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Interruption Devices

Eckert IV map with simply interrupted lobes Eckert IV map with simply interrupted lobes
Eckert IV map with interruptions and recentered meridians
Eckert IV map with interruptions and recentered meridians
Top left: uninterrupted Eckert IV map; top right: an interrupted version retains the projection's properties, including equivalence, while reducing angular distortion in privileged areas like the continents. Above and on the right, the same projection interrupted with lobes recentered: only one meridian (not necessarily the middle one) in each lobe is mapped to a straight line — as shown by the distortion pattern, again changing the privileged areas, e.g. Western Europe and Australia.

The main purpose of interrupting a map is moving significant regions to less-distorted places, usually near the center of each lobe. Several cartographic tricks enhance the usefulness of interruptions.

Recentering and Cropping

Especially with pseudocylindrical projections, each lobe of an interrupted map may easily be projected with its own, arbitrary central meridian, not necessarily the same as the central one. This introduces asymmetrical angular distortion, privileging regions near the straight central meridian while detracting from others. The central meridian may even change with latitude, like in Philbrick's Sinu-Mollweide projection and in the Eurasian lobe of Boggs's eumorphic map.

Recentering is also an effective device for uninterrupted continental or regional maps. The region of interest is centered, minimizing distortion, and the remaining projected area is cropped off. Recentering may resort to different aspects or even oblique maps.

Recentering to exploit areas of lesser distortion
Angular deformation map, Eckert IV. Equatorial map, default central meridian
Eckert IV map of Japan. Equatorial map, default central meridian

Ordinary equatorial map, centered on meridian 0°

Angular deformation map, Eckert IV projection. Equatorial map, centered on Japan
Eckert IV map of Japan. Equatorial map, default central meridian

Equatorial, meridians recentered on 137°E: the best choice

Eckert IV map of Japan. Equatorial map, default central meridian
Oblique Eckert IV map of Japan

Oblique, fully recentered on Japan

These three regional maps show the Japanese islands using the same Eckert IV projection. Analysis of the angular deformation patterns for this projection shows that, although it preserves area everywhere, only two small “sweet spots” at the intersection of the central meridian and the standard parallels 40°30′ N and S (in the equatorial aspect) are free of angular distortion. All three maps cover the same area but a slightly different region, which in the second version is nearer the optimal spot — Tokyo lies near 35°N 139°E. The oblique version on the third map is actually more distorted, while losing the equatorial's useful property of straight parallels.

Condensing and Insets

Interrupted, condensed Eckert IV map
Above, map using the Eckert IV projection, interrupted with meridians recentered, condensed at the Atlantic Ocean. Antarctica is presented uninterrupted in an inset drawn with Lambert's azimuthal equal-area projection at identical scale.
Antarctica in Eckert IV maps
Eckert's projection is not the best choice for the inset: in the transverse aspect, there's strong angular distortion (right); in oblique aspects moving the South Pole to the standard parallels, distortion is reduced, but also less symmetrical (far right details).
Some cartographic devices are actually editorial tricks, intended for clarity or printing convenience. They do not affect distortion patterns, and can be employed purely as lay-out tools.

Frequently applied simultaneously with interruption, condensing the map means removing unimportant areas and joining the remaining sections. It can save publishing space or, conversely, allow a larger scale and better detail in the same printed area.

Brazil in Mercator and azimuthal orthographic maps

Brazil and its immediate neighborhood, in a main Mercator map and (shaded) in the inset.

Also an editorial tool, an inset is a small illustration detached or superimposed on the main map, useful:

Abusing Interruptions

Eckert IV map with interruptions and recentered meridians

Interrupted Eckert IV map, not condensed but with lobe gaps colored like additional sea area; partial graticule and removal of Antarctica help hiding the flaw. Although continental shapes are better presented than in rectangular maps created by cylindrical projections, land/water area ratios are misleading and distances between, e.g., Iceland and Greenland, or Siberia and Alaska, are greatly stretched.

Like several cartographic techniques, interruption can be misused or thought of as purely editorial convenience. Hastily or carelessly prepared maps may suffer from:

Such maps may be good enough for advertisement, but unacceptable for didactic or scientific purposes.

HomeSite MapArbitrary Interrupted MapsInterrupted MapsPolyhedral Projections - part 1    June 16, 2018
Copyright © 2001 Carlos A. Furuti