Related papers: A unifying moving mesh method for curves, surfaces…
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…
The Merriman-Bence-Osher (MBO) scheme, also known as thresholding or diffusion generated motion, is an efficient numerical algorithm for computing mean curvature flow (MCF). It is fairly well understood in the case of hypersurfaces. This…
This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a…
This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer…
We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending…
Maps from a source manifold $ {\mathcal M}$ to a target manifold ${\mathcal N}$ appear in liquid crystals, colour image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems…
Solutions of certain partial differential equations (PDEs) are often represented by the steepest descent curves of corresponding functionals. Minimizing movement scheme was developed in order to study such curves in metric spaces.…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
The velocity and trajectory of particle moving along the corrugated (rough) surface under action of gravity is obtained by meshless Boundary Singularity Method (BSM). This physical situation is found often in biological systems and…
The geometry and topology of the region in which a director field is embedded impose limitations on the kind of supported orientational order. These limitations manifest as compatibility conditions that relate the quantities describing the…
When folding a 3D object from a 2D material like paper, typically only an approximation of the original surface geometry is needed. Such an approximation can effectively be created by a (progressive) mesh simplification approach, e.g. using…
Due to Poinsot's theorem, the motion of a rigid body about a fixed point is represented as rolling without slipping of the moving hodograph of the angular velocity over the fixed one. If the moving hodograph is a closed curve, visualization…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
Motion by (weighted) mean curvature is a geometric evolution law for surfaces, representing steepest descent with respect to (an)isotropic surface energy. It has been proposed that this motion could be computed by solving the analogous…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
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 discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…
Recent advances in 3D vision have led to specialized models for either 3D understanding (e.g., shape classification, segmentation, reconstruction) or 3D generation (e.g., synthesis, completion, and editing). However, these tasks are often…
The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies…
Approximating PDEs on surfaces by the diffuse interface approach allows us to use standard numerical tools to solve these problems. This makes it an attractive numerical approach. We extend this approach to vector-valued surface PDEs and…