Related papers: POLYLLA: Polygonal meshing algorithm based on term…
We introduce a geometric stencil selection algorithm for Laplacian in 3D that significantly improves octant-based selection considered earlier. The goal of the algorithm is to choose a small subset from a set of irregular points surrounding…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
Every surface that is intrinsically polyhedral can be represented by a portalgon: a collection of polygons in the Euclidean plane with some pairs of equally long edges abstractly identified. While this representation is arguably simpler…
Mesh reconstruction from a 3D point cloud is an important topic in the fields of computer graphic, computer vision, and multimedia analysis. In this paper, we propose a voxel structure-based mesh reconstruction framework. It provides the…
3D models are commonly used in computer vision and graphics. With the wider availability of mesh data, an efficient and intrinsic deep learning approach to processing 3D meshes is in great need. Unlike images, 3D meshes have irregular…
Alexandrov's Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of a unique convex polyhedron. Recent work by Bobenko and Izmestiev describes a…
In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging…
This article presents an algorithm to compute digital images of Voronoi, Johnson-Mehl or Laguerre diagrams of a set of punctual sites, in a domain of a Euclidean space of any dimension. The principle of the algorithm is, in a first step, to…
We consider the combinatorial question of how many convex polygons can be made by using the edges taken from a fixed triangulation of n vertices. For general triangulations, there can be exponentially many: we show a construction that has…
This paper studies the straight skeleton of polyhedra in three dimensions. We first address voxel-based polyhedra (polycubes), formed as the union of a collection of cubical (axis-aligned) voxels. We analyze the ways in which the skeleton…
The triangular mesh-based gyrokinetic scheme enables comprehensive axis-to-edge studies across the entire plasma volume. Our approach employs triangular finite elements with first-derivative continuity (C1), building on previous work to…
This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which…
The area query, to find all elements contained in a specified area from a certain set of spatial objects, is a very important spatial query widely required in various fields. A number of approaches have been proposed to implement this…
The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not…
Mesh generation is a crucial step in numerical simulations, significantly impacting simulation accuracy and efficiency. However, generating meshes remains time-consuming and requires expensive computational resources. In this paper, we…
The properties and applications of superconvergence on size-guaranteed Delaunay triangulation generated by bubble placement method (BPM), are studied in this paper. First, we derive a mesh condition that the difference between the actual…
The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete…
Given a convex polyhedral surface P, we define a tailoring as excising from P a simple polygonal domain that contains one vertex v, and whose boundary can be sutured closed to a new convex polyhedron via Alexandrov's Gluing Theorem. In…
We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with $n$ vertices. We give exact algorithms that solve these problems in time…
We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration…