Abstract
We study the flow of water on fat terrains, that is, triangulated terrains where the minimum angle of any triangle is bounded from below by a positive constant. We give improved bounds for the worst-case complexity of river networks on fat terrains, and show how to compute the river network and other flow-related structures i/o-efficiently.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Agarwal, P.K., Arge, L., Murali, T.M., Varadarajan, K.R., Vitter, J.S.: I/O-efficient algorithms for contour-line extraction and planar graph blocking. In: Symp. on Discrete Algorithms 1998, pp. 117–126 (1998)
Aggarwal, A., Vitter, J.S.: The Input/Output complexity of sorting and related problems. Communications of the ACM 31(9), 1116–1127 (1988)
Arge, L.: The buffer tree: A technique for designing batched external data structures. Algorithmica 37(1), 1–24 (2003)
Arge, L., Chase, J., Halpin, P., Toma, L., Urban, D., Vitter, J.S., Wickremesinghe, R.: Flow computation on massive grid terrains. GeoInformatica 7(4), 283–313 (2003)
Arge, L., Vahrenhold, J.: I/O-efficient dynamic planar point location. Comp. Geom. 29, 147–162 (2004)
de Berg, M., Bose, P., Dobrint, K., van Kreveld, M., Overmars, M., de Groot, M., Roos, T., Snoeyink, J., Yu, S.: The complexity of rivers in triangulated terrains. In: Canad. Conf. Comp. Geom. 1996, pp. 325–330 (1996)
Chiang, Y.-J., Goodrich, M.T., Grove, E.F., Tamassia, R., Vengroff, D.E., Vitter, J.S.: External-memory graph algorithms. In: Symp. on Discr. Alg. 1995, pp. 139–149 (1995)
Hutchinson, D., Maheshwari, A., Zeh, N.: An external memory data structure for shortest path queries. In: ACM-SIAM Computing and Combin. Conf. 1999, pp. 51–60 (1999)
Jones, N.L., Wright, S.G., Maidment, D.R.: Watershed delineation with triangle-based terrain models. Journal of Hydraulic Engineering 116(10), 1232–1251 (1990)
van Kreveld, M.: Digital elevation models and TIN algorithms. In: van Kreveld, M., Roos, T., Nievergelt, J., Widmayer, P. (eds.) Algorithmic Foundations of Geographic Information Systems. LNCS, vol. 1340, pp. 37–78. Springer, Heidelberg (1997)
McAllister, M.: The computational geometry of hydrology data in geographic information systems. PhD th., Univ. of British Columbia (1999)
McAllister, M.: A watershed algorithm for triangulated terrains. Canad. Conf. Comp. Geom. 1999 (1999)
McAllister, M., Snoeyink, J.: Extracting consistent watersheds from digital river and elevation data. Ann. Conf. Amer. Soc. for Photogrammetry and Remote Sensing 1999 (1999)
Moet, E., Kreveld, M.v., v/d Stappen, A.F.: On realistic terrains. In: Symp. on Computational Geom. 2006, pp. 177–186 (2006)
Palacios-Velez, O., Gandoy-Bernasconi, W., Cuevas-Renaud, B.: Geometric analysis of surface runoff and computation of unit elements in distributed hydrological models. J. Hydrology 211, 266–274 (1998)
Silfer, A.T., Kinn, G.J., Hassett, J.M.: A geographic information system utilizing the triangulated irregular network as a basis for hydrologic modeling. Auto-Carto 8, 129–136 (1987)
Theobald, D.M., Goodchild, M.F.: Artifacts of TIN-based surface flow modeling. In: Proc. GIS/LIS 1990, pp. 955–964 (1990)
Tucker, G., Lancaster, S., Gasparini, N., Rybarczyk, S.: An object-oriented framework for hydrology and geomorphic modeling using TINs. Computers and Geosc. 27(8), 959–973 (2001)
Yu, S., van Kreveld, M., Snoeyink, J.: Drainage Queries in TINS: from local to global and back again. In: Symp. on Spatial Data Handling 1996, pp. 1–14 (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Berg, M., Cheong, O., Haverkort, H., Lim, J.G., Toma, L. (2007). I/O-Efficient Flow Modeling on Fat Terrains. In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-73951-7_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73948-7
Online ISBN: 978-3-540-73951-7
eBook Packages: Computer ScienceComputer Science (R0)