Related papers: A 3D Advancing-Front Delaunay Mesh Refinement Algo…
This paper addresses the problem of improving the query performance of the triangular expansion algorithm (TEA) for computing visibility regions by finding the most advantageous instance of the triangular mesh, the preprocessing structure.…
A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating \emph{sweep-hull} (sequentially created from the radially sorted set of 2D…
We examine the dimensions of various inf-sup stable mixed finite element spaces on tetrahedral meshes in 3D with exact divergence constraints. More precisely, we compare the standard Scott-Vogelius elements of higher polynomial degree and…
Triangle meshes play a crucial role in 3D applications for efficient manipulation and rendering. While auto-regressive methods generate structured meshes by predicting discrete vertex tokens, they are often constrained by limited face…
We present a numerically robust algorithm for computing the constrained Delaunay tetrahedrization (CDT) of a piecewise-linear complex, which has a 100% success rate on the 4408 valid models in the Thingi10k dataset. We build on the…
The development of higher order finite elements methods has become an active research area. The deformation method for mesh generation has achieved a prescribed positive Jacobian determinant constraint and it has been a useful method for…
This paper proposes two contributions to the calculation of free surface flows using the particle finite element method (PFEM). The PFEM is based on a Lagrangian approach: a set of particles defines the fluid. Then, unlike a pure Lagrangian…
Mixed elements meshes based on the modified octree approach contain several co-spherical point configurations. While generating Delaunay tessellations to be used together with the finite volume method, it is not necessary to partition them…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…
There are very few mathematical results governing the interpolation of functions or their gradients on Delaunay meshes in more than two dimensions. Unfortunately, the standard techniques for proving optimal interpolation properties are…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…
The 3D mesh is an important representation of geometric data. In the generation of mesh data, geometric deficiencies (e.g., duplicate elements, degenerate faces, isolated vertices, self-intersection, and inner faces) are unavoidable and may…
We present an asymptotically faster algorithm for solving linear systems in well-structured 3-dimensional truss stiffness matrices. These linear systems arise from linear elasticity problems, and can be viewed as extensions of graph…
We develop an all-hex meshing strategy for the interstitial space in beds of densely packed spheres that is tailored to turbulent flow simulations based on the spectral element method (SEM). The SEM achieves resolution through elevated…
We introduce TetWeave, a novel isosurface representation for gradient-based mesh optimization that jointly optimizes the placement of a tetrahedral grid used for Marching Tetrahedra and a novel directional signed distance at each point.…
We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we…
This research proposes a novel adjustable algorithm for reconstructing 3D body shapes from front and side silhouettes. Most recent silhouette-based approaches use a deep neural network trained by silhouettes and key points to estimate the…
Compared with the remarkable progress made in parallel numerical solvers of partial differential equations,the development of algorithms for generating unstructured triangular/tetrahedral meshes has been relatively sluggish. In this paper,…
This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that…