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Advances in Applied Clifford Algebras

, Volume 27, Issue 4, pp 3039–3062 | Cite as

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

  • Juan Du
  • Ron Goldman
  • Stephen Mann
Article

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.

Keywords

Mother algebra Affine geometry Computer graphics 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.College of Mechanical and Electrical EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Department of Computer ScienceRice UniversityHoustonUSA
  3. 3.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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