Related papers: Tetrahedral frame fields via constrained third ord…
Three-dimensional frame fields computed on CAD models often contain singular curves that are not compatible with hexahedral meshing. In this paper, we show how CAD feature curves can induce non meshable 3-5 singular curves and we study four…
A generalization of vector fields, referred to as N-direction fields or cross fields when N = 4, has been recently introduced and studied for geometry processing, with applications in quadrilateral (quad) meshing, texture mapping, and…
We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger--Reissner mixed…
An $n$-cross field is a locally-defined orthogonal coordinate system invariant with respect to the cubic symmetry group. Cross fields are finding wide-spread use in mesh generation, computer graphics, and materials science among many…
We develop a geometrical framework that allows to obtain the electromagnetic field quantities in accelerated frames. The frame of arbitrary accelerated observers in space-time is defined by a suitable set of tetrad fields, whose timelike…
Two important classes of three-dimensional elements in computational meshes are hexahedra and tetrahedra. While several efficient methods exist that convert a hexahedral element to a tetrahedral elements, the existing algorithm for…
For a tensor triangulated category and any regular cardinal $\alpha$ we study the frame of $\alpha$-localizing tensor ideals and its associated space of points. For a well-generated category and its frame of localizing tensor ideals we…
Neural Radiance Fields (NeRFs) are a very recent and very popular approach for the problems of novel view synthesis and 3D reconstruction. A popular scene representation used by NeRFs is to combine a uniform, voxel-based subdivision of the…
This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to…
We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via the linearized deformation operator, the linearized curvature…
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied…
Spherical harmonics of degree 4 are widely used in volumetric frame fields design due to their ability to reproduce octahedral symmetry. In this paper we show how to use harmonics of degree 3 (octupoles) for the same purpose, thereby…
Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3 dimensional self-dual space-like warped $AdS_3$ black hole background. We argue that in this background, symmetric conditions and…
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…
We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet…
This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on…
We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…
In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods because it can represent the microstructural design at a much finer length-scale than…
One remarkable feature of virtual element methods (VEMs) is their great flexibility and robustness when used on almost arbitrary polytopal meshes. This very feature makes it widely used in both fitted and unfitted mesh methods. Despite…
In this paper, we study geometric points in tensor triangular geometry. In doing so, we construct a counter-example to Balmer's Nerves of Steel conjecture using free constructions in higher Zariski geometry. We then go on to introduce and…