Abstract
Navigation meshes are commonly employed as a practical representation for path planning and other navigation queries in animated virtual environments and computer games. This paper explores the use of triangulations as a navigation mesh, and discusses several useful triangulation–based algorithms and operations: environment modeling and validity, automatic agent placement, tracking moving obstacles, ray–obstacle intersection queries, path planning with arbitrary clearance, determination of corridors, etc. While several of the addressed queries and operations can be applied to generic triangular meshes, the efficient computation of paths with arbitrary clearance requires a new type of triangular mesh, called a Local Clearance Triangulation, which enables the efficient and correct determination if a disc of arbitrary size can pass through any narrow passages of the mesh. This paper shows that triangular meshes can support the efficient computation of several navigation procedures and an implementation of the presented methods is available.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albers, G., Mitchell, J.S., Guibas, L.J., Roos, T.: Voronoi diagrams of moving points. Internat. J. Comput. Geom. Appl. 8, 365–380 (1992)
Berg, J., Lin, M., Manocha, D.: Reciprocal velocity obstacles for real-time multi-agent navigation. In: Proceedings of the International Conference on Robotics and Automation, ICRA 2008 (2008)
De Berg, M., Cheong, O., van Kreveld, M.: Computational geometry: algorithms and applications. Springer, Heidelberg (2008)
Demyen, D., Buro, M.: Efficient triangulation-based pathfinding. In: Proceedings of the 21st National Conference on Artificial Intelligence, AAAI 2006, pp. 942–947. AAAI Press, Menlo Park (2006)
Fiorini, L.P., Shiller, Z.: Motion planning in dynamic environments using velocity obstacles. International Journal of Robotics Research 17(7), 760–772 (1998)
Gayle, R., Sud, A., Andersen, E., Guy, S.J., Lin, M.C., Manocha, D.: Interactive navigation of heterogeneous agents using adaptive roadmaps. IEEE Transactions on Visualization and Computer Graphics 15, 34–48 (2009)
Geraerts, R.: Planning short paths with clearance using explicit corridors. In: Proceedings of the IEEE International Conference on Robotics and Automation, ICRA 2010 (2010)
Geraerts, R., Overmars, M.H.: The corridor map method: a general framework for real-time high-quality path planning: Research articles. Computer Animation and Virtual Worlds 18(2), 107–119 (2007)
Guibas, L., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of voronoi. ACM Trans. Graph. 4(2), 74–123 (1985)
Hershberger, J., Snoeyink, J.: Computing minimum length paths of a given homotopy class. Computational Geometry Theory and Application 4(2), 63–97 (1994)
Hershberger, J., Suri, S.: An optimal algorithm for euclidean shortest paths in the plane. SIAM Journal on Computing 28, 2215–2256 (1997)
Hoff III, K.E., Culver, T., Keyser, J., Lin, M., Manocha, D.: Fast computation of generalized voronoi diagrams using graphics hardware. In: Proceedings of the Sixteenth Annual Symposium on Computational Geometry (2000)
Kallmann, M.: Shortest paths with arbitrary clearance from navigation meshes. In: Proceedings of the Eurographics / SIGGRAPH Symposium on Computer Animation, SCA (2010)
Kallmann, M., Bieri, H., Thalmann, D.: Fully dynamic constrained delaunay triangulations. In: Brunnett, G., Hamann, B., Mueller, H., Linsen, L. (eds.) Geometric Modeling for Scientific Visualization, pp. 241–257. Springer, Heidelberg (2003) ISBN 3-540-40116-4
Kallmann, M., Thalmann, D.: Star vertices: A compact representation for planar meshes with adjacency information. Journal of Graphics Tools 6(1), 7–18 (2001)
Lamarche, F.: TopoPlan: a topological path planner for real time human navigation under floor and ceiling constraints. Computer Graphics Forum 28 (03 2009)
Lozano-Pérez, T., Wesley, M.A.: An algorithm for planning collision-free paths among polyhedral obstacles. Communications of ACM 22(10), 560–570 (1979)
Mäntylä, M.: An introduction to solid modeling. Computer Science Press, Inc., New York (1987)
Mekni, M.: Hierarchical path planning for situated agents in informed virtual geographic environments. In: Proceedings of the 3rd International ICST Conference on Simulation Tools and Techniques, SIMUTools 2010, pp. 1–10 (2010)
Mitchell, J.S.B.: Shortest paths among obstacles in the plane. In: Proceedings of the Ninth Annual Symposium on Computational Geometry, SCG 1993, pp. 308–317. ACM, New York (1993)
Overmars, M.H., Welzl, E.: New methods for computing visibility graphs. In: Proceedings of the fourth Annual Symposium on Computational Geometry, SCG 1988, pp. 164–171. ACM Press, New York (1988)
Rong, G., Tan, T.-s., Cao, T.-t.: Computing two-dimensional delaunay triangulation using graphics hardware. In: Proceedings of the Symposium on Interactive 3D Graphics and Games, I3D (2008)
Shewchuk, J.R.: Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In: Lin, M.C., Manocha, D. (eds.) FCRC 1996 and WACG 1996. LNCS, vol. 1148, pp. 203–222. Springer, Heidelberg (1996); from the First ACM Workshop on Applied Computational Geometry
Storer, J.A., Reif, J.H.: Shortest paths in the plane with polygonal obstacles. J. ACM 41(5), 982–1012 (1994)
Subramanian, S., Klein, P., Klein, P., Rao, S., Rao, S., Rauch, M., Rauch, M.: Faster shortest-path algorithms for planar graphs. Journal of Computer and System Sciences, 27–37 (1994)
Sud, A., Andersen, E., Curtis, S., Lin, M.C., Manocha, D.: Real-time path planning in dynamic virtual environments using multiagent navigation graphs. IEEE Transactions on Visualization and Computer Graphics 14, 526–538 (2008)
Wein, R., van den Berg, J.P., Halperin, D.: The visibility–voronoi complex and its applications. In: Proceedings of the Twenty-First Annual Symposium on Computational Geometry, SCG 2005, pp. 63–72. ACM, New York (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kallmann, M. (2010). Navigation Queries from Triangular Meshes. In: Boulic, R., Chrysanthou, Y., Komura, T. (eds) Motion in Games. MIG 2010. Lecture Notes in Computer Science, vol 6459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16958-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-16958-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16957-1
Online ISBN: 978-3-642-16958-8
eBook Packages: Computer ScienceComputer Science (R0)