Part 2: Distortion-Spectrum Applications Projection Cross-breeding

Abstract

The applications of the distortion spectrum are extended to the domain of minimum-error projections. Several new concepts in analytic cartography are introduced, the most prominent being the Minimum-Constraint Minimum-Error (MCME) representation of the distortion measure, the MCME Atlas, and projection cross-breeding. The concept of projection cross-breeding is introduced as a technique of mixing two or more 'parent' MCME projections selected from the MCME Atlas in order to produce an 'offspring' projection that minimizes cartographic distortions and inherits the most desirable cartographic characteristics for the specific data-mapping task. A step-by-step demonstration of the application of projection cross-breeding technology to the design of minimum-error projections is provided, using the example of the Tri-Optimal projection. Each MCME projection provides a visual characterization of a map-distortion measure. The MCME and its distortion spectrum together provide a cartographic insight into the nature of map-distortion measures. A practical methodology for creating a visual dictionary (called the MCME Atlas) of map distortion measures is presented, and its use in projection cross-breeding explained. An explanation of the use of the Atlas to study map-distortion measures by means of the scientific classification of measures is also included.

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