Related papers: Stereographic Projections for Designs on the Spher…
In this work, we present an adaptation of the classical stereographic projection, originally formulated for the sphere, now considering the context of the ellipsoid and the elliptic paraboloid. We begin by constructing the stereographic…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
The double orthogonal projection of the 4-space onto two mutually perpendicular 3-spaces is a method of visualization of four-dimensional objects in a three-dimensional space. We present an interactive animation of the stereographic…
This short paper is concerned with the use of spherical t-designs as optimal designs for the spherical harmonic regression model in three dimensions over a range of specified criteria. The nature of the designs is explored and their…
A spherical $t$-design is a set of points on the sphere that are nodes of a positive equal weight quadrature rule having algebraic accuracy $t$ for all spherical polynomials with degrees $\le t$. Spherical $t$-designs have many…
We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic…
In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…
Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…
Graph Neural Networks leverage the connectivity structure of graphs as an inductive bias. Latent graph inference focuses on learning an adequate graph structure to diffuse information on and improve the downstream performance of the model.…
We construct a number of sculptures, each based on a geometric design native to the three-dimensional sphere. Using stereographic projection we transfer the design from the three-sphere to ordinary Euclidean space. All of the sculptures are…
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…
Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…
In this paper, we introduce a new method for classifying 3D objects. Our main idea is to project a 3D object onto a spherical domain centered around its barycenter and develop neural network to classify the spherical projection. We…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
Stereoscopic visualization is seldom used in Astrophysical publications and presentations compared to other scientific fields, e.g., Biochemistry, where it has been recognized as a valuable tool for decades. We put forth the view that…
Spherical $t$-designs on $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ provide $N$ nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of degree at most $t$. This paper considers the generation of…
In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple, yet interesting problem, has both a scholarly value and applications for data extraction techniques to…
3D scatterplots are a well-established plotting technique that can be used to represent data with three or more dimensions. On paper and computer monitors they are essentially two-dimensional projections of the three-dimensional Cartesian…
We present a technique for Stereoscopic Cylindrical Screen (SCS) Projection of a world scene to a 360-degree canvas for viewing with 3D glasses. To optimize the rendering pipeline, we render the scene to four cubemaps, before sampling…
In this short note, we compute the conformal stereographic projection on the standard metric of a sphere quotient. The result is a Majumdar-Papapetrou metric, which might be useful.