Geometric Algebra for Computer Science Revised Edition

This book explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics.

Author: Leo Dorst

Publisher: Morgan Kaufmann

ISBN: 9780080958798

Category: Computers

Page: 664

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Geometric Algebra for Computer Science (Revised Edition) presents a compelling alternative to the limitations of linear algebra. Geometric algebra (GA) is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. This book explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. It systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. It covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Numerous drills and programming exercises are helpful for both students and practitioners. A companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book; and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter. The book will be of interest to professionals working in fields requiring complex geometric computation such as robotics, computer graphics, and computer games. It is also be ideal for students in graduate or advanced undergraduate programs in computer science. Explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. Systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. Covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Presents effective approaches to making GA an integral part of your programming. Includes numerous drills and programming exercises helpful for both students and practitioners. Companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book, and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter.
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Intelligent Robotics and Applications

The authors would like to acknowledge the financial support of the Natural Science Foundation of China (NSFC) under ... CRC Press (2006) Dorst, L., Fontijne, D., Mann, S.: Geometric algebra for computer science (revised edition): An ...

Author: Xianmin Zhang

Publisher: Springer

ISBN: 9783319139661

Category: Computers

Page: 514

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This two volume set LNAI 8917 and 8918 constitutes the refereed proceedings of the 7th International Conference on Intelligent Robotics and Applications, ICIRA 2014, held in Guangzhou, China, in December 2014. The 109 revised full papers presented were carefully reviewed and selected from 159 submissions. The papers aim at enhancing the sharing of individual experiences and expertise in intelligent robotics with particular emphasis on technical challenges associated with varied applications such as biomedical applications, industrial automations, surveillance, and sustainable mobility.
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Topological and Statistical Methods for Complex Data

Dorst, L., Fontijne, D., Mann, S: Geometric Algebra for Computer Science (Revised Edition): An Object-Oriented Approach to Geometry. Morgan Kaufmann (2009) 8. Dieudonné, J.: Sur les groupes classiques. Hermann & cie (1948) 9.

Author: Janine Bennett

Publisher: Springer

ISBN: 9783662449004

Category: Mathematics

Page: 297

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This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.
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Advances in Computer Graphics

Procedia Technol. 11, 614–620 (2013) 18. Dorst, L., Fontijne, D., Mann, S.: Why geometric algebra? In: Geometric Algebra for Computer Science, Revised edn. Morgan Kaufmann Publishers, Burlington (2009) 19. Hitzer, E., Nitta, T., ...

Author: Nadia Magnenat-Thalmann

Publisher: Springer Nature

ISBN: 9783030618643

Category: Computers

Page: 556

View: 317

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This book constitutes the refereed proceedings of the 37th Computer Graphics International Conference, CGI 2020, held in Geneva, Switzerland, in October 2020. The conference was held virtually. The 43 full papers presented together with 3 short papers were carefully reviewed and selected from 189 submissions. The papers address topics such as: virtual reality; rendering and textures; augmented and mixed reality; video processing; image processing; fluid simulation and control; meshes and topology; visual simulation and aesthetics; human computer interaction; computer animation; geometric computing; robotics and vision; scientific visualization; and machine learning for graphics.
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Geometric Algebra Computing

in Engineering and Computer Science Eduardo Bayro-Corrochano, Gerik Scheuermann ... References Engineering Graphics in Geometric Algebra Alyn Rockwood and Dietmar Hildenbrand ... Second revised printing 2009.

Author: Eduardo Bayro-Corrochano

Publisher: Springer Science & Business Media

ISBN: 9781849961080

Category: Computers

Page: 526

View: 820

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This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Its accessible style is enhanced by examples, figures and experimental analysis.
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Guide to Geometric Algebra in Practice

... geometric algebra from the known transformation of n vectors. In: Proceedings of GraVisMa 2009, Plzen 5. Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science: An Object Oriented Approach to Geometry, revised edn ...

Author: Leo Dorst

Publisher: Springer Science & Business Media

ISBN: 0857298119

Category: Computers

Page: 458

View: 139

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This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
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Computer Algebra and Geometric Algebra with Applications

Peter J. Olver Gerald Sommer (Eds.) Computer Algebra and Geometric Algebra with Applications 6th memon workshop www. ... 2004, Revised Selected Papers : Ø Springer Lecture Notes in Computer Science Commenced Publication in 1973 Founding.

Author: Hongbo Li

Publisher: Springer

ISBN: 9783540321194

Category: Computers

Page: 449

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MathematicsMechanization consistsoftheory,softwareandapplicationofc- puterized mathematical activities such as computing, reasoning and discovering. ItsuniquefeaturecanbesuccinctlydescribedasAAA(Algebraization,Algori- mization, Application). The name “Mathematics Mechanization” has its origin in the work of Hao Wang (1960s), one of the pioneers in using computers to do research in mathematics, particularly in automated theorem proving. Since the 1970s, this research direction has been actively pursued and extensively dev- oped by Prof. Wen-tsun Wu and his followers. It di?ers from the closely related disciplines like Computer Mathematics, Symbolic Computation and Automated Reasoning in that its goal is to make algorithmic studies and applications of mathematics the major trend of mathematics development in the information age. The International Workshop on Mathematics Mechanization (IWMM) was initiated by Prof. Wu in 1992, and has ever since been held by the Key L- oratory of Mathematics Mechanization (KLMM) of the Chinese Academy of Sciences. There have been seven workshops of the series up to now. At each workshop, several experts are invited to deliver plenary lectures on cutting-edge methods and algorithms of the selected theme. The workshop is also a forum for people working on related subjects to meet, collaborate and exchange ideas.
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Image and Video Technology PSIVT 2013 Workshops

IEICE Transactions 93-D, 2836–2845 (2010) 9. Dorst, L., Fontijne, D., Mann, S.: Geometric algebra for computer science: an object-oriented approach to geometry, revised 1st edn. Morgan Kaufmann series in computer graphics.

Author: Fay Huang

Publisher: Springer

ISBN: 9783642539268

Category: Computers

Page: 241

View: 704

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This book constitutes the thoroughly refereed post-conference proceedings of the four workshops on Photographic Aesthetics and Non-Photorealistic Rendering (PAESNPR13), Geometric Properties from Incomplete Data (GPID), Quality Assessment and Control by Image and Video Analysis (QACIVA) and Geometric Computation for Computer Vision (GCCV2013), held in conjunction with the 6th Pacific-Rim Symposium on Image and Video Technology (PSIVT) in Guanajuato, Mexico during October 28-November 1, 2013. The 38 revised full papers presented were carefully selected from numerous submissions and cover all aspects of Imaging and Graphics Hardware and Visualization, Image/Video Coding and Transmission; Processing and Analysis; Retrieval and Scene Understanding, but also Applications of Image and Video Technology, Biomedical Image Processing and Analysis, Biometrics and Image Forensics, Computational Photography and Arts, Computer and Robot Vision, Pattern Recognition and Video Surveillance.
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Mathematics for Computer Graphics

Mathematics for Computer Graphics covers all of the key areas of the subject, including: • Number sets • Algebra • Trigonometry • Complex numbers • Coordinate systems • Determinants • Vectors • Quaternions • Matrix algebra ...

Author: John Vince

Publisher: Springer

ISBN: 1447175190

Category: Computers

Page: 564

View: 643

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John Vince explains a comprehensive range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, special effects, virtual reality, CAD and other areas of computer graphics in this completely revised and expanded sixth edition. The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on determinants, vectors, matrix algebra, complex numbers, geometric transforms, quaternion algebra, quaternions in space, interpolation, curves and patches, analytical geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new subject of geometric algebra, followed by two chapters that introduce differential and integral calculus. Finally, there is a chapter on worked examples. Mathematics for Computer Graphics covers all of the key areas of the subject, including: • Number sets • Algebra • Trigonometry • Complex numbers • Coordinate systems • Determinants • Vectors • Quaternions • Matrix algebra • Geometric transforms • Interpolation • Curves and surfaces • Analytic geometry • Barycentric coordinates • Geometric algebra • Differential calculus • Integral calculus This sixth edition contains approximately 150 worked examples and over 330 colour illustrations, which are central to the author’s descriptive writing style. Mathematics for Computer Graphics provides a sound understanding of the mathematics required for computer graphics software and setting the scene for further reading of more advanced books and technical research papers
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Lectures on Clifford Geometric Algebras and Applications

Homogeneous Rigid Body Mechanics with Elastic Coupling , in Applications of Geometric Algebra in Computer Science and Engineering , eds . L. Dorst , C. Doran and J. Lasenby , Birkhäuser , Boston 2002 , pp . 197–212 . [ 8 ] B.K.P Horn .

Author: Rafal Ablamowicz

Publisher: Springer Science & Business Media

ISBN: 0817632573

Category: Mathematics

Page: 221

View: 465

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The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.
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