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2020 | OriginalPaper | Chapter

1. Geometric Algebra for Modeling in Robotic Physics

Author : Eduardo Bayro-Corrochano

Published in: Geometric Algebra Applications Vol. II

Publisher: Springer International Publishing

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Abstract

In this chapter, we will discuss the advantages for geometric computing that geometric algebra offers for solving problems and developing algorithms in the fields of artificial intelligence, robotics, and intelligent machines acting within the perception and action cycle. We begin with a short tour of the history of mathematics to find the roots of the fundamental concepts of geometry and algebra.

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Literature
1.
go back to reference Grassmann, H. (1877). Der Ort der Hamilton’schen Quaternionen in der Ausdehnungslehre. Mathematische Annalen, 12, 375.MathSciNetCrossRef Grassmann, H. (1877). Der Ort der Hamilton’schen Quaternionen in der Ausdehnungslehre. Mathematische Annalen, 12, 375.MathSciNetCrossRef
2.
go back to reference Clifford, W. K. (1878). Applications of Grassmann’s extensive algebra. American Journal of Mathematics, 1, 350–358.MathSciNetCrossRef Clifford, W. K. (1878). Applications of Grassmann’s extensive algebra. American Journal of Mathematics, 1, 350–358.MathSciNetCrossRef
3.
go back to reference Hestenes, D. (1966). Space-time algebra. London: Gordon and Breach.MATH Hestenes, D. (1966). Space-time algebra. London: Gordon and Breach.MATH
4.
go back to reference Hestenes, D., & Sobczyk, G. (1984). Clifford algebra to geometric calculus: A unified language for mathematics and physics. Dordrecht: D. Reidel.CrossRef Hestenes, D., & Sobczyk, G. (1984). Clifford algebra to geometric calculus: A unified language for mathematics and physics. Dordrecht: D. Reidel.CrossRef
5.
go back to reference Hestenes, D. (1986). New foundations for classical mechanics. Dordrecht: D. Reidel.CrossRef Hestenes, D. (1986). New foundations for classical mechanics. Dordrecht: D. Reidel.CrossRef
6.
go back to reference Hestenes, D., & Ziegler, R. (1991). Projective geometry with Clifford algebra. Acta Applicandae Mathematicae, 23, 25–63.MathSciNetCrossRef Hestenes, D., & Ziegler, R. (1991). Projective geometry with Clifford algebra. Acta Applicandae Mathematicae, 23, 25–63.MathSciNetCrossRef
7.
go back to reference Li, H., Hestenes, D., & Rockwood, A. (2001). Generalized homogeneous coordinates for computational geometry. In G. Sommer (Ed.), Geometric computing with Clifford algebra (pp. 27–59). New York: Springer-Verlag.CrossRef Li, H., Hestenes, D., & Rockwood, A. (2001). Generalized homogeneous coordinates for computational geometry. In G. Sommer (Ed.), Geometric computing with Clifford algebra (pp. 27–59). New York: Springer-Verlag.CrossRef
8.
go back to reference Hestenes, D. (2003). Orsted medal lecture 2002: Reforming the mathematical language of physics. American Journal of Physics, 71(2), 104–121.CrossRef Hestenes, D. (2003). Orsted medal lecture 2002: Reforming the mathematical language of physics. American Journal of Physics, 71(2), 104–121.CrossRef
9.
go back to reference Hartley, R. I., & Zissermann, A. (2003). Multiple view geometry in computer vision (2nd ed.). Cambridge: Cambridge University Press. Hartley, R. I., & Zissermann, A. (2003). Multiple view geometry in computer vision (2nd ed.). Cambridge: Cambridge University Press.
10.
go back to reference Bayro-Corrochano, E. (2018). Geometric algebra applications vol. I computer vision, graphics and neurocomputing. Springer Verlag. Bayro-Corrochano, E. (2018). Geometric algebra applications vol. I computer vision, graphics and neurocomputing. Springer Verlag.
11.
go back to reference Rivera-Rovelo, J., & Bayro-Corrochano, E. (2009). The use of geometric algebra for 3D modelling and registration of medical data. Journal of Mathematical Imaging and Vision, 34(1), 48–60.MathSciNetCrossRef Rivera-Rovelo, J., & Bayro-Corrochano, E. (2009). The use of geometric algebra for 3D modelling and registration of medical data. Journal of Mathematical Imaging and Vision, 34(1), 48–60.MathSciNetCrossRef
12.
go back to reference Fritzke, B. (1995). A growing neural gas network learns topologies. In Advances in neural information processing systems (Vol. 7, pp. 625–632). MIT Press, Cambridge, MA. Fritzke, B. (1995). A growing neural gas network learns topologies. In Advances in neural information processing systems (Vol. 7, pp. 625–632). MIT Press, Cambridge, MA.
Metadata
Title
Geometric Algebra for Modeling in Robotic Physics
Author
Eduardo Bayro-Corrochano
Copyright Year
2020
DOI
https://doi.org/10.1007/978-3-030-34978-3_1

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