Guide to Geometric Algebra in Practice

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.

Author: Leo Dorst

Publisher: Springer Science & Business Media

ISBN: 9780857298119

Category: Computers

Page: 458

View: 295

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.

Guide to Geometric Algebra in Practice

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.

Author: Leo Dorst

Publisher: Springer

ISBN: 9780857298126

Category: Computers

Page: 458

View: 280

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.

Foundations of Geometric Algebra Computing

Guide to Geometric Algebra in Practice. Springer, 201 1. Leo Dorst and Stephen Mann. Geometric algebra: A computational framework for geometrical applications (part i: Algebra). Computer Graphics and Application, 22(3):24—31, 2002.

Author: Dietmar Hildenbrand

Publisher: Springer Science & Business Media

ISBN: 3642317944

Category: Computers

Page: 196

View: 441

The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.

Geometric Algebra Applications Vol II

Clifford algebra to geometric calculus: A unified language for mathematics and physics. Dordrecht: D. Reidel. 2. Doran, C., Hestenes, D., Sommen, ... In L. Dorst & J. Lasenby (Eds.), Guide to geometric algebra in practice (pp. 253–272).

Author: Eduardo Bayro-Corrochano

Publisher: Springer Nature

ISBN: 3030349780

Category: Mathematics

Page: 600

View: 872

This book presents a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford or geometric alge- bra. By addressing a wide spectrum of problems in a common language, it offers both fresh insights and new solutions that are useful to scientists and engineers working in areas related with robotics. It introduces non-specialists to Clifford and geometric algebra, and provides ex- amples to help readers learn how to compute using geometric entities and geomet- ric formulations. It also includes an in-depth study of applications of Lie group theory, Lie algebra, spinors and versors and the algebra of incidence using the universal geometric algebra generated by reciprocal null cones. Featuring a detailed study of kinematics, differential kinematics and dynamics using geometric algebra, the book also develops Euler Lagrange and Hamiltoni- ans equations for dynamics using conformal geometric algebra, and the recursive Newton-Euler using screw theory in the motor algebra framework. Further, it comprehensively explores robot modeling and nonlinear controllers, and discusses several applications in computer vision, graphics, neurocomputing, quantum com- puting, robotics and control engineering using the geometric algebra framework. The book also includes over 200 exercises and tips for the development of future computer software packages for extensive calculations in geometric algebra, and a entire section focusing on how to write the subroutines in C++, Matlab and Maple to carry out efficient geometric computations in the geometric algebra framework. Lastly, it shows how program code can be optimized for real-time computations. An essential resource for applied physicists, computer scientists, AI researchers, roboticists and mechanical and electrical engineers, the book clarifies and demon- strates the importance of geometric computing for building autonomous systems to advance cognitive systems research.

Geometric Algebra Applications Vol I

In Guide to geometric algebra in practice, ed. L. Dorst, and J. Lasenby, 253–272. New York: Springer. Li, H., L. Huang, Ch. Shao, and L. Dong. 2015. Three-dimensional projective geometry with geometric algebra. arXiv:1507.06634v1.

Author: Eduardo Bayro-Corrochano

Publisher: Springer

ISBN: 3319748300

Category: Technology & Engineering

Page: 742

View: 142

The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.

Advances in Computer Graphics

Guide to Geometric Algebra in Practice, pp. 297–327. Springer, London (2011). https://doi.org/10.1007/978-0-85729-811-915 2. Pottmann, H., Wallner, J.: Computational Line Geometry. MATHVISUAL. Springer, Heidelberg (2001).

Author: Nadia Magnenat-Thalmann

Publisher: Springer Nature

ISBN: 3030618641

Category: Computers

Page: 556

View: 660

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.

Discrete Geometry for Computer Imagery

Dorst, L., Lasenby, J. (eds.): Guide to Geometric Algebra in Practice (Proceedings of AGACSE 2010). Springer (2011) 8. Fontijne, D., Dorst, L., Bouma, T., Mann, S.: GAviewer, interactive visualization software for geometric algebra ...

Author: Elena Barcucci

Publisher: Springer

ISBN: 3319099558

Category: Computers

Page: 423

View: 254

This book constitutes the thoroughly refereed proceedings of the 18th International Conference on Discrete Geometry for Computer Imagery, DGCI 2014, held in Siena, Italy, September 2014. The 34 revised full papers presented were carefully selected from 60 submissions. The papers are organized in topical sections on Models for Discrete Geometry, Discrete and Combinatorial Topology, Geometric Transforms, Discrete Shape Representation, Recognition and Analysis, Discrete Tomography, Morphological Analysis, Discrete Modelling and Visualization, Discrete and Combinatorial Tools for Image Segmentation and Analysis.

SAGA Advances in ShApes Geometry and Algebra

R. Goldman, A Homogeneous model for three-dimensional computer graphics based on the clifford algebra for R3, in Guide to Geometric Algebra in Practice, ed. by L. Dorst, J. Lasenby (Springer, New York, 2011), pp. 329–352 9.

Author: Tor Dokken

Publisher: Springer

ISBN: 3319086359

Category: Mathematics

Page: 323

View: 918

This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design.

Real Spinorial Groups

J. Cameron, J. Lasenby, Oriented conformal geometric algebra. ... Applications of Geometric Algebra in Computer 41. 42. 43. ... Guide to Geometric Algebra in Practice (Springer, Berlin, 2011) Science and Engineering (Springer, Berlin, ...

Author: Sebastià Xambó-Descamps

Publisher: Springer

ISBN: 303000404X

Category: Mathematics

Page: 151

View: 169

This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.

Intelligent Robotics and Applications

Springer (1999) Clifford, W.K.: On the classification of geometric algebras. ... Hitzer, E., Helmstetter, J., Abłamowicz, R.: Square roots of–1 in real Clifford algebras. ... Guide to Geometric Algebra in Practice.

Author: Xianmin Zhang

Publisher: Springer

ISBN: 3319139665

Category: Computers

Page: 514

View: 425

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.