Related papers: Diffuse Reflection Radius in a Simple Polygon
We prove that the set of visible points of any lattice of dimension at least 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the…
We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and…
In this paper, we study the problem of reproducing the world lighting from a single image of an object covered with random specular microfacets on the surface. We show that such reflectors can be interpreted as a randomized mapping from the…
A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the…
The illumination conjecture is a classical open problem in convex and discrete geometry, asserting that every compact convex body~$K$ in $\mathbb R^n$ can be illuminated by a set of no more than $2^n$ points. If $K$ has smooth boundary, it…
We calculate the optical diffraction radiation generated by a bunch of high energy particles as they pass through a round hole within an annular metallic ring. We derive expressions for the differential angular spectrum in the far-field and…
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 consider random $n\times n$ matrices $X$ with independent and centered entries and a general variance profile. We show that the spectral radius of $X$ converges with very high probability to the square root of the spectral radius of the…
This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search for bodies that are, in a sense, close to invisible. We…
We consider the possibility that most of the reflection component, observed in the hard X-ray spectra of Seyfert galaxies, could be formed on an extended medium, at large distance from the central source of primary radiation (e.g. on a…
An exact formulation of the propagation of a monochromatic wave packet impinging upon a transparent, homogeneous, isotropic and parallel slab at oblique incidence is presented. Approximate formulas are derived for low divergence Gaussian…
We prove that a well-distributed subset of R^2 can have a separated distance set only if the distance is induced by a polygon.
A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we apply this formalism to study the…
In this paper we demonstrate that the light diffracted by a simple compact disc can be used to generate photographic images of a certain kind. Being the compact disc an axicon that generates a diffraction-free beam, we show that the…
Relighting radiance fields is severely underconstrained for multi-view data, which is most often captured under a single illumination condition; It is especially hard for full scenes containing multiple objects. We introduce a method to…
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…
The diffuse intensity propagating in turbid media is sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects can be described by a stationary diffusion…
The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the…
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…
Reflections are very common phenomena in our daily photography, which distract people's attention from the scene behind the glass. The problem of removing reflection artifacts is important but challenging due to its ill-posed nature. The…