Related papers: Reflection in a Translation Invariant Surface

Motivated by non-destructive testing of optical fiber, we consider the problem of determining the index of refraction of a two-dimensional medium from magnitude of the total field resulting from known incident plane waves at a fixed…

This note summarizes the steps to computing the best-fitting affine reflection that aligns two sets of corresponding points.

Describing the phenomenon of total internal reflection in terms of a reflection coefficient of unit magnitude, we found that, not only can propagating plane waves be total internally reflected at the planar interface of two dissimilar,…

A translation surface of Euclidean space $\r^3$ is the sum of two regular curves $\alpha$ and $\beta$, called the generating curves. In this paper we classify the minimal translation surfaces of $\r^3$ and we give a method of construction…

Summary. A modified version of the two-slit experiment is proposed in which the moveable detector/counter used to obtain the fringe distribution by counting single photons at different positions on the screen plane is replaced with a mirror…

A formula for the wavefront of a wave reflected from a diffraction grating with an arbitrary surface profile, as well as with arbitrary non-equidistant and non-parallel grooves was obtained. It was shown that the wavefront of the reflected…

In this work, we propose a novel method for the detailed reconstruction of transparent objects by exploiting polarimetric cues. Most of the existing methods usually lack sufficient constraints and suffer from the over-smooth problem. Hence,…

This paper introduces advances in the geometry of the transforms for cross ratio of four points in a line in the Desargues affine plane. The results given here have a clean, based Desargues affine plan axiomatic's and definitions of…

This manuscript will unify inverse freeform reflector design and surface light scattering to design freeform reflectors with a scattering surface. We use microfacets, which are small, tilted mirrors superimposed on a smooth surface. We form…

Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…

We present here a general approach to treat reflection and refraction of light of arbitrary polarization from single axis anisotropic plates. We show that reflection from interface inside the anisotropic medium is accompanied by beam…

View-dependent effects such as reflections pose a substantial challenge for image-based and neural rendering algorithms. Above all, curved reflectors are particularly hard, as they lead to highly non-linear reflection flows as the camera…

We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded…

In this work we define the trajectory coset of an affine map and use it to study the similarity classes of affine maps. We use the trajectory coset, a tool which allows us to gain a deeper understanding of the interplay between geometry…

We introduce a high resolution spatially adaptive light source, or a projector, into a neural reflectance field that allows to both calibrate the projector and photo realistic light editing. The projected texture is fully differentiable…

The reflecting features (reflected spectrum and phase) on the surface of pure-material plate depend on refractive index, extinction coefficient, incident angle, polarization direction and so on. The features, however, do not depend on a cut…

We give a geometric characterization of compact Riemann surfaces admitting orientation reversing involutions with fixed points. Such surfaces are generally called real surfaces and can be represented by real algebraic curves with non-empty…

We find an explicit matrix model computing the refined topological vertex, starting from its representation in terms of plane partitions. We then find the spectral curve of that matrix model, and thus the mirror symmetry of the refined…

In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the…

This purpose of this paper is to prove the following result: let phi be a strictly convex, smooth, convex body in the Euclidean plane, if the intersection of n translates of phi has a non-empty interior, and all of the translates contribute…