Quaternions and Rotation Sequences

Author: Jack B. Kuipers
Publisher: Princeton University Press
ISBN: 9780691102986
Format: PDF
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Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations. The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.

Geometriekalk le

Author: Jürgen Richter-Gebert
Publisher: Springer-Verlag
ISBN: 3642025307
Format: PDF, Mobi
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Wie kann man geometrische Objekte und Operationen so darstellen, dass sie durch möglichst einfache algebraische Manipulationen verarbeitet werden können? Dieser Leitfrage geht das Buch in insgesamt zwölf Kapiteln nach und schlägt damit eine Brücke vom Grundwissen in der Linearen Algebra zu modernen Ansätzen der Geometrie. Neben Übungsaufgaben und Abbildungen wird jedes Kapitel durch einen Exkurs zu Anwendungen und weiterführenden Themen ergänzt. Das Buch richtet sich an Studierende und Dozenten der Mathematik, Informatik und Physik (ab 3. Semester).

Multisensor Attitude Estimation

Author: Hassen Fourati
Publisher: CRC Press
ISBN: 1315351757
Format: PDF, Mobi
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There has been an increasing interest in multi-disciplinary research on multisensor attitude estimation technology driven by its versatility and diverse areas of application, such as sensor networks, robotics, navigation, video, biomedicine, etc. Attitude estimation consists of the determination of rigid bodies’ orientation in 3D space. This research area is a multilevel, multifaceted process handling the automatic association, correlation, estimation, and combination of data and information from several sources. Data fusion for attitude estimation is motivated by several issues and problems, such as data imperfection, data multi-modality, data dimensionality, processing framework, etc. While many of these problems have been identified and heavily investigated, no single data fusion algorithm is capable of addressing all the aforementioned challenges. The variety of methods in the literature focus on a subset of these issues to solve, which would be determined based on the application in hand. Historically, the problem of attitude estimation has been introduced by Grace Wahba in 1965 within the estimate of satellite attitude and aerospace applications. This book intends to provide the reader with both a generic and comprehensive view of contemporary data fusion methodologies for attitude estimation, as well as the most recent researches and novel advances on multisensor attitude estimation task. It explores the design of algorithms and architectures, benefits, and challenging aspects, as well as a broad array of disciplines, including: navigation, robotics, biomedicine, motion analysis, etc. A number of issues that make data fusion for attitude estimation a challenging task, and which will be discussed through the different chapters of the book, are related to: 1) The nature of sensors and information sources (accelerometer, gyroscope, magnetometer, GPS, inclinometer, etc.); 2) The computational ability at the sensors; 3) The theoretical developments and convergence proofs; 4) The system architecture, computational resources, fusion level.

Advanced Methods in Computer Graphics

Author: Ramakrishnan Mukundan
Publisher: Springer Science & Business Media
ISBN: 1447123409
Format: PDF, ePub, Docs
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This book brings together several advanced topics in computer graphics that are important in the areas of game development, three-dimensional animation and real-time rendering. The book is designed for final-year undergraduate or first-year graduate students, who are already familiar with the basic concepts in computer graphics and programming. It aims to provide a good foundation of advanced methods such as skeletal animation, quaternions, mesh processing and collision detection. These and other methods covered in the book are fundamental to the development of algorithms used in commercial applications as well as research.

3D User Interfaces

Author: Doug Bowman
Publisher: Addison-Wesley
ISBN: 013339056X
Format: PDF, ePub, Mobi
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Here’s what three pioneers in computer graphics and human-computer interaction have to say about this book: “What a tour de force—everything one would want—comprehensive, encyclopedic, and authoritative.” —Jim Foley “At last, a book on this important, emerging area. It will be an indispensable reference for the practitioner, researcher, and student interested in 3D user interfaces.” —Andy van Dam “Finally, the book we need to bridge the dream of 3D graphics with the user-centered reality of interface design. A thoughtful and practical guide for researchers and product developers. Thorough review, great examples.” —Ben Shneiderman As 3D technology becomes available for a wide range of applications, its successful deployment will require well-designed user interfaces (UIs). Specifically, software and hardware developers will need to understand the interaction principles and techniques peculiar to a 3D environment. This understanding, of course, builds on usability experience with 2D UIs. But it also involves new and unique challenges and opportunities. Discussing all relevant aspects of interaction, enhanced by instructive examples and guidelines, 3D User Interfaces comprises a single source for the latest theory and practice of 3D UIs. Many people already have seen 3D UIs in computer-aided design, radiation therapy, surgical simulation, data visualization, and virtual-reality entertainment. The next generation of computer games, mobile devices, and desktop applications also will feature 3D interaction. The authors of this book, each at the forefront of research and development in the young and dynamic field of 3D UIs, show how to produce usable 3D applications that deliver on their enormous promise. Coverage includes: The psychology and human factors of various 3D interaction tasks Different approaches for evaluating 3D UIs Results from empirical studies of 3D interaction techniques Principles for choosing appropriate input and output devices for 3D systems Details and tips on implementing common 3D interaction techniques Guidelines for selecting the most effective interaction techniques for common 3D tasks Case studies of 3D UIs in real-world applications To help you keep pace with this fast-evolving field, the book’s Web site, www.3dui.org, will offer information and links to the latest 3D UI research and applications.

Kalman Filter F r Einsteiger

Author: Phil Kim
Publisher: Createspace Independent Publishing Platform
ISBN: 9781502723789
Format: PDF, Mobi
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Das Kalman-Filter ist eine Wunderwaffe, wenn es darum geht digitale Signale in Echtzeit vom Rauschen zu befreien,nicht messbare Signale zu sch�tzen, Objekte zu tracken, Daten zu fusionieren und Messaussetzer zu �berbr�cken.Es findet Anwendung in Robotern, Raketen, Automobilen und selbst in M�hrobotern und autonomen Staubsaugern. H�ufig sind Ingenieurinnen und Ingenieure jedoch von der umfassenden Mathematik abgeschreckt. Das Buch "Kalman-Filter f�r Einsteiger" w�hlt einen unkonventionellen Einstieg in diese aktuelle Filtertechnik.Es beschreibt pragmatisch anhand von zahlreichen MATLAB(R)-Beispielen die Grundlagen des Filters und lehrt die Auslegung ohnemathematische Herleitungen. Dieses Buch erleichtert den Einstieg in die Signalverarbeitung und macht Sie in kurzer Zeit zu Kalman-Filter-Anwendungsprofis.

1089 oder das Wunder der Zahlen

Author: David J. Acheson
ISBN: 9783866470200
Format: PDF, ePub, Docs
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Das Buch beginnt mit einem alten Zaubertrick - Man nehme eine 3-stellige Zahl, etwa 782, kehre sie um, ziehe die kleinere von der größeren ab und addiere dazu die Umkehrung. Also - 782 - 287 = 495, dann 495 + 594. Und schon ist man mitten in der Wunderwelt der Mathematik, denn das Ergebnis ist immer - 1089. Mit solchen und vielen weiteren Beispielen aus Alltag, Geschichte und Wissenschaft gelingt es David Acheson, die faszinierende Welt der Mathematik zu erschließen - ein geistreicher Überblick, eine für jeden verständliche Einführung.