Related papers: Diffuse Reflection Radius in a Simple Polygon
The smallest possible focus is achieved when the focused wave front is the time reversed copy of the light wave packet emitted from a point in space (S. Quabis et al., Opt. Commun. 179 (2000) 1-7). The best physical implementation of such a…
We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path.…
We prove a reflection principle for minimal surfaces in smooth (non necessarily analytic) three manifolds and we give an explicit application when the ambient space is just a smooth manifold.
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
Capturing depth and reflectivity images at low light levels from active illumination of a scene has wide-ranging applications. Conventionally, even with single-photon detectors, hundreds of photon detections are needed at each pixel to…
We describe a simple geometrical derivation of the formula for reflection of light from a uniformly moving plane mirror directly from the postulates of special relativity.
Given a simple polygon $\cal P$, in the Art Gallery problem, the goal is to find the minimum number of guards needed to cover the entire $\cal P$, where a guard is a point and can see another point $q$ when $\overline{pq}$ does not cross…
A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre…
We consider light ray reflections in $n$-dimensional semi-infinite tube, for $n\geq 3$, made of Lambertian material. The source of light is placed far away from the exit, and the light ray is assumed to reflect so that the distribution of…
Sensing and manipulating targets hidden under scattering media are universal problems that take place in applications ranging from deep-tissue optical imaging to laser surgery. A major issue in these applications is the shallow light…
Many real-world materials are characterized by a glittery appearance. Reproducing this effect in physically based renderings is a challenging problem due to its discrete nature, especially in real-time applications which require a…
We establish tight bounds for beacon-based coverage problems, and improve the bounds for beacon-based routing problems in simple rectilinear polygons. Specifically, we show that $\lfloor \frac{n}{6} \rfloor$ beacons are always sufficient…
We construct a subset $A$ of the unit disc with the following properties. (i) The set $A$ is the finite union of disjoint line segments. (ii) The shadow of $A$ is arbitrarily close to the shadow of the unit disc in "most" directions. (iii)…
Light refraction, i.e. the bending of the path of a light wave at the interface between two different dielectric media, is ubiquitous in optics. Refraction arises from the different speed of light and is unavoidable in continuous media…
Take a multidimensional normally or obliquely reflected diffusion in a smooth domain. Approximate it by solutions of stochastic differential equations without reflection using the penalty method. That is, we approximate the reflection term…
Reflection of light from surfaces is a very common, but complex phenomenon not only in science and technology, but in every day life. The underlying basic optical principles have been developed within the last five centuries using visible…
The purpose of this note is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons. A visibility path is a curve such that every point inside a simple polygon is visible from at least one…
We derive a formula for the light field of a monochromatic plane wave that is truncated and reflected by a spherical mirror. Our formula is valid even for deep mirrors, where the aperture radius approaches the radius of curvature. We apply…
We prove existence and uniqueness for semimartingale reflecting diffusions in 2-dimensional piecewise smooth domains with varying, oblique directions of reflection on each "side", under geometric, easily verifiable conditions. Our…
We show how to relight a scene, depicted in a single image, such that (a) the overall shading has changed and (b) the resulting image looks like a natural image of that scene. Applications for such a procedure include generating training…