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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Geometric algebra computing on the CUDA platform
 Skala, Vaclav (Ed.); Hildenbrand, Dietmar (Ed.) ; European Association for Computer Graphics EUROGRAPHICS: GraVisMa 2009, International Workshop on Computer Graphics, Computer Vision and Mathematics. Workshop proceedings : Held at the University of West Bohemia in Plzen, Czech Republic on September 2  4, 2009 / in cooperation with EUROGRAPHICS Pilsen: University of West Bohemia, 2009 ISBN: 9788086943909 pp.111117 
 International Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) <1, 2009, Plzen> 

 English 
 Conference Paper 
 Fraunhofer IGD () 
 geometric algebra; geometric computing; Graphics Processing Unit (GPU); Compute Unified Device Architecture (CUDA); Forschungsgruppe Geometric Algebra Computing (GACO) 
Abstract
Geometric Algebra (GA) is a mathematical framework that allows a compact, geometrically intuitive description of geometric relationships and algorithms. These algorithms require significant computational power because of the intrinsically high dimensionality of geometric algebras. Algorithms in an ndimensional GA require 2n elements to be computed for each multivector. GA is not restricted to a maximum of dimensions, so arbitrary geometric algebras can be constructed over a vector space Vn. Since computations in GA can be highly parallelized, the benefits of a parallel computing architecture can lead to a significant speedup compared to standard CPU implementations, where elements of the algebra have to be calculated sequentially. An upcoming approach of coping with parallel computing is to use generalpurpose computation on graphics processing units (GPGPU). In this paper, we focus on the Compute Unified Device Architecture (CUDA) from NVIDIA [9]. We present a code generator that takes as input the description of an arbitrary geometric algebra and produces an implementation of geometric products for the underlying algebra on the CUDA platform.