Bulletin of the Belgian Mathematical Society - Simon Stevin

Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity}

Eckhard M.S. Hitzer

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Abstract

This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and (useful) parametrizations of the 3D Euclidean object models are explicitly demonstrated in order to show how 3D Euclidean information on positions, orientations and radii can be extracted.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 11, Number 5 (2005), 653-662.

Dates
First available in Project Euclid: 7 March 2005

Permanent link to this document
http://projecteuclid.org/euclid.bbms/1110205625

Mathematical Reviews number (MathSciNet)
MR2130631

Zentralblatt MATH identifier
1083.15045

Subjects
Primary: 15A66: Clifford algebras, spinors 51M15: Geometric constructions 51M25: Length, area and volume [See also 26B15]

Keywords
Clifford algebra geometric algebra Horosphere position orientation radius 3D Euclidean object modeling

Citation

Hitzer, Eckhard M.S. Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity}. Bull. Belg. Math. Soc. Simon Stevin 11 (2005), no. 5, 653--662. http://projecteuclid.org/euclid.bbms/1110205625.


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