Guide To Geometric Algebra In Practice

Author : Leo Dorst,Joan Lasenby
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 44,6 Mb
Release : 2011-08-28
Category : Computers
ISBN : 0857298119

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Guide to Geometric Algebra in Practice by Leo Dorst,Joan Lasenby Pdf

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.

Author : Leo Dorst,Joan Lasenby
Publisher : Springer
Page : 458 pages
File Size : 51,8 Mb
Release : 2011-09-18
Category : Computers
ISBN : 0857298127

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Guide to Geometric Algebra in Practice by Leo Dorst,Joan Lasenby Pdf

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.

Author : David William Honorio Araujo Da Silva
Publisher : Springer Nature
Page : 263 pages
File Size : 53,6 Mb
Release : 2024-06-12
Category : Electronic
ISBN : 9783031559853

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Advanced Computational Applications of Geometric Algebra by David William Honorio Araujo Da Silva Pdf

Author : Dietmar Hildenbrand
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 40,9 Mb
Release : 2012-12-31
Category : Computers
ISBN : 9783642317941

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Foundations of Geometric Algebra Computing by Dietmar Hildenbrand Pdf

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.

Author : Eduardo Bayro-Corrochano
Publisher : Springer Nature
Page : 609 pages
File Size : 48,8 Mb
Release : 2020-06-19
Category : Mathematics
ISBN : 9783030349783

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Geometric Algebra Applications Vol. II by Eduardo Bayro-Corrochano Pdf

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.

Author : Chris Doran,Anthony Lasenby
Publisher : Cambridge University Press
Page : 596 pages
File Size : 45,8 Mb
Release : 2003-05-29
Category : Mathematics
ISBN : 0521480221

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Geometric Algebra for Physicists by Chris Doran,Anthony Lasenby Pdf

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering.

Author : Eduardo Bayro-Corrochano
Publisher : Springer
Page : 742 pages
File Size : 52,9 Mb
Release : 2018-06-20
Category : Technology & Engineering
ISBN : 9783319748306

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Geometric Algebra Applications Vol. I by Eduardo Bayro-Corrochano Pdf

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.

Author : Eckhard Hitzer,George Papagiannakis,Petr Vasik
Publisher : Springer Nature
Page : 138 pages
File Size : 53,6 Mb
Release : 2023-04-26
Category : Mathematics
ISBN : 9783031309236

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Empowering Novel Geometric Algebra for Graphics and Engineering by Eckhard Hitzer,George Papagiannakis,Petr Vasik Pdf

This book constitutes the proceedings of the Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2022, held in conjunction with Computer Graphics International conference, CGI 2022, which took place virtually, in September 2022. The 10 full papers included in this volume were carefully reviewed and selected from 12 submissions. The workshop focused specifically on important aspects of geometric algebra including algebraic foundations, digitized transformations, orientation, conic fitting, protein modelling, digital twinning, and multidimensional signal processing.

Author : Nadia Magnenat-Thalmann,Constantine Stephanidis,Enhua Wu,Daniel Thalmann,Bin Sheng,Jinman Kim,George Papagiannakis,Marina Gavrilova
Publisher : Springer Nature
Page : 556 pages
File Size : 43,7 Mb
Release : 2020-10-17
Category : Computers
ISBN : 9783030618643

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Advances in Computer Graphics by Nadia Magnenat-Thalmann,Constantine Stephanidis,Enhua Wu,Daniel Thalmann,Bin Sheng,Jinman Kim,George Papagiannakis,Marina Gavrilova Pdf

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.

Author : Elena Barcucci,Andrea Frosini,Simone Rinaldi
Publisher : Springer
Page : 423 pages
File Size : 55,7 Mb
Release : 2014-09-03
Category : Computers
ISBN : 9783319099552

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Discrete Geometry for Computer Imagery by Elena Barcucci,Andrea Frosini,Simone Rinaldi Pdf

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.

Author : Tor Dokken,Georg Muntingh
Publisher : Springer
Page : 323 pages
File Size : 52,9 Mb
Release : 2014-10-24
Category : Mathematics
ISBN : 9783319086354

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SAGA – Advances in ShApes, Geometry, and Algebra by Tor Dokken,Georg Muntingh Pdf

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.

Author : Sebastià Xambó-Descamps
Publisher : Springer
Page : 151 pages
File Size : 45,6 Mb
Release : 2018-11-22
Category : Mathematics
ISBN : 9783030004040

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Real Spinorial Groups by Sebastià Xambó-Descamps Pdf

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.

Author : Sebastià Xambó-Descamps
Publisher : Springer Nature
Page : 179 pages
File Size : 55,6 Mb
Release : 2021-07-16
Category : Mathematics
ISBN : 9783030744861

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Systems, Patterns and Data Engineering with Geometric Calculi by Sebastià Xambó-Descamps Pdf

The intention of this collection agrees with the purposes of the homonymous mini-symposium (MS) at ICIAM-2019, which were to overview the essentials of geometric calculus (GC) formalism, to report on state-of-the-art applications showcasing its advantages and to explore the bearing of GC in novel approaches to deep learning. The first three contributions, which correspond to lectures at the MS, offer perspectives on recent advances in the application GC in the areas of robotics, molecular geometry, and medical imaging. The next three, especially invited, hone the expressiveness of GC in orientation measurements under different metrics, the treatment of contact elements, and the investigation of efficient computational methodologies. The last two, which also correspond to lectures at the MS, deal with two aspects of deep learning: a presentation of a concrete quaternionic convolutional neural network layer for image classification that features contrast invariance and a general overview of automatic learning aimed at steering the development of neural networks whose units process elements of a suitable algebra, such as a geometric algebra. The book fits, broadly speaking, within the realm of mathematical engineering, and consequently, it is intended for a wide spectrum of research profiles. In particular, it should bring inspiration and guidance to those looking for materials and problems that bridge GC with applications of great current interest, including the auspicious field of GC-based deep neural networks.

Author : Ronald Goldman
Publisher : CRC Press
Page : 279 pages
File Size : 40,8 Mb
Release : 2023-09-29
Category : Computers
ISBN : 9781000903492

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Dual Quaternions and Their Associated Clifford Algebras by Ronald Goldman Pdf

Provides an extensive rigorous treatment of dual quaternions, collecting in one place the main formulas and theorems. Presents two models of Clifford algebra associated to the dual quaternions. Shows how these two Clifford algebras both emerge naturally from the theory of dual quaternions. Easily accessible to anyone with a basic knowledge of quaternion algebra. Provides exercises after each section to help readers practice and sharpen their knowledge of what they have read.

Author : Xianmin Zhang,Honghai Liu,Zhong Chen,Nianfeng Wang
Publisher : Springer
Page : 514 pages
File Size : 42,9 Mb
Release : 2014-11-14
Category : Computers
ISBN : 9783319139661

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Intelligent Robotics and Applications by Xianmin Zhang,Honghai Liu,Zhong Chen,Nianfeng Wang Pdf

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.