Advances in Applied Clifford Algebras

, Volume 25, Issue 1, pp 113–149 | Cite as

R(4, 4) As a Computational Framework for 3-Dimensional Computer Graphics

  • Ron Goldman
  • Stephen Mann


We investigate the efficacy of the Clifford algebra R(4, 4) as a computational framework for contemporary 3-dimensional computer graphics. We give explicit rotors in R(4, 4) for all the standard affine and projective transformations in the graphics pipeline, including translation, rotation, reflection, uniform and nonuniform scaling, classical and scissor shear, orthogonal and perspective projection, and pseudoperspective. We also explain how to represent planes by vectors and quadric surfaces by bivectors in R(4, 4), and we show how to apply rotors in R(4, 4) to these vectors and bivectors to transform planes and quadric surfaces by affine transformations.


Clifford Algebra Homogeneous Model Perspective Projection Rotor Quadric surfaces computer graphics 


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© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceRice UniversityHoustonUSA
  2. 2.Cheriton School of Computer Science, uWaterlooWaterlooCanada

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