Related papers: Specular reflection on the surface of a sphere: co…
Given a light source, a spherical reflector, and an observer, where on the surface of the sphere will the light be directly reflected to the observer, i.e. where is the the specular point? This is known as the Alhazen-Ptolemy problem, and…
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
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…
We propose methods that use specular, multibounce lidar returns to detect and map specular surfaces that might be invisible to conventional lidar systems that rely on direct, single-scatter returns. We derive expressions that relate 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…
We consider random flights in $\mathbb{R}^d$ reflecting on the surface of a sphere $\mathbb{S}^{d-1}_R,$ with center at the origin and with radius $R,$ where reflection is performed by means of circular inversion. Random flights studied in…
A method is proposed which allows a complete determination of the complex reflection coefficient for any free unknown real potential (i.e., in the case where there is no effective absorption). In this method the unknown layer mounted on top…
In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection…
The differential cross-section for the reflection of light beams off rigid bodies obtained by the rotation of a generic derivable convex function is calculated. The calculation is developed using elementary notions of calculus and is…
A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly…
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…
Specular reflections pose a significant challenge for object segmentation, as their sharp intensity transitions often mislead both conventional algorithms and deep learning based methods. However, as the specular reflection must lie on the…
This study introduces an approximation for rendering one bounce glossy interreflection in real time. The solution is based on the most representative point (MRP) and extends to a sampling disk near the MRP. Our algorithm represents geometry…
In this paper we propose a method to compute a freeform reflector system for collimating and shaping a beam from a point source. We construct these reflectors such that the radiant intensity of the source is converted into a desired target.…
In this paper, we discuss a mathematical model for inverse freeform design of an optical system with two reflectors in which light transfers from a point source to a point target. In this model, the angular light intensity emitted from the…
We obtain a construction of the total spherical perspective with ruler, compass, and nail. This is a generalization of the spherical perspective of Barre and Flocon to a 360 degree field of view. Since the 1960s, several generalizations of…
Shape from Polarization (SfP) estimates surface normals using photos captured at different polarizer rotations. Fundamentally, the SfP model assumes that light is reflected either diffusely or specularly. However, this model is not valid…
In this work, we present a detailed procedure of computer implementation of the laws of refraction and reflection on an arbitrary surface with rotational symmetry with respect to the propagation axis. The goal is to facilitate the…
We combine two-dimensional freeform reflector design with a scattering surface modelled using microfacets, i.e., small specular surfaces representing surface roughness. The model results in a convolution integral for the scattered light…
We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target…