A Geometric Algebra Implementation using Binary Tree

Abstract : This paper presents an efficient implementation of geometric algebra, based on a recursive representation of the algebra elements using binary trees. The proposed approach consists in restructuring a state of the art recursive algorithm to handle parallel optimizations. The resulting algorithm is described for the outer product and the geometric product. The proposed implementation is usable for any dimensions, including high dimension (e.g. algebra of dimension 15). The method is compared with the main state of the art geometric algebra implementations , with a time complexity study as well as a practical benchmark. The tests show that our implementation is at least as fast as the main geometric algebra implementations.
Type de document :
Article dans une revue
Advances in Applied Clifford Algebras, Springer Verlag, 2017, 1, pp.1-19. 〈10.1007/s00006-017-0770-6〉
Liste complète des métadonnées

Littérature citée [12 références]  Voir  Masquer  Télécharger

https://hal-upec-upem.archives-ouvertes.fr/hal-01510078
Contributeur : Vincent Nozick <>
Soumis le : mercredi 3 mai 2017 - 03:14:02
Dernière modification le : jeudi 11 janvier 2018 - 06:27:35

Fichier

breuils_aaca_2016.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Stéphane Breuils, Vincent Nozick, Laurent Fuchs. A Geometric Algebra Implementation using Binary Tree. Advances in Applied Clifford Algebras, Springer Verlag, 2017, 1, pp.1-19. 〈10.1007/s00006-017-0770-6〉. 〈hal-01510078v2〉

Partager

Métriques

Consultations de la notice

168

Téléchargements de fichiers

1069