Related papers: Generating $N$-point spherical configurations with…
There are many ways to generate a set of nodes on the sphere for use in a variety of problems in numerical analysis. We present a survey of quickly generated point sets on $\mathbb{S}^2$, examine their equidistribution properties,…
This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This…
A formalism is developed which allows to determine the locations of all local symmetry axes of three-dimensional particles with overall icosahedral symmetry. It relies on the fact that the root system of the non-crystallographic Coxeter…
The architecture of infinite structures with non-crystallographic symmetries can be modeled via aperiodic tilings, but a systematic construction method for finite structures with non-crystallographic symmetry at different radial levels is…
The problem of uniformly placing N points onto a sphere finds applications in many areas. For example, points on the sphere correspond to unit quaternions as well as to the group of rotations SO(3) and the online version of generating…
With the explosive deployment of non-terrestrial networks (NTNs), the computational complexity of network performance analysis is rapidly escalating. As one of the most suitable mathematical tools for analyzing large-scale network…
In this paper we propose a heuristic technique for distributing points on the surface of a unit n-dimensional Euclidean sphere, generated as the orbit of a finite cyclic subgroup of orthogonal matrices, the so called cyclic group codes.…
Many of the mathematical models used in quasicrystal physics are based on tilings of the plane or space obtained by using strip projection method in a superspace of dimension four, five or six. We present some mathematical results which…
We generalize the concept of optical scattering matrix ($S$-matrix) to characterize harmonic generation and frequency mixing in planar metasurfaces in the limit of undepleted pump approximation. We show that the symmetry properties of such…
This paper provides triangular spherical designs for the complex unit sphere $\Omega^d$ by exploiting the natural correspondence between the complex unit sphere in $d$ dimensions and the real unit sphere in $2d-1$. The existence of…
For a compact $ d $-dimensional rectifiable subset of $ \mathbb{R}^{p} $ we study asymptotic properties as $ N\to\infty $ of $N$-point configurations minimizing the energy arising from a Riesz $ s $-potential $ 1/r^s $ and an external field…
We introduce a projective Riesz $s$-kernel for the unit sphere $\mathbb{S}^{d-1}$ and investigate properties of $N$-point energy minimizing configurations for such a kernel. We show that these configurations, for $s$ and $N$ sufficiently…
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis…
This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…
We propose a neural network for 3D point cloud processing that exploits `spherical' convolution kernels and octree partitioning of space. The proposed metric-based spherical kernels systematically quantize point neighborhoods to identify…
This paper presents a method to generate high quality triangular or quadrilateral meshes that uses direction fields and a frontal point insertion strategy. Two types of direction fields are considered: asterisk fields and cross fields. With…
Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in X-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically…
This paper develops an explicit and implementable framework for constructing spherical designs by lifting point sets from tight fusion frames. By combining existing ingredients, we obtain, in every dimension, explicit spherical $5$-designs…
Many analyses and parameter estimations undertaken in astronomy require a large set (> 10^5) of non-analytical, theoretical spectra, each of these defined by multiple parameters. We describe the construction of an N-dimensional grid which…
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of…