Related papers: Illumination problems on translation surfaces with…
We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…
We obtain tilings with a singular point by applying conformal maps on regular tilings of the Euclidean plane, and determine its symmetries. The resulting tilings are then symmetrically colored by applying the same conformal maps on…
A fundamental problem in computer vision is that of inferring the intrinsic, 3D structure of the world from flat, 2D images of that world. Traditional methods for recovering scene properties such as shape, reflectance, or illumination rely…
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…
Here we demonstrate existence of a piecewise smooth obstacle having connected interior and invisible from a point in the framework of geometric optics.
Polarization is well known for its ability to decompose diffuse and specular reflections. However, the existing decomposition methods only focus on direct reflection and overlook multiple reflections, especially specular inter-reflection.…
Metasurfaces have revolutionized nonlinear and quantum light manipulation in the past decade, enabling the design of materials that can tune polarization, frequency, and direction of light simultaneously. However, tuning of metasurfaces is…
Increasing the light scattering efficiency of nanostructured materials is becoming an active field of research both in fundamental science and commercial applications. In this context, the challenge is to use inexpensive organic materials…
In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level…
We prove lower and upper bounds for the chromatic number of certain hypergraphs defined by geometric regions. This problem has close relations to conflict-free colorings. One of the most interesting type of regions to consider for this…
A \emph{surface of translation} is a sum $(u,v)\mapsto\gt\alpha(u)+\gt\beta(v)$ of two space curves: a \emph{path} $\gt\alpha$ and a \emph{profile} $\gt\beta$. A fundamental problem of differential geometry and shell theory is to determine…
We analyze the performance of a planar lens based on realistic negative index material in a generalized geometry. We demonstrate that the conventional superlens design (where the lens is centered between the object and the image) is not…
We consider the isoperimetric problem in planar sectors with density $r^{p}$, and with density $a>1$ inside the unit disk and $1$ outside. We characterize solutions as a function of sector angle. We also solve the isoperimetric problem in…
Illumination complexes are examples of 'flat polyhedral complexes' which arise if several copies of a convex polyhedron (convex body) Q are glued together along some of their common faces (closed convex subsets of their boundaries). A…
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…
A Platonic surface is a Riemann surface that underlies a regular map and so we can consider its vertices, edge-centres and face-centres. A symmetry (anticonformal involution) of the surface will fix a number of simple closed curves which we…
We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union…
Although many spectral unmixing models have been developed to address spectral variability caused by variable incident illuminations, the mechanism of the spectral variability is still unclear. This paper proposes an unmixing model, named…
We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.
A perfect focus telescope is one in which all rays parallel to the axis meet at a point and give equal magnification there. It is shown that these two conditions define the shapes of both primary and secondary mirrors. Apart from scale, the…