Related papers: Visibility Extension via Reflective Edges to an Ex…
We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a non-unitary term of the Lindblad type proportional to -[q,[q,\rho]], with q the…
We present an abstract method in the setting of compact metric spaces which is applied to solve a number of problems in geometric optics. In particular, we solve the one source near field refraction problem. That is, we construct surfaces…
We estimate whether there is an embedding from one n-dimensional rectangle into another which expands every k-dimensional area. Our estimate is sharp up to a constant factor in each dimension.
We perform a theoretical study of finesse limitations of a Fabry-Perot (FP) cavity occurring due to finite size, asymmetry, as well as imperfections of the cavity mirrors. A method of numerical simulations of the eigenvalue problem…
We explore the problem of $M$-guarding polygons with holes using $k$-visibility guards, where a set of guards is said to $M$-guard a polygon if every point in the polygon is visible to at least $M$ guards, with the constraint that there may…
In this article we explore some finer properties of equi-areal mirrors and introduce techniques for developing new mirror surfaces that simultaneously minimize angular and areal distortion.
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
We consider a variant of the art gallery problem where all guards are limited to seeing to the right inside a monotone polygon. We call such guards: half-guards. We provide a polynomial-time approximation for point guarding the entire…
In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection…
Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which…
Mirror reflections are common in everyday environments and can provide stereo information within a single capture, as the real and reflected virtual views are visible simultaneously. We exploit this property by treating the reflection as an…
Optical cavities are frequently used in quantum technologies to enhance light matter interactions, with applications including single photon generation and entanglement of distant emitters. The Fabry-P\'{e}rot resonator is a popular choice…
Based on the concept of complementary media, we propose a novel design which can enhance the electromagnetic wave scattering cross section of an object so that it looks like a scatterer bigger than the scale of the device. Such a…
We consider the problem of camouflaging for bodies with specular surface in the framework of geometric optics. The index of visibility introduced in [Plakhov 2017] measures the mean deviation of light rays incident on the body's surface. We…
Students in introductory physics courses struggle to understand virtual image formation by a plane mirror and the proper construction of ray diagrams. This difficulty, if not sufficiently addressed, results in further problems throughout…
We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb{R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting…
Based on transformation optics, a strategy is proposed to expose the inner one-dimensional space of a wave field inside a beam volume to the surface of the propagation medium and extend the space from one-dimensional to two-dimensional,…
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 analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…
We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…