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Geometric Algebra Computing on the CUDA Platform

Schwinn, Christian ; Görlitz, Andreas ; Hildenbrand, Dietmar (2009)
Geometric Algebra Computing on the CUDA Platform.
International Workshop on Computer Graphics, Computer Vision and Mathematics.
Konferenzveröffentlichung, Bibliographie

Kurzbeschreibung (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 n-dimensional 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 speed-up 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 general-purpose 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.

Typ des Eintrags: Konferenzveröffentlichung
Erschienen: 2009
Autor(en): Schwinn, Christian ; Görlitz, Andreas ; Hildenbrand, Dietmar
Art des Eintrags: Bibliographie
Titel: Geometric Algebra Computing on the CUDA Platform
Sprache: Englisch
Publikationsjahr: 2009
Verlag: University of West Bohemia, Plzen
Veranstaltungstitel: International Workshop on Computer Graphics, Computer Vision and Mathematics
Kurzbeschreibung (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 n-dimensional 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 speed-up 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 general-purpose 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.

Freie Schlagworte: Forschungsgruppe Geometric Algebra Computing (GACO), Geometric algebra (GA), Geometric computing, Graphics Processing Unit (GPU), Compute Unified Device Architecture (CUDA)
Fachbereich(e)/-gebiet(e): 20 Fachbereich Informatik
20 Fachbereich Informatik > Graphisch-Interaktive Systeme
Hinterlegungsdatum: 12 Nov 2018 11:16
Letzte Änderung: 12 Nov 2018 11:16
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