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Published in:
Geometric Algebra for Modeling in Robotic Physics Read chapter Read first chapter

2020 | OriginalPaper | Chapter

5. Kinematics of the 2D and 3D Spaces

Author : Eduardo Bayro-Corrochano

Published in: Geometric Algebra Applications Vol. II

Publisher: Springer International Publishing

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Abstract

This chapter presents the geometric algebra framework for dealing with 3D kinematics. The reader will see the usefulness of this mathematical approach for applications in computer vision and kinematics. We start with an introduction to 4D geometric algebra for 3D kinematics. Then we reformulate, using 3D and 4D geometric algebras, the classic model for the 3D motion of vectors. Finally, we compare both models, that is, the one using 3D Euclidean geometric algebra and our model, which uses 4D motor algebra.

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previous chapter 2D, 3D, and 4D Geometric Algebras
next chapter Conformal Geometric Algebra
Literature
1.
Bayro-Corrochano, E., Daniilidis, K., & Sommer, G. (1997). Hand-eye calibration in terms of motions of lines using geometric algebra. In 10th Scandinavian Conference on Image Analysis (Vol. I, pp. 397–404). Finland: Lappeenranta.
2.
Doran, C. (1994). Geometric algebra and its applications to mathematical physics. Ph.D. thesis, University of Cambridge.
3.
Hestenes, D., & Sobczyk, G. (1984). Clifford algebra to geometric calculus: A unified language for mathematics and physics. Dordrecht: D. Reidel.CrossRef
4.
Blaschke, W. (1960). Kinematik und Quaternionen. Berlin: VEB Deutscher Verlag der Wissenschaften.
5.
Selig, J. M. (1999). Clifford algebra of points, lines and planes. Technical report SBU-CISM-99-06, South Bank University, School of Computing, Information Technology and Maths.
6.
Lounesto, P. (1987). CLICAL software packet and user manual. Helsinki University of Technology of Mathematics, Research report A248.
7.
8.
Doran, C., & Lasenby, A. (2005). Geometric algebra for physicists. Cambridge University Press.
Metadata
Title
Kinematics of the 2D and 3D Spaces
Author
Eduardo Bayro-Corrochano
Copyright Year
2020
Book
Geometric Algebra Applications Vol. II

Print ISBN: 978-3-030-34976-9

Electronic ISBN: 978-3-030-34978-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-34978-3_5

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