# Modeling 3D Geometry in the Clifford Algebra R(4, 4)

@article{Du2017Modeling3G,
title={Modeling 3D Geometry in the Clifford Algebra R(4, 4)},
author={Juan Du and Ron Goldman and Stephen Mann},
year={2017},
volume={27},
pages={3039-3062}
}
• Published 20 July 2017
• Mathematics
• Advances in Applied Clifford Algebras
We flesh out the affine geometry of $${{\mathbb {R}}^3}$$R3 represented inside the Clifford algebra $${\mathbb {R}}(4,4)$$R(4,4). We show how lines and planes as well as conic sections and quadric surfaces are represented in this model. We also investigate duality between different representations of points, lines, and planes, and we show how to represent intersections between these geometric elements. Formulas for lengths, areas, and volumes are also provided.

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