**Author**: J. B. Kuipers

**Publisher:**Princeton University Press

**ISBN:**0691211701

**Category :**Mathematics

**Languages :**en

**Pages :**

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## Quaternions and Rotation Sequences

**Author**: J. B. Kuipers

**Publisher:** Princeton University Press

**ISBN:** 0691211701

**Category : **Mathematics

**Languages : **en

**Pages : **

**Book Description**

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.

## Quaternions and Rotation Sequences

**Author**: J. B. Kuipers

**Publisher:** Princeton University Press

**ISBN:** 0691211701

**Category : **Mathematics

**Languages : **en

**Pages : **

**Book Description**

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.

## Quaternions and Rotation Sequences

**Author**: Jack B. Kuipers

**Publisher:**

**ISBN:**

**Category : **

**Languages : **en

**Pages : **371

**Book Description**

## Interaction Design for 3D User Interfaces

**Author**: Francisco R. Ortega

**Publisher:** CRC Press

**ISBN:** 1482216957

**Category : **Computers

**Languages : **en

**Pages : **805

**Book Description**

In this new era of computing, where the iPhone, iPad, Xbox Kinect, and similar devices have changed the way to interact with computers, many questions have risen about how modern input devices can be used for a more intuitive user interaction. Interaction Design for 3D User Interfaces: The World of Modern Input Devices for Research, Applications, a

## Multisensor Attitude Estimation

**Author**: Hassen Fourati

**Publisher:** CRC Press

**ISBN:** 1315351757

**Category : **Technology & Engineering

**Languages : **en

**Pages : **580

**Book Description**

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.

## Visualizing Quaternions

**Author**: Andrew J. Hanson

**Publisher:** Elsevier

**ISBN:** 0080474772

**Category : **Mathematics

**Languages : **en

**Pages : **530

**Book Description**

Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available. The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. Covers both non-mathematical and mathematical approaches to quaternions.

## CRC Concise Encyclopedia of Mathematics

**Author**: Eric W. Weisstein

**Publisher:** CRC Press

**ISBN:** 1420035223

**Category : **Mathematics

**Languages : **en

**Pages : **3252

**Book Description**

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

## Small Unmanned Aircraft

**Author**: Randal W. Beard

**Publisher:** Princeton University Press

**ISBN:** 0691149216

**Category : **Mathematics

**Languages : **en

**Pages : **318

**Book Description**

Includes bibliographical references (p. [291]-298) and index.

## Crystallography and Crystal Defects

**Author**: Anthony Kelly

**Publisher:** John Wiley & Sons

**ISBN:** 1119420172

**Category : **Science

**Languages : **en

**Pages : **584

**Book Description**

The classic book that presents a unified approach to crystallography and the defects found within crystals, revised and updated This new edition of Crystallography and Crystal Defects explains the modern concepts of crystallography in a clear, succinct manner and shows how to apply these concepts in the analyses of point, line and planar defects in crystalline materials. Fully revised and updated, this book now includes: Original source references to key crystallographic terms familiar to materials scientists Expanded discussion on the elasticity of cubic materials New content on texture that contains more detail on Euler angles, orientation distribution functions and an expanded discussion on examples of textures in engineering materials Additional content on dislocations in materials of symmetry lower than cubic An expanded discussion of twinning which includes the description and classification of growth twins The inclusion and explanation of results from atomistic modelling of twin boundaries Problem sets with new questions, detailed worked solutions, supplementary lecture material and online computer programs for crystallographic calculations. Written by authors with extensive lecturing experience at undergraduate level, Crystallography and Crystal Defects, Third Edition continues to take its place as the core text on the topic and provides the essential resource for students and researchers in metallurgy, materials science, physics, chemistry, electrical, civil and mechanical engineering.

## Quaternion Fourier Transforms for Signal and Image Processing

**Author**: Todd A. Ell

**Publisher:** John Wiley & Sons

**ISBN:** 1118930924

**Category : **Technology & Engineering

**Languages : **en

**Pages : **160

**Book Description**

Based on updates to signal and image processing technology made inthe last two decades, this text examines the most recent researchresults pertaining to Quaternion Fourier Transforms. QFT is acentral component of processing color images and complex valuedsignals. The book’s attention to mathematical concepts,imaging applications, and Matlab compatibility render it anirreplaceable resource for students, scientists, researchers, andengineers.

## Advanced Methods in Computer Graphics

**Author**: Ramakrishnan Mukundan

**Publisher:** Springer Science & Business Media

**ISBN:** 1447123409

**Category : **Computers

**Languages : **en

**Pages : **314

**Book Description**

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.

eBook Journalism in PDF, ePub, Mobi and Kindle

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.

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.

In this new era of computing, where the iPhone, iPad, Xbox Kinect, and similar devices have changed the way to interact with computers, many questions have risen about how modern input devices can be used for a more intuitive user interaction. Interaction Design for 3D User Interfaces: The World of Modern Input Devices for Research, Applications, a

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.

Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available. The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. Covers both non-mathematical and mathematical approaches to quaternions.

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

Includes bibliographical references (p. [291]-298) and index.

The classic book that presents a unified approach to crystallography and the defects found within crystals, revised and updated This new edition of Crystallography and Crystal Defects explains the modern concepts of crystallography in a clear, succinct manner and shows how to apply these concepts in the analyses of point, line and planar defects in crystalline materials. Fully revised and updated, this book now includes: Original source references to key crystallographic terms familiar to materials scientists Expanded discussion on the elasticity of cubic materials New content on texture that contains more detail on Euler angles, orientation distribution functions and an expanded discussion on examples of textures in engineering materials Additional content on dislocations in materials of symmetry lower than cubic An expanded discussion of twinning which includes the description and classification of growth twins The inclusion and explanation of results from atomistic modelling of twin boundaries Problem sets with new questions, detailed worked solutions, supplementary lecture material and online computer programs for crystallographic calculations. Written by authors with extensive lecturing experience at undergraduate level, Crystallography and Crystal Defects, Third Edition continues to take its place as the core text on the topic and provides the essential resource for students and researchers in metallurgy, materials science, physics, chemistry, electrical, civil and mechanical engineering.

Based on updates to signal and image processing technology made inthe last two decades, this text examines the most recent researchresults pertaining to Quaternion Fourier Transforms. QFT is acentral component of processing color images and complex valuedsignals. The book’s attention to mathematical concepts,imaging applications, and Matlab compatibility render it anirreplaceable resource for students, scientists, researchers, andengineers.

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.