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The Computer Journal 2003 46(1):76-83; doi:10.1093/comjnl/46.1.76
© 2003 by British Computer Society
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Inverting Dirichlet Tessellations

Frederic Paik Schoenberg1,3, Thomas Ferguson1 and Cheng Li2

1 Department of Statistics, 8142 Math–Science Building, University of California, Los Angeles, CA 90095–1554, USA Email: frederic@stat.ucla.edu 2 Department of Statistics, Harvard University, Cambridge, MA 02138, USA 3 Corresponding author.

Given a collection of points in the plane, one may draw a cell around each point in such a way that each point's cell is the portion of the plane consisting of all locations closer to that point than to any of the other points. The resulting geometric figure is called a Dirichlet tessellation. An algorithm for obtaining the boundaries of the cells given the points was derived by Green and Sibson in 1978. Here, methods are described for obtaining the locations of the points, given only the cell boundaries.


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