ANALYSIS OF POINT CLOUDS - Using Conformal Geometric Algebra

Dietmar Hildenbrand, Eckhard Hitzer

Abstract

This paper presents some basics for the analysis of point clouds using the geometrically intuitive mathematical framework of conformal geometric algebra. In this framework it is easy to compute with osculating circles for the description of local curvature. Also methods for the fitting of spheres as well as bounding spheres are presented. In a nutshell, this paper provides a starting point for shape analysis based on this new, geometrically intuitive and promising technology.

References

  1. Adamson, A. (2007). Computing Curves and Surfaces from Points. PhD thesis, Darmstadt University of Technology.
  2. Doran, C. and Lasenby, A. (2003). Geometric Algebra for Physicists. Cambridge University Press.
  3. Dorst, L. and Mann, S. (2002). Geometric algebra: a computational framework for geometrical applications (part i: algebra). Computer Graphics and Application, 22(3):24-31.
  4. Fontijne, D. and Dorst, L. (2003). Modeling 3D euclidean geometry. IEEE Computer Graphics and Applications, 23(2):68-78.
  5. Hildenbrand, D. (2005). Geometric computing in computer graphics using conformal geometric algebra. Computers & Graphics, 29(5):802-810.
  6. Hildenbrand, D., Fontijne, D., Perwass, C., and Dorst, L. (2004). Tutorial geometric algebra and its application to computer graphics. In Eurographics conference Grenoble.
  7. Hildenbrand, D., Fontijne, D., Wang, Y., Alexa, M., and Dorst, L. (2006). Competitive runtime performance for inverse kinematics algorithms using conformal geometric algebra. In Eurographics conference Vienna.
  8. L.Dorst, Fontijne, D., Mann, S., and Kaufman, M. (2007). Geometric Algebra for Computer Science, An ObjectOriented Approach to Geometry. Morgan Kaufman.
  9. Mann, S. and Dorst, L. (2002). Geometric algebra: a computational framework for geometrical applications (part ii: applications). Computer Graphics and Application, 22(4):58-67.
  10. Rosenhahn, B. (2003). Pose Estimation Revisited. PhD thesis, Inst. f. Informatik u. Prakt. Mathematik der Christian-Albrechts-Universit├Ąt zu Kiel.
  11. Schnabel, R., Wahl, R., and Klein, R. (2007). Efficient ransac for point-cloud shape detection. Computer Graphics Forum, 26(2):214-226.
  12. Welzl, E. (1991). Smallest enclosing disks (balls and ellipsoids. In Lecture Notes in Computer Science, pages 555:359-370.
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Paper Citation


in Harvard Style

Hildenbrand D. and Hitzer E. (2008). ANALYSIS OF POINT CLOUDS - Using Conformal Geometric Algebra . In Proceedings of the Third International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2008) ISBN 978-989-8111-20-3, pages 99-106. DOI: 10.5220/0001094100990106


in Bibtex Style

@conference{grapp08,
author={Dietmar Hildenbrand and Eckhard Hitzer},
title={ANALYSIS OF POINT CLOUDS - Using Conformal Geometric Algebra},
booktitle={Proceedings of the Third International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2008)},
year={2008},
pages={99-106},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001094100990106},
isbn={978-989-8111-20-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2008)
TI - ANALYSIS OF POINT CLOUDS - Using Conformal Geometric Algebra
SN - 978-989-8111-20-3
AU - Hildenbrand D.
AU - Hitzer E.
PY - 2008
SP - 99
EP - 106
DO - 10.5220/0001094100990106