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Titlebook: Geometric Algebra for Computer Graphics; John Vince Textbook 2008 Springer-Verlag London 2008 3D.Algebra.Clifford Algebra.Geometric algebr

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发表于 2025-3-21 19:23:39 | 显示全部楼层 |阅读模式
书目名称Geometric Algebra for Computer Graphics
编辑John Vince
视频video
概述Filled with lots of clear examples.Very well illustrated.Tackles the complex subject of geometric algebra and explains, in detail, how the algebra operates together with its relationship with traditio
图书封面Titlebook: Geometric Algebra for Computer Graphics;  John Vince Textbook 2008 Springer-Verlag London 2008 3D.Algebra.Clifford Algebra.Geometric algebr
描述.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..
出版日期Textbook 2008
关键词3D; Algebra; Clifford Algebra; Geometric algebra; calculus; computer graphics; geometry; reflection
版次1
doihttps://doi.org/10.1007/978-1-84628-997-2
isbn_softcover978-1-84996-697-9
isbn_ebook978-1-84628-997-2
copyrightSpringer-Verlag London 2008
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发表于 2025-3-21 22:37:52 | 显示全部楼层
https://doi.org/10.1007/978-1-84628-997-23D; Algebra; Clifford Algebra; Geometric algebra; calculus; computer graphics; geometry; reflection
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发表于 2025-3-22 07:17:53 | 显示全部楼层
https://doi.org/10.1007/978-1-4684-1770-8overed in Michael Crowe’s excellent book . [6]. No one mathematician can claim that he or she discovered vectors—although the word . was coined by the Irish physicist and mathematician, William Rowan Hamilton [1805–1865]. However, long before Hamilton was born, the German diplomat and natural philos
发表于 2025-3-22 12:40:25 | 显示全部楼层
Dirac Operators in Representation Theorytity zero and taking square-roots of negative numbers. In this chapter we look at how geometric conventions give rise to negative areas and volumes which we must understand before proceeding with GA. Readers already familiar with computer graphics will understand the importance of using a left-hande
发表于 2025-3-22 15:11:49 | 显示全部楼层
Horacio R. Corti,Ernesto R. Gonzalezshed the first edition of his geometric calculus ., which offered an original algebra for describing geometric operations. The word ‘.’ translates as ‘.’ and the principal algebraic product of the theory was the .. The notion of . is something that Euclid was aware of, in that the product of two len
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发表于 2025-3-22 23:53:45 | 显示全部楼层
https://doi.org/10.1007/978-3-531-94304-6thods, rather demonstrate that GA can be used alongside classic vectorial techniques. The classic vectorial approach often depends upon the scalar and cross products and normal vectors to lines and planes. The GA approach is to avoid such vectors and work with the inner, outer and geometric products
发表于 2025-3-23 02:19:09 | 显示全部楼层
,“Hybrid Democracy” and Its Consequences,for the algebra – after all, it is just an algebra for vectorial quantities. It is difficult to think of an area of CGI where vectors are not used –and sometimes when GA has been used, there are minor considerations of efficiency in execution time, although there is general agreement that it outperf
发表于 2025-3-23 07:53:14 | 显示全部楼层
https://doi.org/10.1007/978-1-4615-4923-9ersity of Amsterdam (Netherlands) and MPI Saarbruecken (Germany). Research at Cambridge University focuses on the areas of physics, computer vision, motion analysis and computer graphics [24], [25], [26], [27], [28], [29]. Research at the University of Amsterdam is in computer science and computer g
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