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Geometric Algebra Computing pp 3–33Cite as

New Tools for Computational Geometry and Rejuvenation of Screw Theory

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Abstract

Conformal Geometric Algebraic (CGA) provides ideal mathematical tools for construction, analysis, and integration of classical Euclidean, Inversive & Projective Geometries, with practical applications to computer science, engineering, and physics. This paper is a comprehensive introduction to a CGA tool kit. Synthetic statements in classical geometry translate directly to coordinate-free algebraic forms. Invariant and covariant methods are coordinated by conformal splits, which are readily related to the literature using methods of matrix algebra, biquaternions, and screw theory. Designs for a complete system of powerful tools for the mechanics of linked rigid bodies are presented.

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References

  1. Hestenes, D.: Old Wine in New Bottles: A new algebraic framework for computational geometry. In: Bayro-Corrochano, E., Sobczyk, G. (eds.) Advances in Geometric Algebra with Applications in Science and Engineering, pp. 1–14. Birkhäuser, Basel (2001)

    Google Scholar 

  2. Hestenes, D., Fasse, E.: Homogeneous rigid body mechanics with elastic coupling. In: Dorst, L., Doran, C., Lasenby, J. (eds.) Applications of Geometric Algebra in Computer Science and Engineering, pp. 197–212. Birkhäuser, Basel (2002)

    Google Scholar 

  3. Hestenes, D.: A unified language for mathematics and physics. In: Chisholm, J.S.R., Common, A.K. (eds.) Clifford Algebras and their Applications in Mathematica Physics, pp. 1–23. Reidel, Dordrecht (1986)

    Google Scholar 

  4. Hestenes, D.: Space-Time Algebra. Gordon & Breach, New York (1966)

    MATH  Google Scholar 

  5. Hestenes, D., Sobczyk, G.: Clifford algebra to geometric calculus, a unified language for mathematics and physics. Kluwer, Dordrecht (1984). Paperback (1985). Fourth printing 1999

    MATH  Google Scholar 

  6. Doran, C., Lasenby, A.: Geometric Algebra for Physicists. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  7. Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science. Morgan Kaufmann Publ., Elsevier, San Mateo, Amsterdam (2007/2009)

    Google Scholar 

  8. Li, H.: Invariant Algebras and Geometric Reasoning. World Scientific, Singapore (2008)

    Book  MATH  Google Scholar 

  9. Hestenes, D.: Grassmann’s vision. In: Schubring, G. (ed.) Hermann Günther Grassmann (1809–1877)—Visionary Scientist and Neohumanist Scholar, pp. 191–201. Kluwer, Dordrecht (1996)

    Google Scholar 

  10. Clifford, W.K.: Mathematical Papers. Macmillan, London (1882). Ed. by R. Tucker. Reprinted by Chelsea, New York (1968)

    Google Scholar 

  11. Doran, C., Hestenes, D., Sommen, F., Van Acker, N.: Lie groups as spin groups. J. Math. Phys. 34, 3642–3669 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. Lasenby, A.: Recent applications of conformal geometric algebra. In: Li, H., et al. (ed.) Computer Algebra and Geometric Algebra with Applications. LNCS, vol. 3519, pp. 298–328. Springer, Berlin (2005)

    Google Scholar 

  13. Hestenes, D.: The design of linear algebra and geometry. Acta Appl. Math. 23, 65–93 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  14. Onishchik, A., Sulanke, R.: Projective and Cayley–Klein Geometries. Springer, Berlin (2006)

    MATH  Google Scholar 

  15. Hestenes, D.: New Foundations for Classical Mechanics. Kluwer, Dordrecht (1986). Paperback (1987). Second edition (1999)

    MATH  Google Scholar 

  16. Selig, J.: Geometrical Methods in Robotics. Springer, Berlin (1996)

    MATH  Google Scholar 

  17. Ball, R.S.: A Treatise on the Theory of Screws. Cambridge University Press, Cambridge (1900). Reprinted in paperback (1998)

    Google Scholar 

  18. Davidson, J., Hunt, K.: Robots and Screw Theory: Applications of Kinematics and Statics to Robotics. Oxford University Press, London (2004)

    MATH  Google Scholar 

  19. Featherstone, R., Orin, D.: Dynamics. In: Siciliano, B., Khatib, O. (eds.) Springer Handbook of Robotics, pp. 35–65. Springer, Berlin (2008)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Arizona State University, Tempe, AZ, 85287, USA

    David Hestenes

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  1. David Hestenes
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Correspondence to David Hestenes .

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Editors and Affiliations

  1. , CINVESTAV, Unidad Guadalajara, Av. Científica 1145, Colonia el Bajío, Zapopan, 45015, Mexico

    Eduardo Bayro-Corrochano

  2. Inst. Informatik, Universität Leipzig, Leipzig, Germany

    Gerik Scheuermann

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Hestenes, D. (2010). New Tools for Computational Geometry and Rejuvenation of Screw Theory. In: Bayro-Corrochano, E., Scheuermann, G. (eds) Geometric Algebra Computing. Springer, London. https://doi.org/10.1007/978-1-84996-108-0_1

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  • DOI: https://doi.org/10.1007/978-1-84996-108-0_1

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  • Print ISBN: 978-1-84996-107-3

  • Online ISBN: 978-1-84996-108-0

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