Related papers: Specular reflection on the surface of a sphere: co…
In specular reflection experiments the reflected beam from the end side of thick substrates is typically neglected. This is equivalent to assuming the substrates as semi-infinite matter. However, it is known that we should also consider the…
The goal of the proposed method is to directly obtain a pose matrix of a known rectangular target, without estimation, using geometric techniques. This method is specifically tailored for real-time, extreme imaging setups exceeding…
Differentiable rendering has received increasing interest for image-based inverse problems. It can benefit traditional optimization-based solutions to inverse problems, but also allows for self-supervision of learning-based approaches for…
The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively. If we are using compass and ruler the way we construct new points is by first…
We give an optimal bound for the remainder when counting the number of rational points on the $n$-dimensional sphere with bounded denominator for any $n\geq 2$.
Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and…
We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both…
In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic B\'ezier patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal…
Light rays incident on a transparent object of uniform refractive index undergo deflections, which uniquely characterize the surface geometry of the object. Associated with each point on the surface is a deflection map (or spectrum) which…
Recently the Event Horizon Telescope observed black holes at event horizon scales for the first time, enabling us to now test the existence of event horizons. Although event horizons have by definition no observable features, one can look…
High-quality time series provided by space instrumentation such as CoRoT and Kepler, allow us to measure modulations in the light curves due to changes in the surface of stars related to rotation and activity. Therefore, we are able to…
The five-layer nanorod-mediated surface plasmon sensor with inhomogeneous liquid crystal layer was theoretically investigated. The reflectance as the function of the incident angle was calculated at different voltages applied to the liquid…
Ellipses, parabolas and hyperbolas all have beautiful reflective properties. However, an intuitive explanation for why they have those properties has been lacking. There exist many mathematical proofs, but they tend to involve several…
Doppler reflectometry spatial and wavenumber resolution is analyzed within the framework of the linear Born approximation in slab plasma model. Explicit expression for its signal backscattering spectrum is obtained in terms of wavenumber…
We derive optimal filters on the sphere in the context of detecting compact objects embedded in a stochastic background process. The matched filter and the scale adaptive filter are derived on the sphere in the most general setting,…
The Circumcentered Reflection Method (CRM) is a recently developed projection method for solving convex feasibility problems. It offers preferable convergence properties compared to classic methods such as the Douglas-Rachford and the…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
We derive certain constraints on the reflection matrix for reflection from a plane, nonmagnetic, optically anisotropic surface using a reciprocity theorem stated long ago by van de Hulst in the context of scattering of polarized light. The…
Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…
Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point…