Computational Visual Media

, Volume 1, Issue 2, pp 105–118 | Cite as

Subregion graph: A path planning acceleration structure for characters with various motion types in very large environments

  • Nicholas Mario WardhanaEmail author
  • Henry Johan
  • Hock Soon Seah
Open Access
Research Article


Modern computer graphics applications commonly feature very large virtual environments and diverse characters which perform different kinds of motions. To accelerate path planning in such a scenario, we propose the subregion graph data structure. It consists of subregions, which are clusters of locally connected waypoints inside a region, as well as subregion connectivities. We also present a fast algorithm to automatically generate a subregion graph from an enhanced waypoint graph map representation, which also supports various motion types and can be created from large virtual environments. Nevertheless, a subregion graph can be generated from any graphbased map representation. Our experiments show that a subregion graph is very compact relative to the input waypoint graph. By firstly planning a subregion path, and then limiting waypoint-level planning to this subregion path, over 8 times average speedup can be achieved, while average length ratios remain as low as 102.5%.


path planning acceleration very large environments motion types abstraction 

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  1. [1]
    Grand Theft Auto III (DVD). Rockstar Games, 2001.Google Scholar
  2. [2]
    Just Cause II(Steam). Eidos Interactive, 2010. Available at Scholar
  3. [3]
    The Elder Scrolls V: Skyrim (Steam). Bethesda Softworks, 2011. Available at Scholar
  4. [4]
    Plaku, E.; Kavraki, L. E. Distributed sampling-based roadmap of trees for large-scale motion planning. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 3868–3873, 2005.CrossRefGoogle Scholar
  5. [5]
    Samperi, K.; Hawes, N.; Beale, R. Improving map generation in large-scale environments for intelligent virtual agents. In: The AAMAS-2013 Workshop on Cognitive Agents for Virtual Environments, 2013. Available at Scholar
  6. [6]
    Wardhana, N. M.; Johan, H.; Seah, H. S. Enhanced waypoint graph for surface and volumetric path planning in virtual worlds. The Visual Computer Vol. 29, No. 10, 1051–1062, 2013.CrossRefGoogle Scholar
  7. [7]
    Hart, P. E.; Nilsson, N. J.; Raphael, B. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics Vol. 4, No. 2, 100–107, 1968.CrossRefGoogle Scholar
  8. [8]
    Holtë, R. C.; Mkadmi, T.; Zimmer, R. M.; MacDonald, A. J. Speeding up problem solving by abstraction: A graph oriented approach. Artificial Intelligence Vol. 85, Nos. 1–2, 321–361, 1996.CrossRefGoogle Scholar
  9. [9]
    Sturtevant, N.; Buro, M. Partial pathfinding using map abstraction and refinement. In: Proceedings of the 20th National Conference on Artificial Intelligence, Vol. 3, 1392–1397, 2005.Google Scholar
  10. [10]
    Bulitko, V.; Sturtevant, N.; Lu, J.; Yau, T. Graph abstraction in real-time heuristic search. Journal of Artificial Intelligence Research Vol. 30, No. 1, 51–100, 2007.zbMATHGoogle Scholar
  11. [11]
    Frederickson, G. N. Fast algorithms for shortest paths in planar graphs, with applications. SIAM Journal on Computing Vol. 6, No. 6, 1004–1022, 1987.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Köhler, E.; Möhring, R. H.; Schilling, H. Acceleration of shortest path and constrained shortest path computation. Lecture Notes in Computer Science Vol. 3503, 126–138, 2005.CrossRefGoogle Scholar
  13. [13]
    Wagner, D.; Willhalm, T. Geometric speedup techniques for finding shortest paths in large sparse graphs. Lecture Notes in Computer Science Vol. 2832, 776–787, 2003.CrossRefGoogle Scholar
  14. [14]
    Hilger, M.; Köhler, E.; Möhring, R. H.; Schilling, H. Fast point-to-point shortest path computations with arc-flags. In: The Shortest Path Problem: Ninth DIMACS Implementation Challenge. Demetrescu, C.; Goldberg, A. V.; Johnson, D. S. Eds. American Mathematical Society, 41–72, 2009.Google Scholar
  15. [15]
    Lauther, U. An extremely fast, exact algorithm for finding shortest paths in static networks with geographical background. In: Geoinformation und Mobilität–von der Forschung zur praktischen Anwendung, Vol. 22, 219–230, 2004.Google Scholar
  16. [16]
    Möhring, R. H.; Schilling, H.; Schütz, B.; Wagner, D.; Willhalm, T. Partitioning graphs to speed up Dijkstra’s algorithm. Lecture Notes in Computer Science Vol. 3503, 189–202, 2005.CrossRefGoogle Scholar
  17. [17]
    Harabor, D.; Botea, A. Hierarchical path planning for multi-size agents in heterogeneous environments. In: IEEE Symposium on Computational Intelligence and Games, 258–265, 2008.Google Scholar
  18. [18]
    Mould, D.; Horsch, M. C. A hierarchical terrain representation for approximately shortest paths. Lecture Notes in Computer Science Vol. 3157, 104–113, 2004.CrossRefGoogle Scholar
  19. [19]
    Gutman, R. J. Reach-based routing: A new approach to shortest path algorithms optimized for road networks. In: Proceedings of the 6th Workshop on Algorithm Engineering and Experiments and the First Workshop on Analytic Algorithmics and Combinatorics, 100–111, 2004.Google Scholar
  20. [20]
    Goldberg, A. V.; Kaplan, H.; Werneck, R. F. Reach for A*: Efficient point-to-point shortest path algorithms. In: Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments, 129–143, 2006.Google Scholar
  21. [21]
    Sanders, P.; Schultes, D. Highway hierarchies hasten exact shortest path queries. Lecture Notes in Computer Science Vol. 3669, 568–579, 2005.MathSciNetCrossRefGoogle Scholar
  22. [22]
    Floyd, R. W. Algorithm 97: Shortest path. Communications of the ACM Vol. 5, No. 6, 345, 1962.CrossRefGoogle Scholar
  23. [23]
    Warshall, S. A theorem on boolean matrices. Journal of the ACM Vol. 9, No. 1, 11–12, 1962.zbMATHMathSciNetCrossRefGoogle Scholar
  24. [24]
    Goldberg, A. V.; Harrelson, C. Computing the shortest path: A* search meets graph theory. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 156–165, 2005.Google Scholar
  25. [25]
    Felner, A.; Sturtevant, N.; Schaeffer, J. Abstractionbased heuristics with true distance computations. In: Proceedings of the Eighth Symposium on Abstraction, Reformulation, and Approximation, 74–81, 2009.Google Scholar
  26. [26]
    Oliva, R.; Pelechano, N. NEOGEN: Near optimal generator of navigation meshes for 3D multi-layered environments. Computers & Graphics Vol. 37, No. 5, 403–412, 2013.CrossRefGoogle Scholar
  27. [27]
    Van Toll, W. G.; Cook IV, A. F.; Geraerts, R. Navigation meshes for realistic multi-layered environments. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, 3526–3532, 2011.Google Scholar
  28. [28]
    Dijkstra, E. W. A note on two problems in connexion with graphs. Numerische Mathematik Vol. 1, No. 1, 269–271, 1959.zbMATHMathSciNetCrossRefGoogle Scholar
  29. [29]
    Pinter, M. Toward more realistic pathfinding. 2001. Available at Scholar
  30. [30]
    Siek, J.; Lee, L.-Q.; Lumsdaine, A. The Boost Graph Library (BGL) (version 1.57). 2014. Available at Scholar
  31. [31]
    The OGRE Team. OGRE—Object-oriented Graphics Rendering Engine (version 1.7.3). 2011. Available at Scholar
  32. [32]
    Wagner, D.; Willhalm, T. Speed-up techniques for shortest-path computations. Lecture Notes in Computer Science Vol. 4393, 23–36, 2007.MathSciNetCrossRefGoogle Scholar
  33. [33]
    Garcia, F. M.; Kapadia, M.; Badler, N. I. GPU-based dynamic search on adaptive resolution grids. In: 2014 IEEE International Conference on Robotics and Automation, 1631–1638, 2014.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Nicholas Mario Wardhana
    • 1
    • 2
    Email author
  • Henry Johan
    • 3
  • Hock Soon Seah
    • 1
    • 2
  1. 1.Multi-plAtform Game Innovation Centre (MAGIC)Nanyang Technological University, XFrontiers BlockSingaporeSingapore
  2. 2.School of Computer EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.Fraunhofer IDM@NTUNanyang Technological UniversitySingaporeSingapore

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