Related papers: On Covering a Solid Sphere with Concentric Spheres…
Computing occluding contours is a key building block of non-photorealistic rendering, but producing contours with consistent visibility has been notoriously challenging. This paper describes the first general-purpose smooth surface…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
Recently several authors studied the segregation of particles for a system composed of mono-dispersed inelastic spheres contained in a box divided by a wall in the middle. The system exhibited a symmetry breaking leading to an…
The structural properties of additive binary hard-sphere mixtures are addressed as a follow-up of a previous paper [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)]. The so-called rational-function approximation method and an approach…
Geometrically decorated two-dimensional (2D) discrete surfaces can be more effective than conventional smooth reflectors in managing wave radiation. Constructive non-specular wave scattering permits the scattering angle to be other than…
We introduce a recursive procedure for computing the number of realizations of a minimally rigid graph on the sphere up to rotations. We accomplish this by combining two ingredients. The first is a framework that allows us to think of such…
Horizons and bound photon orbits are defining features of black holes that translate into key features of black hole images. We present a purely geometric proof that spherically symmetric, isolated objects with horizons in gravity theories…
In this work, we discuss the scattering features of a dipolar particle made of large refractive index material by employing the concept of virtual gain and virtual loss. The virtual gain and loss can be achieved in a lossless passive…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
In the present paper, we show that the geometry of a screen integrable null hypersurface can be generated from an isometric immersion of a leaf of its screen distribution into the ambient space. We prove, under certain geometric conditions,…
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…
Few equilibrium --even less so nonequilibrium-- statistical-mechanical models with continuous degrees of freedom can be solved exactly. Classical hard-spheres in infinitely many space dimensions are a notable exception. We show that even…
We introduce the notion of locally consistent system of half-spaces for a real hyperplane arrangement. We embed a sphere in the complexified complement by shifting the real unit sphere into the imaginary direction indicated by the…
In this research, we introduce an algorithm that produces what appears to be a new mathematical object as a consequence of projecting the \( n \)-dimensional \( Z \)-curve onto an \( n \)-dimensional sphere. The first part presents the…
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…
There are many applications in which a bounding sphere containing the given triangle E3 is needed, e.g. fast collision detection, ray-triangle intersecting in raytracing etc. This is a typical geometrical problem in E3 and it has also…
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of…
We obtain a construction of the total spherical perspective with ruler, compass, and nail. This is a generalization of the spherical perspective of Barre and Flocon to a 360 degree field of view. Since the 1960s, several generalizations of…
Manipulation ('shaking') of a rigid container filled with incompressible liquid starting from stationary generally results in some displacement, or mixing, of the liquid within it. If the liquid also has zero viscosity, a 'perfect', or…
We present a novel method to generate a synthetic distribution of objects (mock) on a spherical surface (i.e. a sky), by using a real distribution. The resulting surrogate map mimics the clustering features of the real data, including the…