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Moving circles between globe and map
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Suppose a set of concentric circles, with radiuses increasing in
1500km steps, centered on Campinas, Brazil. These are true
circles on Earth, which could demonstrate the theoretical range
of radio waves, airplanes, or missiles; they are represented here
in blue and are identical in all maps in this table. In each pair
of maps with blue shapes, the one on the left is a simple
aspect, while its right counterpart is usually
an oblique aspect centered on Campinas.
On the other hand, the orange lines were directly drawn as circles
on a map on the left column; their true shape on the globe is
presented on the right (they are the same curves only for each pair
of maps). There is only one projection and aspect
where both size and shape of circles are identical on globe and map.
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Like all azimuthal projections, the
azimuthal
equidistant preserves the shape of any circle centered
on the map's center of projection, but not necessarily of others
(above left); however, for those whose center does coincide
with the map's, the scale is also preserved: on the
map on the right, notice how the radiuses are linearly spaced. Given
a proper aspect, this projection is the only correct tool
for graphically finding ranges on a flat map.
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A Mercator map
is conformal, thus
preserving shapes locally but not globally. Scale changes quickly
towards the top and bottom of the map, especially vertically.
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Also conformal, an azimuthal
stereographic map preserves the shape of all
circles, even those not centered on the map (left). Nevertheless, their
scale is not preserved: they do not "grow" linearly, and those on
the left, perhaps surprisingly, are not concentric.
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A very simple design, the Plate Carrée is a particular case of
the equidistant
cylindrical projection. The scale is the same on the Equator
and all meridians (as measured on the equatorial aspect).
Therefore the width and height are identical for the "circles" on
the right only.
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Because all cylindrical projections
exaggerate horizontal scales towards the top and bottom of maps,
if circles are naively drawn with a pair of compasses on a Plate
Carrée map, their correct shapes on Earth are pinched, as shown by
the azimuthal equidistant map on the right.
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A particular case of Lambert's
equal-area cylindrical projection, Gall's
orthographic (also known as Gall-Peters or "Peters") projection preserves areas but
strongly distorts shapes, with vertical scale changing very
nonuniformly.
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Transferring circles drawn on a Gall's orthographic to the real
globe yields shapes even farther from correct. Because scales
are stretched between 45°N and 45°S, and compressed
elsewhere, the true shapes are correspondingly deformed on the globe.
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Eckert's sixth
projection is pseudocylindrical
and equal-area; its poles are shown as lines, but with lesser
horizontal exaggeration than in cylindrical projections. On the other
hand, horizontal distortion depends on the longitude.
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Most interrupted maps
are split at specific lines depending on the mapmaker's priorities;
therefore changing the aspect usually either robs the map's purpose
or demands a whole new set of interruptions. Here are normal aspects of
Goode's
interrupted homolosine (left) and Fuller's
Dymaxion™ maps.
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