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From Grassmann's vision to geometric algebra computing

: Hildenbrand, Dietmar


Petsche, H.-J.:
Hermann Graßmann - From past to future : Graßmann's work in context; Graßmann Bicentennial Conference, September 2009
Basel: Birkhäuser, 2011
ISBN: 978-3-0346-0404-8
ISBN: 3-03-460404-1
ISBN: 978-3-0346-0405-5
Graßmann Bicentennial Conference <2009, Potsdam>
Conference Paper
Fraunhofer IGD ()
geometric algebra (GA); geometric computing; Conformal Geometric Algebra (CGA); Forschungsgruppe Geometric Algebra Computing (GACO)

What mathematicians often call Clifford algebra is called geometric algebra if the focus is on the geometric meaning of the algebraic expressions and operators. Geometric algebra is a mathematical framework to easily describe geometric concepts and operations. It allows us to develop algorithms fast and in an intuitive way. It is based on the work of Hermann Grassmann [A2] and his vision of a general mathematical language for geometry. William Clifford combined Grassmann's exterior algebra and Hamilton's quaternions [Clifford 1882a, 1882b]. Pioneering work has been done by David Hestenes, who first applied geometric algebra to problems in mechanics and physics [Hestenes and Sobczyk 1984; Hestenes 1985]. His work culminated some years ago in the invention of conformal geometric algebra [Hestenes 2001].