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Ray Tracing
Published in Daniel Malacara-Hernández, Brian J. Thompson, Fundamentals and Basic Optical Instruments, 2017
Ricardo Flores-Hernández, Armando Gómez-Vieyra
Under such projective geometry interconnection among these spaces, it can be demonstrated that a line in one of them becomes a point in the second one and a point in one of them becomes a line in the other, called its “dual.” The line's slope in one space is equal to the point's position vector slope in the second one, and the converse is also true. Then, the Lagrange invariant (Equation 4.132) if normalized (Λ = 1) under the projective geometry scope, becomes a two-dimensional bilinear form: 1=yjω¯j′Λ−y¯jωj′Λ=yjΩ¯−y¯jΩ.
Visible Light Communications
Published in Z. Ghassemlooy, W. Popoola, S. Rajbhandari, Optical Wireless Communications, 2019
Z. Ghassemlooy, W. Popoola, S. Rajbhandari
Visible light positioning can be safely used in many places where RF cannot. For example, similar to VLC which can be used in hospital without causing any interference to MRI scanners, VLC-based positioning can be deployed in hospital. It can also be used in other RF-inappropriate environments, such as underwater, in underground mines, and in manufacturing. In recent years, we have seen growing research activities in exploiting light-based IPS for a range of applications. There are a number of positioning techniques that could be adopted for VLC-IPS, including [200], [203], [204] Triangulation methods (or non-imaging) based on (1) the received signal strength (RSS) [205], [206] (2) time of arrival (TOA) [207], (3) time difference of arrival (TDOA) [208], [209], (4) angle of arrival (AOA), and (5) phase of arrival (POA) or phase difference of arrival (PDOA) [210]. These are widely adopted in PD-based IPS systems in order to the position ID and the received power of the LED signal.Scene analysis based on fingerprint of a scene and history location. The PA of the image bases IPS (i.e., using a camera) is higher than non-imaging positioning schemes. However, the positioning algorithm is complex, and the positioning speed is limited by the image processing technique.Proximity algorithms. Is simple but with the accuracy as good as the resolution of the grid [197].Computer vision, which is based on the study of analysing projective geometry where a 3D real world is projected onto a 2D image of a camera, can be employed for IS pose estimation, 3D object reconstruction, object recognition and tracking, motion estimation, etc. It is classified as (1) single-view geometry—a single image is used for extracting the required data. Note that when taking a picture the camera maps every 3D coordinate point onto a 2D image point; and (2) multiple-view geometry—which is applied for a number of images from more than one camera or form multiple views using a single camera. Note that computer vision techniques and optical camera communications can be used jointly to estimate the camera's unknown position and orientation.
Metainferential duality
Published in Journal of Applied Non-Classical Logics, 2020
Bruno Da Ré, Federico Pailos, Damian Szmuc, Paula Teijeiro
Before going to this notion, a few words on the general concept of duality are in order. The notion of duality is very widespread in many fields of thought. In this respect, in Atiyah (2007, p. 1) Atiyah says that fundamentally ‘duality gives two different points of view of looking at the same object’, attributing its origin in mathematics and physics to the invention of projective geometry. Projective planes can be defined by points, lines and an incidence relation, but also by lines, points and the inverse of this relation.7 With the process of algebraization of logic which began in the XIX century, the interest in these sorts of structures was transposed to logic. Its first appearance is attributed to Schröder's (1877), and also Kleene refers to Hilbert and Ackermann (1999, pp. 15–16) and Church (1996, pp. 106–107), respectively.