Related papers: Virtual images and billiards
It is shown that a light beam in free space is representable by an integral over a vectorial angular spectrum that is expressed in terms of an extension matrix, which describes the vectorial nature of the beam. A symmetry axis of the…
An aspirational goal for virtual reality (VR) is to bring in a rich diversity of real world objects losslessly. Existing VR applications often convert objects into explicit 3D models with meshes or point clouds, which allow fast interactive…
This paper presents an illumination estimation method for virtual objects in real environment by learning. While previous works tackled this problem by reconstructing high dynamic range (HDR) environment maps or the corresponding spherical…
The problem of two interacting particles moving in a d-dimensional billiard is considered here. A suitable coordinate transformation leads to the problem of a particle in an unconventional hyperbilliard. A dynamical map can be readily…
Reconstructing the geometry and appearance of objects from photographs taken in different environments is difficult as the illumination and therefore the object appearance vary across captured images. This is particularly challenging for…
Accurately modeling how real-world materials reflect light remains a core challenge in inverse rendering, largely due to the scarcity of real measured reflectance data. Existing approaches rely heavily on synthetic datasets with simplified…
How much does a single image reveal about the environment it was taken in? In this paper, we investigate how much of that information can be retrieved from a foreground object, combined with the background (i.e. the visible part of the…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
We consider a class of random billiards in a tube, where reflection angles at collisions with the boundary of the tube are random variables rather than deterministic (and elastic) quantities. We obtain a (non-standard) Central Limit Theorem…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
We define a new class of plane billiards - the `pensive billiard' - in which the billiard ball travels along the boundary for some distance depending on the incidence angle before reflecting, while preserving the billiard rule of equality…
The possibility of creating crystal bilayers twisted with respect to each other has led to the discovery of a wide range of novel electron correlated phenomena whose full understanding is still under debate. Here we propose and analyze a…
A bilayer lens is proposed based on transformation optics. It is shown that Pendry's perfect lens, perfect bilayer lens made of indefinite media, and the concept of compensated media are well unified under the scope of the proposed bilayer…
In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The…
In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its…
Recently, we put forwarded a redox molecular hypothesis involving the natural biophysical substrate of visual perception and imagery. Here, we explicitly propose that the feedback and feedforward iterative operation processes can be…
We introduce the notion of a Billiard Array. This is an equilateral triangular array of one-dimensional subspaces of a vector space $V$, subject to several conditions that specify which sums are direct. We show that the Billiard Arrays on…
Illusions are fascinating and immediately catch people's attention and interest, but they are also valuable in terms of giving us insights into human cognition and perception. A good theory of human perception should be able to explain the…
The design of a serious game is presented that served as an instrument to motivate and aid to Physics education using active and ludic learning, specifically the topic of free fall of objects, with diverse educational purposes, first to…