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G 6,3 Geometric Algebra; Description and Implementation

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Abstract

This paper introduces a new non-Euclidean geometry, that consist in a generalization of conformal geometry G 4,1. In this geometry, it is possible to handle not only spheres, but also quadratic surfaces and their intersections easily as well. The Clifford algebra G 6,3 is being used as the framework, which allows the creation of a nine dimensional geometry with some additional transformations, i.e. anisotropic dilatation, allowing rotations for all G 4,1 entities. It also eases the use of quadratic surfaces including conics in the 3D space.

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Authors and Affiliations

  1. Intel Labs, Guadalajara Design Center, Mexico, Mexico

    Julio Zamora-Esquivel

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  1. Julio Zamora-Esquivel
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Correspondence to Julio Zamora-Esquivel.

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Zamora-Esquivel, J. G 6,3 Geometric Algebra; Description and Implementation. Adv. Appl. Clifford Algebras 24, 493–514 (2014). https://doi.org/10.1007/s00006-014-0442-8

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  • DOI: https://doi.org/10.1007/s00006-014-0442-8

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