An Optimized Rubber-Sheet Algorithm for Continuous Area Cartograms

  title={An Optimized Rubber-Sheet Algorithm for Continuous Area Cartograms},
  author={Shipeng Sun},
  journal={The Professional Geographer},
  pages={16 - 30}
  • Shipeng Sun
  • Published 1 February 2013
  • Computer Science
  • The Professional Geographer
This article optimizes a continuous area cartogram algorithm published in The Professional Geographer by Dougenik, Chrisman, and Niemeyer (DCN) in 1985. The DCN algorithm simulates a rubber sheet and is an iterative and approximate solution of cartogram construction. Although it remains popular because of its conceptual simplicity and cartographic quality, the DCN algorithm cannot completely preserve topology and its mathematical properties are inadequately explained. This article presents an… 

A fast, free-form rubber-sheet algorithm for contiguous area cartograms

  • Shipeng Sun
  • Computer Science
    Int. J. Geogr. Inf. Sci.
  • 2013
Quantitative measures show that Carto3F outperforms the optimized rubber-sheet algorithm and the diffusion algorithm in both transformation effectiveness and computational efficiency.

Optimization-Based Construction of Quadrilateral Table Cartograms

The proposed method is formulated as a simple minimization problem to achieve mathematical clarity and can generate quadrilateral table cartograms with smaller deformation of rows and columns, thereby aiding readers to recognize the correspondence between table cartogram and original tables.

Applying forces to generate cartograms: a fast and flexible transformation framework

A fast and flexible force-based computational framework for general space transformation with solid physical and mathematical foundations that provides a fast, flexible, and robust alternative to the diffusion method for cartogram production.

Manual construction of continuous cartograms through mesh transformation

A computer-assisted framework employs a joint triangulation, similar to that used in rubber-sheeting, to define a piecewise affine transformation between map space and cartogram space that guarantees preservation of all topological relations within and among transformed datasets with insertion of a finite number of points.

Circular cartograms via the elastic beam algorithm originated from cartographic generalization

The evaluation results indicate that the circular cartograms generated by the proposed approach have a higher quality for the maintenance of topology relations, contiguities, and relative relations with smaller displacement distances compared to the existing approaches.

Parallel construction of large circular cartograms using graphics processing units

  • Wenwu Tang
  • Computer Science
    Int. J. Geogr. Inf. Sci.
  • 2013
Experimental results suggest that the GPU-enabled parallel computing approach offers significant acceleration performance for the construction of large circular cartograms, and thus sheds further light on the resolution of computationally intensive spatial and spatiotemporal problems using advanced cartographic and geovisualization approaches.

Symbolize map distortion with inscribed circles in polygons

ABSTRACT For the representation of geographic information, the distortion resulting from map projections and transformations is unwanted but unavoidable. Identical circles systematically arranged on

The State of the Art in Cartograms

This work surveys cartogram research in visualization, cartography and geometry, covering a broad spectrum of different cartogram types: from the traditional rectangular and table cartograms, to Dorling and diffusion cartograms.

Visual Encoding of Dissimilarity Data via Topology-Preserving Map Deformation

An efficient technique for topology-preserving map deformation is presented and it is demonstrated how these techniques can be useful in several-quite different-applied contexts: travel-time visualization, social demographics research and understanding energy flowing in a wide-area power-grid.

Usability of value-by-alpha maps compared to area cartograms and proportional symbol maps

A systematic evaluation of the value-by-alpha map in terms of effectiveness, efficiency and satisfaction concluded that it is as effective and as efficient as area cartograms in bivariate mapping, but are generally less effective and efficient than bivariate proportional symbol maps.



A New Algorithm for Continuous Area Cartogram Construction with Triangulation of Regions and Restriction on Bearing Changes of Edges

This study proposes a construction algorithm that involves triangulation of regions and regularization through restrictions on the bearing changes of the edges in order to obtain visually clear results and application to the USA population datasets reveals that the algorithm has mathematical clarity and is user friendly.

CartoDraw: a fast algorithm for generating contiguous cartograms

An efficient iterative scanline algorithm to reposition edges while preserving local and global shapes and a shape similarity function, which is based on a Fourier transformation of the polygons' curvatures are proposed.

Medial-axis-based cartograms

A method for generating cartograms that combines iterative relocation of a map's vertices with medial-axis-based transformations retains the input map's topology.

Thirty Five Years of Computer Cartograms

A direct and simple introduction is given to the design of a computer algorithm for the construction of contiguous value-by-area cartograms, based on a presentation from the 1960s.

Continuous cartogram construction

A new algorithm for the construction of continuous area cartograms is presented that was developed by viewing their construction as a constrained optimization problem and uses a relaxation method that exploits hierarchical resolution, constrained dynamics, and a scheme that alternates goals of achieving correct region areas and adjusting region shapes.

Carto‐SOM: cartogram creation using self‐organizing maps

This paper presents a new method for building cartograms, based on self-organizing neural networks (Kohonen's self‐organizing maps or SOM), which is competitive and can perform better then existing algorithms.


A computer algorithm is presented which can handle more realistic descriptions of polygon boundaries than previous algorithms and manual methods, thus enhancing visual recognition.

Rectangular cartograms: construction & animation

This work presents the first algorithms for rectangular cartogram construction, introduced by Raisz in 1934, where each region is represented by a rectangle, and has the advantage that the sizes of the regions can be estimated much better than with the first two types.

On rectangular cartograms

The first algorithms for rectangular cartogram construction are presented and a non-trivial class of rectangular subdivisions for which exact cartograms can be efficiently computed is characterized.

The Rectangular Statistical Cartogram

T HE idea of the statistical cartogram occurred to the author when he had occasion to prepare maps of the United States showing the distribution of various economic units, such as steel factories,