Related papers: Automatic surface mesh generation for discrete mod…

In the context of high performance finite element analysis, the cost of iteratively modifying a computational domain via re-meshing and restarting the analysis becomes time prohibitive as the size of simulations increases. In this paper, we…

Triangular meshes are a widely used representation in the field of 3D modeling. In this paper, we present a novel approach for edge length-based linear subdivision on triangular meshes, along with two auxiliary techniques. We conduct a…

This paper presents a methodology aiming at easing considerably the generation of high-quality meshes for complex 3D domains. We show that the whole mesh generation process can be controlled with only five parameters to generate in one…

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…

Since the seminal work of Idelsohn, O\~nate and Del-Pin (2004), the Particle Finite Element Method (PFEM) has relied on a Delaunay triangulation and the Alpha--Shape (AS) algorithm in the remeshing process. This approach guarantees a good…

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…

Electromagnetic simulations of complex geologic settings are computationally expensive. One reason for this is the fact that a fine mesh is required to accurately discretize the electrical conductivity model of a given setting. This…

Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or…

Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased,…

In this paper we propose a new approach to incrementally initialize a manifold surface for automatic 3D reconstruction from images. More precisely we focus on the automatic initialization of a 3D mesh as close as possible to the final…

We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…

Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…

We study one-dimensional topological models with dimerization and trimerization and show that these models can be generated using interaction or optical superlattice. The topological properties of these models are demonstrated by the…

This paper presents a fast an robust mesh generation procedure that is able to generate meshes of the earth system (ocean and continent) in matters of seconds. Our algorithm takes as input a standard shape-file i.e. geospatial vector data…

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…

In this work, we present a boundary and hole detection approach that traverses all the boundaries of an edge-manifold triangular mesh, irrespectively of the presence of singular vertices, and subsequently determines and labels all holes of…

We investigate a finite element discretization of an elastic bending-plate model with an effective prestrain. The model has been obtained via homogenization and dimension reduction by B\"onlein at al. (2023). Its energy functional is the…

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…

Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation.…