Related papers: Virtual images and billiards
The reflective nature of the human eye is an underappreciated source of information about what the world around us looks like. By imaging the eyes of a moving person, we can collect multiple views of a scene outside the camera's direct line…
Scattering, especially multiple scattering, is a well known problem in imaging, ranging from astronomy to medicine. In particular it is often desirable to be able to perform non-invasive imaging through turbid and/or opaque media. Many…
Formation of a bright-field microscopic image of a transparent phase object is described in terms of elementary geometrical optics. Our approach is based on the premise that image replicates the intensity distribution (real or virtual) at…
This paper proposes a novel algorithm of discovering the structure of a kaleidoscopic imaging system that consists of multiple planar mirrors and a camera. The kaleidoscopic imaging system can be recognized as the virtual multi-camera…
Understanding and modeling lighting effects are fundamental tasks in computer vision and graphics. Classic physically-based rendering (PBR) accurately simulates the light transport, but relies on precise scene representations--explicit 3D…
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…
This paper addresses the problem of inverse rendering from photometric images. Existing approaches for this problem suffer from the effects of self-shadows, inter-reflections, and lack of constraints on the surface reflectance, leading to…
A general formula for the linearized Poincar\'e map of a billiard with a potential is derived. The stability of periodic orbits is given by the trace of a product of matrices describing the piecewise free motion between reflections and the…
The billiard table is modeled as an $n$-dimensional box $[0,a_1]\times [0,a_2]\times \ldots \times [0,a_n] \subset \mathbb{R}^n$, with each side having real-valued lengths $a_i$ that are pairwise commensurable. A ball is launched from the…
Diffusion models have revolutionized generative modeling, enabling unprecedented realism in image and video synthesis. This success has sparked interest in leveraging their representations for visual understanding tasks. While recent works…
We investigate if the visual representation of vectors can affect which methods students use to add them. We gave students one of four questions with different graphical representations, asking students to add the same two vectors. For…
In this article, we define an information-theoretic entropy based on the Ihara zeta function of a graph which is called the Ihara entropy. A dynamical system consists of a billiard ball and a set of reflectors correspond to a combinatorial…
Lighting effects such as shadows or reflections are key in making synthetic images realistic and visually appealing. To generate such effects, traditional computer graphics uses a physically-based renderer along with 3D geometry. To…
This paper proposed a new interaction paradigm in the virtual reality (VR) environments, which consists of a virtual mirror or window projected onto a virtual surface, representing the correct perspective geometry of a mirror or window…
A pseudoscopic (inverted depth) image made with spiral diffracting elements intermediated by a pinhole is explained by its symmetry properties. The whole process is made under common white light illumination and allows the projection of…
We address the problem of the determination of the images of three-dimensional geometric and modular Galois representations. In the modular case the existence of these representations is only conjectural. We give conditions to ensure that…
The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…
We study rational circular billiards. By viewing the trajectory formed after each reflection point to another inside the circle as the number of circle divisions into regions we derive a general formula for the number of division regions…
The renowned Fagnano problem asks for the inscribed triangle of minimal perimeter within a given reference triangle. Equivalently, it seeks a billiard trajectory inside the triangle that closes after three reflections. In this note, we…
Invisible persons are seen in fiction stories only, but in the real world it is proved that invisibility is possible. This paper describes the creation of invisibility with the help of technologies like Optical camouflage; Image based…