Geometric algebra (also known as Clifford algebra) is a powerful mathematical tool that offers a natural and direct way to model geometric objects and their transformations. It is gaining growing attention in different research fields as physics, robotics, CAD/CAM and computer graphics. In particular, 4D geometric algebra implements homogeneous coordinates, which are used to model 3D scenery in most computer graphics applications. The research work on Clifford algebra is actually aimed at finding efficient implementations of the algebra. This paper wants to give a contribution to this research effort by proposing a direct hardware support for geometric algebra operators. The paper introduces a 4D Clifford algebra based on fixed-size elements and demonstrates that this choice leads to a simple and compact hardware implementation of geometric algebra operations.

Geometric algebra (also known as Clifford algebra) is a powerful mathematical tool that offers a natural and direct way to model geometric objects and their transformations. It is gaining growing attention in different research fields as physics, robotics, CAD/CAM and computer graphics. In particular, 4D geometric algebra implements homogeneous coordinates, which are used to model 3D scenery in most computer graphics applications. The research work on Clifford algebra is actually aimed at finding efficient implementations of the algebra. This paper wants to give a contribution to this research effort by proposing a direct hardware support for geometric algebra operators. The paper introduces a 4D Clifford algebra based on fixed-size elements and demonstrates that this choice leads to a simple and compact hardware implementation of geometric algebra operations.

Franchini, S.g., Vassallo, G., Sorbello, F., De Marchis, M., Vassallo, G. (2008). 4D Clifford algebra based on fixed-size representation. In Atti dell'Accademia Nazionale di Scienze, Lettere e Arti di Palermo, Serie V, Volume XXIV, Anni Accademici 2004-2008, Tomo I: Scienze, 2008 (pp.249-273).

4D Clifford algebra based on fixed-size representation

FRANCHINI, Silvia Giuseppina;VASSALLO, Giorgio;SORBELLO, Filippo;DE MARCHIS, Mauro;VASSALLO, Giorgio
2008-01-01

Abstract

Geometric algebra (also known as Clifford algebra) is a powerful mathematical tool that offers a natural and direct way to model geometric objects and their transformations. It is gaining growing attention in different research fields as physics, robotics, CAD/CAM and computer graphics. In particular, 4D geometric algebra implements homogeneous coordinates, which are used to model 3D scenery in most computer graphics applications. The research work on Clifford algebra is actually aimed at finding efficient implementations of the algebra. This paper wants to give a contribution to this research effort by proposing a direct hardware support for geometric algebra operators. The paper introduces a 4D Clifford algebra based on fixed-size elements and demonstrates that this choice leads to a simple and compact hardware implementation of geometric algebra operations.
2008
Atti dell'Accademia Nazionale di Scienze, Lettere e Arti di Palermo, Serie V, Volume XXIV, Anni Accademici 2004-2008, Tomo I: Scienze, 2008
Palermo
2008
mag-2008
2008
25
A stampa
Franchini, S.g., Vassallo, G., Sorbello, F., De Marchis, M., Vassallo, G. (2008). 4D Clifford algebra based on fixed-size representation. In Atti dell'Accademia Nazionale di Scienze, Lettere e Arti di Palermo, Serie V, Volume XXIV, Anni Accademici 2004-2008, Tomo I: Scienze, 2008 (pp.249-273).
Proceedings (atti dei congressi)
Franchini, Sg; Vassallo, G; Sorbello, F; De Marchis, M; Vassallo, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/48076
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