Shape deformation in continuous map generalization

Authors:
Jeff Danciger;Satyan L. Devadoss;John Mugno;Don Sheehy;Rachel Ward
Affiliations:
Stanford University, Stanford, USA 94305;Williams College, Williamstown, USA 01267;University of Maryland, College Park, USA 20742;Carnegie Mellon University, Pittsburgh, USA 15213;Princeton University, Princeton, USA 08544
Venue:
Geoinformatica
Year:
2009

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Abstract

Given a collection of regions on a map, we seek a method of continuously altering the regions as the scale is varied. This is formalized and brought to rigor as well-defined problems in homotopic deformation. We ask the regions to preserve topology, area-ratios, and relative position as they change over time. A solution is presented using differential methods and computational geometric techniques. Most notably, an application of this method is used to provide an algorithm to obtain cartograms.