Abstract
We flesh out the affine geometry of \({{\mathbb {R}}^3}\) represented inside the Clifford algebra \({\mathbb {R}}(4,4)\). 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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Communicated by Leo Dorst
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Du, J., Goldman, R. & Mann, S. Modeling 3D Geometry in the Clifford Algebra R(4, 4). Adv. Appl. Clifford Algebras 27, 3039–3062 (2017). https://doi.org/10.1007/s00006-017-0798-7
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DOI: https://doi.org/10.1007/s00006-017-0798-7