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

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, reflec...

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Bibliographic Details
Published inAdvances in applied Clifford algebras Vol. 25; no. 1; pp. 113 - 149
Main Authors Goldman, Ron, Mann, Stephen
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.03.2015
Subjects
Applications of Mathematics
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Theoretical
Perspective Projection
computer graphics
Clifford Algebra
Rotor
Quadric surfaces
Homogeneous Model
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Summary: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.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-014-0480-2