Related papers: Virtual images and billiards
This paper links the conjecture that the physical world is a virtual reality to the findings of modern physics. What is usually the subject of science fiction is here proposed as a scientific theory open to empirical evaluation. We know…
Reconstructing an object's geometry and appearance from multiple images, also known as inverse rendering, is a fundamental problem in computer graphics and vision. Inverse rendering is inherently ill-posed because the captured image is an…
The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays.…
While billiard systems of various shapes have been used as paradigmatic model systems in the fields of nonlinear dynamics and quantum chaos, few studies have investigated anisotropic billiards. Motivated by the tremendous advances in using…
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…
We have developed a relativistically-accurate computer graphics code and have used it to produce photo-realistic images and videos of scenes where special relativistic effects dominate, either in astrophysical contexts or in imaginary…
An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the solution of a quartic equation, which we solve and analyze…
Recent advances in implicit neural representations and differentiable rendering make it possible to simultaneously recover the geometry and materials of an object from multi-view RGB images captured under unknown static illumination.…
University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students…
Let $T\subset \R^{m+1}$ be a strictly convex domain bounded by a smooth hypersurface $X=\partial T$. In this paper we find lower bounds on the number of billiard trajectories in $T$ which have a prescribed intial point $A\in X$, a…
The special theory of relativity teaches us that, although distinct inertial frames perceive the same dynamical laws, space and time intervals differ in value. We revisit the problem of time contraction using the paradigmatic model of a…
We study the deep interplay between geometry of quadrics in d-dimensional space and the dynamics of related integrable billiard systems. Various generalizations of Poncelet theorem are reviewed. The corresponding analytic conditions of…
Environment maps are used to simulate reflections off curved objects. We present a technique to reflect a user, or a group of users, in a real environment, onto a virtual object, in a virtual reality application, using the live video feeds…
Suppose we are given an environment consisting of axis-parallel and diagonal line segments with integer endpoints, each of which may be reflective or non-reflective, with integer endpoints, and an initial position for a light ray passing…
Realistic indoor or outdoor image synthesis is a core challenge in computer vision and graphics. The learning-based approach is easy to use but lacks physical consistency, while traditional Physically Based Rendering (PBR) offers high…
We study finite two dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape. We show that such systems can be quantum simulated by…
We study the effect of edge diffraction on the semiclassical analysis of two dimensional quantum systems by deriving a trace formula which incorporates paths hitting any number of vertices embedded in an arbitrary potential. This formula is…
The simple reflection of a light beam of finite transverse extent from a homogenous interface gives rise to a surprisingly large number of subtle shifts and deflections which can be seen as diffractive corrections to the laws of geometrical…
We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations on a mirror surface which have interesting structure as seen…
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…