Abstract
In this paper we study how to recognize when a dissection of the plane has been constructed in one of several natural ways each of which models some phenomena in the natural or social sciences. The prototypical case is the nearest-neighbor or Dirichlet tessellation.
Similar content being viewed by others
References
Ash, P. and Bolker, E., ‘Recognizing Dirichlet Tessellations’, Geom. Dedicata 19 (1985) 175–206.
Aurenhammer, F., ‘The One-Dimensional Weighted Voronoi Diagram’, Technical Report F110, Institut fur Informationsverarbeitung, Technische Institut Graz und Osterreichische Computergesellschaft, Graz, Austria, January, 1983.
Aurenhammer, F., ‘Power Diagrams: Properties, Algorithms and Applications’, Technical Report F120, Institut fur Informationsverarbeitung, Technische Institut Graz und Osterreichische Computergesellschaft, Graz, Austria, June 1983.
Aurenhammer, F., ‘On the Generality of Power Diagrams’, Technical Report F126, Institut fur Informationsverarbeitung, Technische Institut Graz and Osterreichische Computergesellschaft, Graz, Austria, December, 1983.
Bowyer, A., ‘Computing Dirichlet Tessellations’, The Computer Journal 24 (1981), 162–166.
Conway, J. H. and Sloane, N. J. A., ‘Voronoi Regions of Lattices, Second Moments of Polytopes, and Quantization’, IEEE Trans. on Information Theory IT-28 (1982), 211–226.
Coxeter, H. S. M., Introduction to Geometry, Wiley, 1961.
Crapo, H., ‘Structural Rigidity’, Structural Topology 1 (1979), 13–45.
Ehrlich, P. E. and Im Hof, H. C., ‘Dirichlet Regions in Manifolds without Conjugate Points’, Comment. Math. Helv. 54 (1979), 642–658.
Guillemin, V. and Pollack, A., Differential Topology, Prentice Hall, Englewood Cliffs, N. J., 1974.
Hyson, C. D. and Hyson, W. P., ‘The Economic Law of Market Areas’, in Spatial Economic Theory (eds R. D. Dean et. al.), The Free Press, New York, 1970, pp. 165–170.
Imai, H., Iri, M., and Murota, K., ‘Voronoi Diagrams in the Laguerre Geometry and its Applications’, Research Memorandum RMI 83-02, Department of Mathematical Engineering and Instrumentation Physics, University of Tokyo, March, 1983 (to appear in SIAM Journal on Computing 14 (1985)).
Maxwell, J. C., ‘On Reciprocal Figures and Diagrams of Forces’, Phil. Mag., Series 4, 27 (1864), 250–261.
Maxwell, J. C., ‘On Reciprocal Figures, Frames, and Diagrams of Forces’, Trans. Roy. Soc. Edinburgh 26 (1869–72), 1–40.
Sibson, R., ‘A Vector Identity for the Dirichlet Tessellation’, Math. Proc. Camb. Phil. Soc. 87 (1980), 151–155.
Whiteley, W., ‘Realizability of Polyhedra’, Structural Topology 1 (1979), 46–58.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ash, P.F., Bolker, E.D. Generalized Dirichlet tessellations. Geom Dedicata 20, 209–243 (1986). https://doi.org/10.1007/BF00164401
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00164401