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Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems.
John Vince (author of numerous books including 'Geometry for Computer Graphics' and 'Vector Analysis for Computer Graphics') has tackled this complex subject in his usual inimitable style, and provided an accessible and very readable introduction.
As well as putting geometric algebra into its historical context, John tackles complex numbers and quaternions; the nature of wedge product and geometric product; reflections and rotations (showing how geometric algebra can offer a powerful way of describing orientations of objects and virtual cameras); and how to implement lines, planes, volumes and intersections. Introductory chapters also look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.
Inhaltsverzeichnis
Elementary Algebra.- Complex Algebra.- Vector Algebra.- Quaternion Algebra.- Geometric Conventions.- Geometric Algebra.- The Geometric Product.- Reflections and Rotations.- Geometric Algebra and Geometry.- Conformal Geometry.- Applications of Geometric Algebra.- Programming Tools for Geometric Algebra.- Conclusion.
Über den Autor / die Autorin
Professor John Vince began working in computer graphics at Middlesex Polytechnic in 1968. His research activities centered on computer animation software and resulted in the PICASO and PRISM animation systems. Whilst at Middlesex, he designed the UK's first MSc course in Computer Graphics and developed a popular program of short courses in computer animation for television designers. In 1986 he joined Rediffusion Simulation as a Research Consultant and worked on the development of real-time computer systems for commercial flight simulators. In 1992 he was appointed Chief Scientist of Thomson Training Simulation Ltd. In 1995 he was appointed Professor of Digital Media at the National Centre for Computer Animation at Bournemouth University and in 1999 he was made Head of Academic Group for Computer Animation. He was awarded a DSc by Brunel University in recognition of his work in computer graphics. He has written and edited over 45 books on computer graphics, computer animation, computer science and virtual reality, including the following Springer titles:
¿ Calculus for Computer Graphics, 2nd edition (2019)
¿ Mathematics for Computer Graphics, 5th edition (2017)
¿ Imaginary Mathematics for Computer Science, (2018)
¿ Foundation Mathematics for Computer Science, 2nd edition (2015)
¿ Matrix Transforms for Computer Games and Animation (2012)
¿ Expanding the Frontiers of Visual Analytics and Visualization (2012)
¿ Quaternions for Computer Graphics (2011)
¿ Rotation Transforms for Computer Graphics (2011)
¿ Geometric Algebra: An Algebraic System for Computer Animation and Games (2009)
¿ Geometric Algebra for Computer Graphics (2008)
Zusammenfassung
Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems.
John Vince (author of numerous books including ‘Geometry for Computer Graphics’ and ‘Vector Analysis for Computer Graphics’) has tackled this complex subject in his usual inimitable style, and provided an accessible and very readable introduction. As well as putting geometric algebra into its historical context, John tackles complex numbers and quaternions. The text is very well illustrated and filled with lots of clear examples. Introductory chapters also look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.
