Related papers: Virtual images and billiards
Perceptual illusions based on the spatial correspondence between objects and displayed images have been pursued by artists and scientists since the 15th century, mastering optics to create crucial techniques as the linear perspective and…
From a geometric viewpoint, billiard trajectories and geodesics are related by mutual approximation results. In one direction, it is known that every geodesic curve in the boundary of a smooth convex body can be approximated by a sequence…
We describe a simple geometrical derivation of the formula for reflection of light from a uniformly moving plane mirror directly from the postulates of special relativity.
We illustrate the theory of one-dimensional pluri-Lagrangian systems with the example of commuting billiard maps in confocal quadrics.
Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being…
Inverse rendering aims to estimate physical attributes of a scene, e.g., reflectance, geometry, and lighting, from image(s). Inverse rendering has been studied primarily for single objects or with methods that solve for only one of the…
This paper has pedagogical motivation. It is not uncommon that students have great difficulty in accepting the new concepts of standard special relativity, since these seem contrary to common sense. Experience shows that geometrical or…
In general, underwater images suffer from color distortion and low contrast, because light is attenuated and backscattered as it propagates through water (differently depending on wavelength and on the properties of the water body). An…
We present a new perspective on gravitational lensing. We describe a new extension of the weak lensing formalism capable of describing strongly lensed images. By integrating the non-linear geodesic deviation equation, the amplification…
Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider…
This colloquium analyzes the interaction of light with two-dimensional periodic arrays of particles and holes. The enhanced optical transmission observed in the latter and the presence of surface modes in patterned metal surfaces are…
The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry. This paper builds on this framework to study "physical realizations" of…
In this work, I use a survey of senior visualization researchers and thinkers to ideate about the notion of progress in visualization research: how are we growing as a field, what are we building towards, and are our existing methods…
The formation of relativistic electron mirror produced via ionization of thin solid target by ultraintense femtosecond laser pulse is considered with the help of computer simulations. It is shown that the reflection of weak…
Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified…
Although the use of technologies like multimedia and virtual reality (VR) in training offer the promise of improved learning, these richer and potentially more engaging materials do not consistently produce superior learning outcomes.…
In recent years there has been a strong development of the concept of virtual reality (VR) which from the first video games developed in the 60s has reached the current immersive systems. VR and the consequent deception of perception pose…
A nice trick for studying the billiard flow in a rational polygon is to unfold the polygon along the trajectories. This gives rise to a translation or half-translation surface tiled by the original polygon, or equivalently an Abelian or…