Numerical Solution of BVP on GPU with Application to Path Planning

  • Lumír JanošekEmail author
  • Martin Němec
  • Radoslav Fasuga


The problem of path planning in a virtual environment is a widely researched area, which finds application in fields such as robotics, simulations, and computer games. This article focuses on a comparison of numerical methods for solving partial differential equations with BVP on the GPU with NVIDIA CUDA, used in the path planning of virtual characters using the potential fields. The most commonly used methods for computing the potential fields on the GPU are compared in this article in terms of time consumption.


Path-planning Agent Iteration methods Potential fields 



This work was partially supported by the SGS in VSB Technical University of Ostrava, Czech Republic, under the grant No. SP2013/185.


  1. 1.
    Kirk, D.B., Hwu, W.-W.: Programming Massively Parallel Processors: A Hands-on Approach, 1st edn. Morgan Kaufmann Publishers Inc, San Francisco, CA (2010)Google Scholar
  2. 2.
    Cui, X, Shi, H.: A*-based pathfinding in modern computer games. IJCNIS 11(1), 125–130 (2011)Google Scholar
  3. 3.
    Silveira, R., Fischer, L., Jos’ e AntônioSalini F., Prestes, E., Nedel, L.: Path-planning for RTS games based on potential fields. In: Proceedings of the Third international conference on Motion in games, MIG’10, pp. 410–421. Springer, Heidelberg (2010)Google Scholar
  4. 4.
    Fischer, L., Fischer L.: Semi-automatic navigation on 3d triangle meshes using bvp based path-planning. In: 24th SIBGRAPI Conference on Graphics, Patterns and Images (Sibgrapi), pp. 33–40, (2011)Google Scholar
  5. 5.
    Marcelo, T., Idiart, M.A., Edson, P., Engel, P.M.: Exploratory navigation based on dynamical boundary value problems. J. Intell. Robotics Syst. 45(2), 101–114 (2006)CrossRefGoogle Scholar
  6. 6.
    Fischer, L.G., Silveira, R., Nedel, L.: Gpu accelerated path-planning for multi-agents in virtual environments. In: VIII Brazilian Symposium on Games and Digital Entertainment (SBGAMES), pp. 101–110, (2009)Google Scholar
  7. 7.
    Connolly, C.I., Grupen, R.A.: On the applications of harmonic functions to robotics. J. Robot. Syst. 10, 931–946 (1993)CrossRefzbMATHGoogle Scholar
  8. 8.
    Strauss, W.A.: Partial Differential Equations: An Introduction. Wiley, New York, NY (1992)zbMATHGoogle Scholar
  9. 9.
    Dapper, F., Prestes, E., Idiart, M.A.P., Nedel, L.P.: Simulating pedestrian behavior with potential fields. In: Proceedings of the 24th international conference on Advances in Computer Graphics, CGI’06, pp. 324–335. Springer, Heidelberg (2006)Google Scholar
  10. 10.
    Klaus, A.: Hoffmann and Steve T Chiang. Computational fluid dynamics vol.i - hoffmann.pdf. Int. J. Comut. Fluid. Dyn. 126(2), 581–594 (2000)MathSciNetGoogle Scholar
  11. 11.
    Zhu, J.: Solving Partial Differential Equations on Parallel Computers. World Scientific Publishing Co. Inc., River Edge, NJ (1994)CrossRefzbMATHGoogle Scholar
  12. 12.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes 3rd Edition: The Art of Scientific Computing, 3rd edn. Cambridge University Press, New York, NY (2007)Google Scholar
  13. 13.
    Gomes, G.A.A.: Linear solvers for stable fluids: GPU vs CPU. In: 17th EncontroPortugues de ComputacaoGrafica (EPCG09), pp. 145–153 (2009)Google Scholar
  14. 14.
    Dapper, F., Prestes, E., Nedel, L.P.: Generating Steering Behaviors for Virtual Humanoids Using BVP Control. In: Proc. of CGI, pp. 105–114 (2007)Google Scholar
  15. 15.
    Konstantinidis, E., Cotronis, Y.: Graphics processing unit acceleration of the red/black SOR method. Concurr Comput. 25(8), 1107–1120, (2012)Google Scholar
  16. 16.
    NVIDIA. CUDA C BEST Practices Guide (2012)Google Scholar
  17. 17.
    Fischer, L.G., Silveira, R., Nedel, L.: Gpu accelerated path-planning for multi-agents in virtual environments. In: VIII Brazilian Symposium on Games and Digital Entertainment (SBGAMES), pp. 101–110, (2009)Google Scholar
  18. 18.
    Silveira, R., e Silva, E.P., Jr., PorcherNedel, L.: Fast path planning using multi-resolution boundary value problems. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, 18–22 October 2010, Taipei, Taiwan, pp. 4710–4715. IEEE (2010)Google Scholar
  19. 19.
    Renato, S., Fbio, D., Edson, P., Luciana, N.: Natural steering behaviors for virtual pedestrians. Vis. Comput. 26(9), 1183–1199 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2015

Authors and Affiliations

  • Lumír Janošek
    • 1
    Email author
  • Martin Němec
    • 1
  • Radoslav Fasuga
    • 1
  1. 1.Department of Computer ScienceVŠB-Technical UniversityOstravaCzech Republic

Personalised recommendations