Related papers: Specular reflection on the surface of a sphere: co…
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and…
The theoretical formulation of x-ray resonant magnetic scattering from rough surfaces and interfaces is given for specular reflectivity. A general expression is derived for both structurally and magnetically rough interfaces in the…
The problem of fitting concentric ellipses is a vital problem in image processing, pattern recognition, and astronomy. Several methods have been developed but all address very special cases. In this paper, this problem has been investigated…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
We present a method for computing all the symmetries of a rational ruled surface defined by a rational parametrization which works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the…
A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…
We consider the reflection of light, from a stationary source, off of a uniformly moving flat mirror, and derive the relativistic reflection law using well-known properties of conic sections. The effective surface of reflection (ESR) is…
This paper studies a variant of the Art Gallery problem in which the ``walls" can be replaced by \emph{reflecting edges}, which allows the guards to see further and thereby see a larger portion of the gallery. Given a simple polygon $\cal…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
We derive efficient, closed form, differentiable, and numerically stable solutions for the flux measured from a spherical planet or moon seen in reflected light, either in or out of occultation. Our expressions apply to the computation of…
Reprocessing of X-ray pulsar radiation by the atmosphere of a companion in a binary system may result in reflected pulse radiation with a period of the pulses equal to the period of the pulsar under suitable conditions. In this paper the…
Based on the background of the 2021 Higher Education Club Cup National College Students Mathematical Contest in Modeling A, according to the relevant data of the China Sky Eye (FAST) radio telescope, the main cable nodes and actuators are…
Exceptional points in an optical dimer of spheres, which have the same size and operate in the spectral region of the dipolar resonance, are considered. By choosing different materials of these spheres, we can offset the radiative loss and…
We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a…
Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
This paper addresses reflection removal, which is the task of separating reflection components from a captured image and deriving the image with only transmission components. Considering that the existence of the reflection changes the…
We characterize the reflectance peak near the Brewster angle for both an interface between two dielectric media and a single slab. To approach this problem analytically, we approximate the reflectance by a first-order diagonal Pad\'e. In…
We consider a PDE approach to numerically solving the reflector antenna problem by solving an Optimal Transport problem on the unit sphere with cost function $c(x,y) = -2\log \left\Vert x - y \right\Vert$. At each point on the sphere, we…
Selective reflection is a high-resolution spectroscopic method that allows the probing of atomic and molecular gases in the near field of dielectric cell windows. It is a sensitive technique for measuring interactions between excited atoms…