Abstract
Our research focuses on the problem of path planning in 3D virtual world applications. The characters we consider are heterogeneous, as they have different sizes, and can perform surface or volumetric motion. In this paper, we propose an enhanced waypoint graph, which consists of point nodes equipped with radius, as well as edges connecting those nodes. Each edge is labeled with the motion type it can support. Given a polygon soup representation of a virtual world, the proposed algorithm starts by subdividing the virtual world into regions. This enables us to process large virtual worlds. Each region is then locally voxelized, one at a time. Two kinds of waypoints are generated: local waypoints using corner detection on the voxelization, and border waypoints at the region boundary. Waypoints are then sparsely connected to form a local waypoint graph, and local graphs are finally connected via the border waypoints to create the final global enhanced waypoint graph. To plan paths between arbitrary points using this graph, the points are connected to the graph using nearest neighbor search and traversability test, then Dijkstra/A* algorithm is used to calculate the final path, taking into account the appropriate size and motion type.
Similar content being viewed by others
References
Amanatides, J., Woo, A.: A fast voxel traversal algorithm for ray tracing. In: Proceedings of Eurographics ’87, Amsterdam, Netherlands, pp. 3–10 (1987)
Botea, A., Müller, M., Schaeffer, J.: Near optimal hierarchical path-finding. J. Game Dev. 1(1), 7–28 (2004)
CGAL Open Source Project: Cgal—Computational Geometry Algorithms Library, version 4.1 (2012). http://www.cgal.org
Clarkson, K.L.: Approximation algorithms for shortest path motion planning. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, STOC ’87, pp. 56–65. ACM, New York (1987)
Coumans, E.: Optimizing proximity queries for CPU, SPU and GPU. In: SIGGRAPH 2010 Talks (2010). http://bullet.googlecode.com/files/SIGGRAPH_2010_Coumans_Erwin_OptimizingCD.pdf
Coumans, E.: Bullet Physics Library, version 2.81 (2012). http://bulletphysics.org/
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)
Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Booth, M., Rossi, F.: GNU Scientific Library Reference Manual, 3rd edn. Network Theory Ltd., London (2009)
Gärtner, B.: Fast and robust smallest enclosing balls. In: ESA ’99: Proceedings of the 7th Annual European Symposium on Algorithms, pp. 325–338 (1999)
Geraerts, R., Overmars, M.: The corridor map method: real-time high-quality path planning. In: Proceedings of 2007 IEEE International Conference on Robotics and Automation, Rome, Italy, pp. 1023–1028 (2007)
Harris, C., Stephens, M.: A combined corner and edge detector. In: Proceedings of the 4th Alvey Vision Conference, pp. 147–151 (1988)
Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)
Hjaltason, G., Samet, H.: Ranking in spatial databases. In: Egenhofer, M., Herring, J. (eds.) Advances in Spatial Databases. Lecture Notes in Computer Science, vol. 951, pp. 83–95. Springer, Berlin (1995)
Kavraki, L., Svestka, P., Latombe, J., Overmars, M.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Robot. Autom. 12(4), 566–580 (1994)
Keil, J.M.: Approximating the complete Euclidean graph. In: Proceedings of 1st Scandinavian Workshop on Algorithm Theory. Lecture Notes in Computer Science, vol. 318, pp. 208–213. Springer, London (1988)
Lozano-Pérez, T.: Spatial planning: a configuration space approach. IEEE Trans. Comput. C-32(2), 108–120 (1983)
Lozano-Pérez, T., Wesley, M.A.: An algorithm for planning collision-free paths among polyhedral obstacles. Commun. ACM 22(10), 560–570 (1979)
Pettré, J., Laummond, J.P., Thalmann, D.: A navigation graph for real-time crowd animation on multilayered and uneven terrain. In: First International Workshop on Crowd Simulation (V-CROWDS ’05), Lausanne, Switzerland, pp. 81–89 (2005)
Pinter, M.: In: Toward More Realistic Pathfinding (2001). http://www.gamasutra.com/features/20010314/pinter_02.htm
Siek, J., Lee, L.Q., Lumsdaine, A.: Boost Graph Library, version 1.52 (2012). http://www.boost.org/libs/graph/
Tozour, P.: Search space representations. In: AI Game Programming Wisdom 2, Chap. 2.1, pp. 113–128. Charles River Media, Newton Center (2004)
Žagar, M., Kovač, M., Knezović, J., Mlinarić, H., Hofman, D.: 3D object classification and segmentation methods. In: Mrak, M., Grgic, M., Kunt, M. (eds.) High-Quality Visual Experience, Signals and Communication Technology, pp. 331–347. Springer, Berlin (2010)
Wardhana, N.M., Johan, H., Seah, H.S.: Automatic generation of enhanced waypoint graph for volumetric path planning. In: Proceedings of the 2012 International Workshop on Advanced Image Technology (IWAIT 2012), pp. 450–455, Ho Chi Minh City, Vietnam (2012)
Wardhana, N.M., Johan, H., Seah, H.S.: Enhanced waypoint graph for path planning in virtual worlds. In: Proceedings of 2012 International Conference on Cyberworlds, Darmstadt, Germany, pp. 69–76 (2012)
Zhang, L., Chen, W., Ebert, D.S., Peng, Q.: Conservative voxelization. Vis. Comput. 23(9), 783–792 (2007)
Acknowledgements
Our sincere gratitude goes to Quah Chee Kwang, Anthony Chansavang, and Budianto Tandianus for the fruitful personal discussions. The small outdoor scene as well as the two-story house models were created by Max Lim Tze Yuen, whereas Kampong Glam were created by the Media Development Authority (MDA) Singapore. These models are used in this research with permissions. This research is supported in part by the Ministry of Education Singapore, Academic Research Fund (AcRF) Tier 1 for project “Volumetric Path Planning in Real-Time 3D Virtual Environments”.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wardhana, N.M., Johan, H. & Seah, H.S. Enhanced waypoint graph for surface and volumetric path planning in virtual worlds. Vis Comput 29, 1051–1062 (2013). https://doi.org/10.1007/s00371-013-0837-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-013-0837-x