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Computing Perspective Projections in 3-Dimensions Using Rotors in the Homogeneous and Conformal Models of Clifford Algebra

Abstract

We show how to compute perspective projections in 3-dimensions using rotations and spherical inversions in the homogeneous and conformal models of Clifford Algebra. One achievement of our paper is to show that although perspective is a purely projective operation, while a Clifford algebra by its very definition is a metric tool, nevertheless and surely somewhat surprisingly we show that perspective projection can also be modeled by rotors in the homogeneous and conformal models of Clifford Algebra.

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Correspondence to Stephen Mann.

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Goldman, R., Mann, S. & Jia, X. Computing Perspective Projections in 3-Dimensions Using Rotors in the Homogeneous and Conformal Models of Clifford Algebra. Adv. Appl. Clifford Algebras 24, 465–491 (2014). https://doi.org/10.1007/s00006-014-0439-3

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Keywords

  • Clifford Algebra
  • Conformal Model
  • Homogeneous Model
  • Perspective Projection
  • Rotor
  • Sandwiching
  • Versor