Preview
Unable to display preview. Download preview PDF.
References
G. Albers, L.J. Guibas, J.S.B. Mitchell, and T. Roos, Voronoi diagrams of moving points, Tech. Rep. 235, ETH Zürich, 1995, to appear in Intl. J. Comp. Geom. & Appl.
F. Aurenhammer, Voronoi diagrams: A survey of a fundamental geometric data structure, ACM Comput. Surv., Vol. 23, pp 345–405, 1991.
J.-D. Boissonnat, O. Devillers, R. Schott, M. Teillaud, and M. Yvinec, Applications of random sampling to on-line algorithms in Computational Geometry, Discrete & Computational Geometry, Vol. 8, pp 51–71, 1992.
P. Chew, Near-quadratic bounds for the L 1 Voronoi diagram of moving points, Proc. 5th Canad. Conf. Comp. Geom. CCCG'93, pp 364–369, 1993.
N.R. Chrisman, J.A. Dougenik, and D. White, Lessons for the design of polygon overlay processing from the Odyssey Whirlpool algorithm, Proc. 5th Intl. Symp. on Spatial Data Handling SDH'92, Charleston, pp 401–410, 1992.
J.P. Corbett, A general topology for spatial reference, SORSA Report, 1985.
B.N. Delaunay, Sur la sphere vide, Bull. Acad. Science USSR VII: Class. Science Math., pp 793–800, 1934.
O. Devillers and M. Golin, Dog bites postman: Point location in the moving Voronoi diagram and related problems, Proc. 1st Annual European Symp. on Algorithms ESA'93, LNCS 726, pp 133–144, 1993.
O. Devillers, S. Meiser, and M. Teillaud, Fully dynamic Delaunay triangulation in logarithmic time per operation, Comp. Geom. Theory & Appl., Vol. 2, pp 55–80, 1992.
G. Dutton (Ed.), First International Advanced Symposium on Topological Data Structures for GIS, Harvard University, Cambridge, MA, Vol. 8, 1978.
S. Fortune, A sweepline algorithm for Voronoi diagrams, Algorithmica, Vol. 2, pp 153–174, 1987.
A.U. Frank, I. Campari, and U. Formentini (Eds.), Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, LNCS 639, 1992.
C.M. Gold, An object-based dynamic spatial model, and its application in the development of a user-friendly digitizing system, Proceedings, 5th Intl. Symp. on Spatial Data Handling SDH'92, Charleston, pp 495–504, 1992.
C.M. Gold, Problems with handling spatial data — the Voronoi approach, CISM Journal, Vol. 45, No. 1, pp 65–80, 1991.
C.M. Gold, Spatial data structures — the extension from one to two dimensions, In: L.F. Pau (Ed.), Mapping and Spatial Modelling for Navigation, NATO ASI Series F, No. 65, Springer-Verlag, Berlin, pp 11–39, 1990.
C.M. Gold, The interactive map, In: M. Molenaar and S. de Hoop (Eds.), Advanced Geographic Data Modelling and Query Languages for 2D and 3D Applications, Netherlands Geodetic Commission, Publications on Geodesy, No. 40, pp 121–128, 1994.
C.M. Gold and A.R. Condal, A spatial data structure integrating GIS and simulation in a marine environment, Marine Geodesy, Vol. 18, pp 213–228, 1995.
C.M. Gold, P.R. Remmele, and T. Roos, Fully dynamic and kinematic Voronoi diagrams in GIS, Special Issue on Cartography and Geographic Information Systems, Algorithmica, to appear.
C.M. Gold, P.R. Remmele, and T. Roos, Voronoi diagrams of line segments made easy, Proc. 7th Canadian Conference on Computational Geometry CCCG'95, Laval University, Quebec City, pp 223–228, 1995.
C.M. Gold and T. Roos, Surface Modelling with Guaranteed Consistency — An Object-Based Approach, Proc. Int. Workshop on Advanced Research in GIS IGIS'94, LNCS 884, pp 70–87, 1994.
P.J. Green and R. Sibson, Computing Dirichlet tessellations in the plane, The Computer Journal, Vol. 21, pp 168–173, 1978.
L.J. Guibas, D.E. Knuth, and M. Sharir, Randomized incremental construction of Delaunay and Voronoi diagrams, Proc. 17th Intl. Colloquium on Automata, Languages and Programming ICALP'90, LNCS 443, Springer, pp 414–431, 1990.
L.J. Guibas, J.S.B. Mitchell, and T. Roos, Voronoi diagrams of moving points in the plane, Proc. 17th Intl. Workshop on Graph Theoretic Concepts in Computer Science WG'91, Fischbachau, Germany, LNCS 570, pp 113–125, 1991.
L.J. Guibas and J. Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams, ACM Transactions on Graphics, Vol. 4, pp 74–123, 1985.
D.T. Lee and R.L. Drysdale, Generalization of Voronoi diagrams in the plane, SIAM J. Comput., Vol. 10, No. 1, pp 73–87, 1981
A. Okabe, B. Boots, and K. Sugihara, Spatial tessellations — concepts and applications of Voronoi diagrams, John Wiley and Sons, Chichester, 1992.
F.P. Preparata and M.I. Shamos, Computational Geometry: An introduction, Springer, New York, 1985.
T. Roos, Dynamic Voronoi diagrams, PhD thesis, University of Würzburg, Germany, 1991.
M.I. Shamos and D. Hoey, Closest point problems, Proc. 16th Annual IEEE Symp. on Foundations of Computer Science FOCS'75, pp 151–162, 1975.
M. Teillaud, Towards dynamic randomized algorithms in computational geometry, LNCS 758, Springer-Verlag, Berlin, 1993.
T. Tokuyama, Deformation of merged Voronoi diagrams with translations, TRL Research Report TR87-0049, IBM Tokyo Research Laboratory, 1988.
G.F. Voronoï, Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier Mémoire: Sur quelques propriétés des formes quadratiques positives parfaites, J. Reine Angew. Mathematik, Vol. 133, pp 97–178, 1907. Deuxième Mémoire: Recherches sur les parallélloèdres primitifs, J. Reine Angew. Mathematik, Vol. 134, pp 198–287, 1908 and Vol. 136, pp 67–181, 1909.
W. Yang and C.M. Gold, Managing spatial objects with the VMO-Tree, Proc. 7th Intl. Symp. on Spatial Data Handling SDH'96, Vol. 2, Delft, The Netherlands, pp 11B-15 to 11B-30, August 1996.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gold, C.M., Remmele, P.R., Roos, T. (1997). Voronoi methods in GIS. In: van Kreveld, M., Nievergelt, J., Roos, T., Widmayer, P. (eds) Algorithmic Foundations of Geographic Information Systems. CISM School 1996. Lecture Notes in Computer Science, vol 1340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63818-0_2
Download citation
DOI: https://doi.org/10.1007/3-540-63818-0_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63818-6
Online ISBN: 978-3-540-69653-7
eBook Packages: Springer Book Archive