Related papers: Specular reflection on the surface of a sphere: co…
Within classical optics, one may add microscopic "roughness" to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly…
We use geometrical optics and the caustic-touching theorem to study, in an exact way, the change in the topology of the image of an object obtained by reflections on an arbitrary smooth surface. Since the procedure that we use to compute…
Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…
Estimating and modelling the appearance of an object under outdoor illumination conditions is a complex process. Although there have been several studies on illumination estimation and relighting, very few of them focus on estimating the…
We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions, both in the near and far field cases, when the input and output energies are prescribed.
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is…
Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera…
First geometric calculus alongside its description of equiangular spirals, reflections and rotations is introduced briefly. Then single and double reflections at such a spiral are investigated. It proves suitable to distinguish incidence…
We present a method of creation of photonic structures whose optical spectrum of the reflection coefficient has an arbitrary shape and has predetermined features. We develop an algorithm for the construction of a photonic crystal structure,…
This paper presents analysis of important issues associated with the design of refractive laser beam shaping systems. The concept of singular radius is introduced along with solutions to minimize its adverse effect on shaper performance. In…
We present a technique to optimize the reflectivity of a surface while preserving its overall shape. The naive optimization of the mesh vertices using the gradients of reflectivity simulations results in undesirable distortion. In contrast,…
Undoing the image formation process and therefore decomposing appearance into its intrinsic properties is a challenging task due to the under-constraint nature of this inverse problem. While significant progress has been made on inferring…
We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the…
An uncommon double-ray scenario of light resonant scattering by a periodic metasurface is proposed to provide strong non-specular reflection. The metasurface is constracted as an array of silicon nanodisks placed on thin silica-on-metal…
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…
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…
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…
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.…