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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