相关论文: Quadrilateral Meshing by Circle Packing

We classify spherical quadrilaterals up to isometry in the case when one inner angle is a multiple of pi while the other three are not. This is equivalent to classification of Heun's equations with real parameters and one apparent…

This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…

Any two polygons of equal area can be partitioned into congruent sets of polygonal pieces, and in many cases one can connect the pieces by flexible hinges while still allowing the connected set to form both polygons. However it is open…

Recent progress in 3D object generation has greatly improved both the quality and efficiency. However, most existing methods generate a single mesh with all parts fused together, which limits the ability to edit or manipulate individual…

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying simple geometric criteria, our construction produces 2n…

The contribution emphasizes the geometric modeling point of view on Minkowski point set operations. In this paper, the Minkowski product is specified as the quaternionic product. Selected point sets are visualized using double orthogonal…

We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…

We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as…

The typical cell of a Voronoi tessellation generated by $n+1$ uniformly distributed random points on the $d$-dimensional unit sphere $\mathbb S^d$ is studied. Its $f$-vector is identified in distribution with the $f$-vector of a beta'…

In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries,…

Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce…

We present a universal crease pattern--known in geometry as the tetrakis tiling and in origami as box pleating--that can fold into any object made up of unit cubes joined face-to-face (polycubes). More precisely, there is one universal…

We propose MeshOn, a method that finds physically and semantically realistic compositions of two input meshes. Given an accessory, a base mesh with a user-defined target region, and optional text strings for both meshes, MeshOn uses a…

Consider a M\"obius strip with $n$ chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can…

A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background…

In this note, we investigate an infinite one parameter family of circle packings, each with a set of three mutually tangent circles. We use these to generate an infinite set of circle packings with the Apollonian property. That is, every…

We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…

We develop a finite element method with continuous displacements and discontinuous rotations for the Mindlin-Reissner plate model on quadrilateral elements. To avoid shear locking, the rotations must have the same polynomial degree in the…

It is well-known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these degrees of freedom associated…