Programming Issues

  • Eduardo Bayro-CorrochanoEmail author


In this chapter, we will discuss the programming issues to compute in the geometric algebra framework. We will explain the technicalities for the programming which you have to take into account to generate a sound source code. At the end, we will discuss the use of specialized hardware as FPGA and Nvidia CUDA to improve the efficiency of the code processing for applications in real time.


  1. 1.
    Lounesto, P. (1997). Clifford algebras and spinors. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  2. 2.
    Dorst, L., Fontjine, D., & Mann, T. GAIGEN 2: Generates fast \(\text{C}{+}{+}\) or JAVA sources for low dimensional geometric algebra.
  3. 3.
    Perwass, C. B. U. (2006). CLUCal.
  4. 4.
    Ablamowicks, R. eCLIFFORD Software packet using Maple for Clifford algebra. Computations.
  5. 5.
    Ashdown, M. A. J. (1998). Maple code for geometric algebra.
  6. 6.
    Dorst, L., Mann, S., & Bouma, T. (1999). GABLE: A Matlab tutorial for geometric algebra.
  7. 7.
    Perwass, C., Gebken, C., & Sommer, G. (2003). Implementation of a Clifford algebra co-processor design on a field programmable gate array. In R. Ablamowicz, (Ed.), Clifford algebras: Application to mathematics, physics, and engineering. 6th International Conference on Clifford Algebras and Applications, Cookeville, TN (pp. 561–575). Progress in Mathematical Physics. Boston: Birkh\(\ddot{a}\)user.Google Scholar
  8. 8.
    Mishra, B., & Wilson, P. (2005). Hardware implementation of a geometric algebra processor core. In Proceedings of IMACS International Conference on Applications of Computer Algebra, Nara, Japan.
  9. 9.
    Gentile, A., Segreto, S., Sorbello, F., Vassallo, G., Vitabile, S., & Vullo, V. (2005). CliffoSor, an innovative FPGA-based architecture for geometric algebra. In Proceedings of 45th Congress of the European Regional Science Association (ERSA) (pp. 211–217), Vrije, Amsterdam, August 23–27.Google Scholar
  10. 10.
    Soria-García, G., Altamirano-Gómez, G., Ortega-Cisneros, S., & Bayro-Corrochano, E. (2017). FPGA implementation of a geometric voting scheme for the extraction of geometric entities from images. Advances in Applications of Clifford Algebras, 27, 685–705.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Bell, I. C++ MV 1.3.0 to 1.6 sources supporting \(N\le 63\).
  12. 12.
    Dorst, L., Fontjine, D., & Mann, S. (2007). Geometric algebra for computer science. An object-oriented approach to geometry. Morgan Kaufmann Series in Computer Science, Cambridge, MA.Google Scholar
  13. 13.
    Fontijne, D. (2007). Efficient implementation of geometric algebra. Ph.D. Thesis, University of Amsterdam.
  14. 14.
    Hildenbrand, D., Pitt, J., & Koch, A. (2009) High-performance geometric algebra computing using Gaalop. In E. Bayro-Corrochano, G. Sheuermann, (Eds.), Geometric algebra computing for engineering and computer science (pp. 477–494). London: Springer.Google Scholar
  15. 15.
    Hildenbrand, D., Pitt, J., & Koch, A. (2010). Gaalop high performance parallel computing based on conformal geometric algebra. In E. Bayro-Corrochano, G. Sheuermann, (Eds.), Geometric algebra computing for engineering and computer science (Chap. 22, pp. 477–494). Springer-Verlag.Google Scholar
  16. 16.
    Sommer, G., & Perwass, C. (2004). Implementation of a Clifford algebra co-processor design on a field-programmable gate array. In Clifford algebras: Applications to mathematics, physics, and engineering. Progress in Mathematical Physics.Google Scholar
  17. 17.
    Franchini, S., Gentile, A., Grimaudo, M., Hung, C., Impastato, S., Sorbello, F., Vassallo, G., & Vitabile, S. (2007). A sliced coprocessor for native Clifford algebra operations. In Proceedings of the 10th IEEE Euromicro Conference on Digital System Design–Architectures, Methods and Tools, DSD’07, Lübeck (pp. 436–439).Google Scholar
  18. 18.
    Soria-García, G., Altamirano-Gómez, A., Ortega-Cisneros, S., & Bayro-Corrochano, E. (2017). Conformal geometric algebra voting scheme implemented in reconfigurable devices for geometric entities extraction. IEEE Transactions on Industrial Electronics.Google Scholar
  19. 19.
    Bayro-Corrochano, E. (2018). Geometric algebra applications vol. I computer vision, graphics and neurocomputing. Springer-Verlag.Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Electrical Engineering and Computer Science DepartmentCINVESTAVGuadalajaraMexico

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