sources
Elastic Curves With Variable Bending Stiffness
Studies in Applied MathematicsABSTRACTWe study stationary points of the bending energy of curves subject to constraints on the arc length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the arc length of the curve. Physically, this can be understood as a model for an elastic wire with isotropic cross section of varying thickness.
Oliver Gros, Ulrich Pinkall
exaly +4 more sources
Analysis of shape data: From landmarks to elastic curves [PDF]
Wiley Interdisciplinary Reviews: Computational Statistics, 2020 Sebastian Kurtek
exaly +2 more sources
Discrete curve theory in space forms: planar elastic and area-constrained elastic curves
Beitrage Zur Algebra Und GeometrieAbstract We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties known from their smooth counterparts.
Tim Hoffmann +2 more
exaly +3 more sources
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
doaj +1 more source
Geometric and topological approaches to shape variation in
Royal Society Open Science, 2021 Leaf shape is a key plant trait that varies enormously. The range of applications for data on this trait requires frequent methodological development so that researchers have an up-to-date toolkit with which to quantify leaf shape. We generated a dataset
Haibin Hang +3 more
doaj +1 more source
A Survey of the Elastic Flow of Curves and Networks [PDF]
Milan Journal of Mathematics, 2021 AbstractWe 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. In particular, we give a complete proof of global existence and smooth convergence to critical points of the solution of the elastic flow of closed curves in$${\mathbb {R}}^2$$
Carlo Mantegazza +2 more
openaire +4 more sources
SIAM Journal on Applied Mathematics, 2011 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. The outer container now becomes just the domain of the phase field.
Patrick W. Dondl +2 more
openaire +4 more sources
Rolling Geodesics, Mechanical Systems and Elastic Curves
Mathematics, 2022 This paper defines a large class of differentiable manifolds that house two distinct optimal problems called affine-quadratic and rolling problem.
Velimir Jurdjevic
doaj +1 more source