Advertisement

Gaalop—High Performance Parallel Computing Based on Conformal Geometric Algebra

  • Dietmar HildenbrandEmail author
  • Joachim Pitt
  • Andreas Koch
Chapter

Abstract

We present Gaalop (Geometric algebra algorithms optimizer), our tool for high-performance computing based on conformal geometric algebra. The main goal of Gaalop is to realize implementations that are most likely faster than conventional solutions. In order to achieve this goal, our focus is on parallel target platforms like FPGA (field-programmable gate arrays) or the CUDA technology from NVIDIA. We describe the concepts, current status, and future perspectives of Gaalop dealing with optimized software implementations, hardware implementations, and mixed solutions. An inverse kinematics algorithm of a humanoid robot is described as an example.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abłamowicz, R., Fauser, B.: Clifford/bigebra, a Maple package for Clifford (co)algebra computations (2009). ©1996–2009, RA&BF Google Scholar
  2. 2.
    Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science, An Object-Oriented Approach to Geometry. Morgan Kaufman, San Mateo (2007) Google Scholar
  3. 3.
    Fontijne, D.: Efficient implementation of geometric algebra. Ph.D. thesis, University of Amsterdam (2007) Google Scholar
  4. 4.
    Franchini, S., Gentile, A., Grimaudo, M., Hung, C.A., Impastato, S., Sorbello, F., Vassallo, G., Vitabile, S.: A sliced coprocessor for native Clifford algebra operations. In: Euromico Conference on Digital System Design, Architectures, Methods and Tools (DSD) (2007) Google Scholar
  5. 5.
    Gentile, A., Segreto, S., Sorbello, F., Vassallo, G., Vitabile, S., Vullo, V.: Cliffosor, an innovative FPGA-based architecture for geometric algebra. In: ERSA 2005, pp. 211–217 (2005) Google Scholar
  6. 6.
    Hildenbrand, D.: Geometric computing in computer graphics using conformal geometric algebra. Comput. Graph. 29(5), 802–810 (2005) CrossRefGoogle Scholar
  7. 7.
    Hildenbrand, D., Pitt, J.: The Gaalop homepage. Available at http://www.gaalop.de (2010)
  8. 8.
    Hildenbrand, D., Fontijne, D., Perwass, C., Dorst, L.: Tutorial geometric algebra and its application to computer graphics. In: Eurographics Conference Grenoble (2004) Google Scholar
  9. 9.
    Hildenbrand, D., Fontijne, D., Wang, Y., Alexa, M., Dorst, L.: Competitive runtime performance for inverse kinematics algorithms using Conformal geometric algebra. In: Eurographics Conference Vienna (2006) Google Scholar
  10. 10.
    Hildenbrand, D., Lange, H., Stock, F., Koch, A.: Efficient inverse kinematics algorithm based on conformal geometric algebra using reconfigurable hardware. In: GRAPP Conference Madeira (2008) Google Scholar
  11. 11.
    Kasprzyk, N., Koch, A.: High-level-language compilation for reconfigurable computers. In: Proceedings International Conference on Reconfigurable Communication-centric SoCs (ReCoSoC) (2005) Google Scholar
  12. 12.
    Mishra, B., Wilson, P.R.: Color edge detection hardware based on geometric algebra. In: European Conference on Visual Media Production (CVMP) (2006) Google Scholar
  13. 13.
    Mishra, B. Wilson, P.R.: VLSI implementation of a geometric algebra parallel processing core. Technical report, Electronic Systems Design Group, University of Southampton, UK (2006) Google Scholar
  14. 14.
    NVIDIA. The CUDA homepage. Available at http://www.nvidia.com/object/cuda_home.html (2009)
  15. 15.
    Perwass, C.: The CLU homepage. Available at http://www.clucalc.info (2010)
  16. 16.
    Perwass, C., Gebken, C., Sommer, G.: Implementation of a Clifford algebra co-processor design on a field programmable gate array. In: Ablamowicz, R. (ed.) CLIFFORD ALGEBRAS: Application to Mathematics, Physics, and Engineering. Progress in Mathematical Physics, pp. 561–575. Birkhäuser, Basel (2003). 6th Int. Conf. on Clifford Algebras and Applications, Cookeville, TN Google Scholar
  17. 17.
    The RoboCup Federation. Robocup official site. Available at http://www.robocup.org

Copyright information

© Springer-Verlag London 2010

Authors and Affiliations

  • Dietmar Hildenbrand
    • 1
    Email author
  • Joachim Pitt
    • 1
  • Andreas Koch
    • 2
  1. 1.Interactive Graphics Systems GroupUniversity of Technology DarmstadtDarmstadtGermany
  2. 2.Embedded Systems and Applications GroupUniversity of Technology DarmstadtDarmstadtGermany

Personalised recommendations