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A combinatorial approach to cartograms

Authors
Journal
Computational Geometry
0925-7721
Publisher
Elsevier
Publication Date
Volume
7
Identifiers
DOI: 10.1016/s0925-7721(96)00006-5
Keywords
  • Combinatorial Topology
  • Algorithms
  • Simplicial Maps
  • Homeomorphisms
  • Singular Value Decomposition
  • Arrays
  • Trees
  • Range Search
Disciplines
  • Computer Science

Abstract

Abstract A homeomorphism from R 2 to itself distorts metric quantities, such as distance and area. We describe an algorithm that constructs homeomorphisms with prescribed area distortion. Such homeomorphisms can be used to generate cartograms, which are geographic maps purposely distorted so their area distributions reflects a variable different from area, as for example population density. The algorithm generates the homeomorphism through a sequence of local piecewise linear homeomorphic changes. Sample results produced by the preliminary implementation of the method are included.

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