Related papers: The problem of camouflaging via mirror reflections
Let $f: [0, +\infty) \to (0, +\infty)$ be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain $Q$ delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. Under certain…
A system of two masses connected with a weightless rod (called dumbbell in this paper) interacting with a flat boundary is considered. The sharp bound on the number of collisions with the boundary is found using billiard techniques. In…
Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds.…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
Optical-window birefringence is frequently a major obstacle in experiments measuring changes in the polarization state of light traversing a sample under investigation. It can contribute a signal indistinguishable from that due to the…
Choose a polynomial in three variables with not more than three or four monomials of moderate degree. Take simple coefficients as 1 and -1. Then draw a picture of the solution variety in real three space using a ray-tracing program like…
Reflections on glossy objects contain valuable and hidden information about the surrounding environment. By converting these objects into cameras, we can unlock exciting applications, including imaging beyond the camera's field-of-view and…
An exact correspondence between a black hole and an accelerating mirror is demonstrated. It is shown that for a massless minimally coupled scalar field the same Bogolubov coefficients connecting the "in" and "out" states occur for a (1+1)D…
We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the…
This paper presents a method for estimating normals of mirrors and transparent objects challenging for cameras to recognize. We propose spraying water vapor onto mirror or transparent surfaces to create a diffuse reflective surface. Using…
Recently it was proved that every billiard trajectory inside a $C^3$ convex cone has a finite number of reflections. Here, by a $C^3$ convex cone, we mean a cone whose section with some hyperplane is a strictly convex closed $C^3$…
Based on the concept of complementary media, we propose an invisibility cloak operating at a finite frequency that can cloak an object with a pre-specified shape and size within a certain distance outside the shell. The cloak comprises of a…
This article gives estimates on covering numbers and diameters of random proportional sections and projections of symmetric quasi-convex bodies in $\mathbb R$. These results were known for the convex case and played an essential role in…
In this paper we present a review of the existing data on interferential mirror birefringence. We also report new measurements of two sets of mirrors that confirm that mirror phase retardation per reflection decreases when mirror…
We report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the shape of mirrors, while fixing the mirror radius and maintaining a low diffractional loss. The result of this…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
From a geometric viewpoint, billiard trajectories and geodesics are related by mutual approximation results. In one direction, it is known that every geodesic curve in the boundary of a smooth convex body can be approximated by a sequence…
The propagation of errors through the uniform disk visibility function is examined. Implications of those errors upon measures of absolute visibility through optical and near-infrared interferometers are considered within the context of…
We entertain the use of light dependent resistors as a viable option as measuring sensors in optics laboratory experiments or classroom demonstrations. The main advantages of theses devices are essentially very low cost, easy handling and…
Moving object detection and tracking have various applications, including surveillance, anomaly detection, vehicle navigation, etc. The literature on object detection and tracking is rich enough, and several essential survey papers exist.…