Skip to main content
SpringerLink
Log in

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

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Bayro-Corrochano, Motor algebra approach for visually guided robotics. Pattern Recognition, 35 (1), (2002).

  2. L. Dorst, D. Fontijne and S. Mann, Geometric Algebra for Computer Science. Morgan-Kaufmann, 2007.

  3. J. Foley, A. van Dam, S. Feiner and J. Hughes, Computer Graphics: Principles and Practice. Second Edition, Addison Wesley, 1990.

  4. D. Fontijne and L. Dorst, GAviewer, interactive visualization software for geometric algebra, 2002-2010. Downloadable at www.geometricalgebra.net/downloads.

  5. R. Goldman, Understanding Quaternions. In: GraphicalModels, Vol. 73 (2011), pp. 21-49.

  6. R. Goldman, A homogeneous model for 3-dimensional computer graphics based on Clifford algebra for R 3In L. Dorst and J. Lasenby, editors, Guide to Geometric Algebra in Practice, pages 329–352. Springer-Verlag, 2011.

  7. R. Goldman, Modeling Perspective Projections in 3-Dimensions by Rotations in 4-Dimensions, In: Graphical Models, Vol. 75 (2013) pp. 41–55.

  8. R. Goldman and S. Mann, Using R(4, 4) As a Model for Computer Graphics. In preparation.

  9. C. Gunn, On the homogeneous model of Euclidean geometry. In L. Dorst and J. Lasenby, editors, Guide to Geometric Algebra in Practice, pages 297–328. Springer, 2011.

  10. Perwass C.: Geometric Algebra with Applications in Engineering. Springer- Verlag, Berlin (2009)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Rice University, 6100 Main Street, Houston, Texas, 77005, USA

    Ron Goldman

  2. Cheriton School of Computer Science, University of Waterloo, 200 University Ave W, Waterloo, ON, N2L 3G1, Canada

    Stephen Mann

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China

    Xiaohong Jia

Authors
  1. Ron Goldman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephen Mann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaohong Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stephen Mann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-014-0439-3

Keywords

Search

Navigation