Map Projections: Interruption Devices

The Wayback Machine - https://web.archive.org/web/20150826101552/http://www.progonos.com:80/furuti/MapProj/Normal/ProjInt/IntDev/intDev.html

Map Projections

Interruption Devices

Eckert IV map with simply interrupted lobes

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


Ordinary equatorial map, centered on meridian 0°	Equatorial, meridians recentered on 137°E	Oblique, fully recentered
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 map 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 right is actually more distorted, while losing the useful property of straight parallels.

Condensing and Insets

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.

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 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:

for presenting an area strongly distorted or interrupted, or impossible to be shown (like in Mercator's projection) by the main projection; the azimuthal equidistant is commonly employed for polar regions
especially for large-scale maps of a small or lesser-known region, for quickly pinpointing its location on Earth; the azimuthal orthographic is frequently used in small hemispheres

Abusing Interruptions

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:

failure to clearly mark condensed areas
interruption gaps not marked, suggesting continuity instead

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

Apr	AUG	Jan
	26
2014	2015	2016