Related papers: Evolution of plane curves with a curvature adjuste…
In this paper we investigate a time dependent family of plane closed Jordan curves evolving in the normal direction with a velocity which is assumed to be a function of the curvature, tangential angle and position vector of a curve. We…
This article deals with flow of plane curves driven by the curvature and external force. We make use of such a geometric flow for the purpose of image segmentation. A parametric model for evolving curves with uniform and curvature adjusted…
A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing finite volume discretization of the intrinsic partial…
In this article we investigate a system of geometric evolution equations describing a curvature driven motion of a family of 3D curves in the normal and binormal directions. Evolving curves may be subject of mutual interactions having both…
We discuss the role of tangential stabilization in a curvature driven flow of planar curves. The governing system of nonlinear parabolic equations includes a nontrivial tangential velocity functional yielding a uniform redistribution of…
We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…
We investigate the motion of closed smooth curves that evolve in space $\mathbb{R}^3$. The governing evolutionary equation for the evolution of the curve is accompanied by a parabolic equation for the scalar quantity evaluated over the…
A common issue in simulating geometric evolution of surfaces is unexpected clustering of points that may cause numerical instability. We propose a novel artificial tangential velocity method for this matter. The artificial tangential…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed…
This paper investigates a discretization scheme for mean curvature motion on point cloud varifolds with particular emphasis on singular evolutions. To define the varifold a local covariance analysis is applied to compute an approximate…
We propose a unified method to visualize curvature on planar curves and surfaces of revolution using the tangential angle parameter. For plane curves, placing markers at equal increments of the tangential angle reveals local bending…
We establish existence and uniqueness results for the modified binormal curvature flow equation that generalizes the binormal curvature flow equation for a curve in $\R^3.$ In this generalization, the velocity of the curve is still directed…
We investigate a system of geometric evolution equations describing a curvature and torsion driven motion of a family of 3D curves in the normal and binormal directions. We explore the direct Lagrangian approach for treating the geometric…
For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the…
We investigate the motion of a family of closed curves evolving according to the geometric evolution law on a given two dimensional manifold which is embedded or immersed in the three-dimensional Euclidean space. We derive a system of…
We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…
For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy, including the Willmore and the Helfrich flows, we consider a numerical approach. In this study, we construct a structure-preserving…
Curve evolution is often used to solve computer vision problems. If the curve evolution fails to converge, we would not be able to solve the targeted problem in a lifetime. This paper studies the theoretical aspect of the convergence of a…
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…