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Aquarius.NET®
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Azimuthal Projections
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Orthographic Projection
The orthographic projection assumes that the light source is an infinite
distance from the projection surface, resulting in parallel rays of light. The
spacing between parallels decreases with distance from the Equator. This
compression of north-south distances exactly compensates for the stretching of
east-west distances towards the poles, resulting in an equivalent projection.
However, because of the extreme distortion of shapes, especially in the polar
regions, other equivalent projections are generally preferred.
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Stereographic Projection
Stereographic projections are rarely used, although Gall's stereographic
projection has been proposed as compromise projection having less distortion of
distances than the cylindrical gnomonic projection and less distortion of
shapes than the cylindrical orthographic projection.
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Gnomonic Projection
The gnomonic projection illustrates the basic pattern of normal cylindrical
projections. The principles are the same as for the azimuthal gnomonic
projection. A light source positioned at the centre of the globe casts shadows
of the graticule on the projection surface, which in this instance, is a
cylinder placed tangent to the globe along the Equator. The Equator is shown as
true to scale on the map, and as is typical of cylindrical projections, there
is a narrow band along the Equator in which distortion of all geometric
characteristics is minimal. The spacing of parallels increases rapidly toward
the poles. The polar regions cannot be represented since the poles would be
located an infinite distance from the Equator. The cylindrical gnomonic
projection has no useful properties other than showing the basic pattern of the
graticule on cylindrical projections.
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Azimuthal Equidistant Projection
Azimuthal equidistant projections are sometimes used to show air-route
distances. Distances measured from the center are true. Distortion of other
properties increases away from the center point.
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Lambert Azimuthal Equal Area
This projection was developed by Lambert in 1772 and is typically used for
mapping large regions like continents and hemispheres. It is an azimuthal,
equal-area projection, but is not perspective. Distortion is zero at the center
of the projection, and increases radially away from this point.
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Universal Polar Stereographic
An azimuthal projection that is conformal. A standard variation of the
Stereographic projection in polar aspect that is used with Universal Transverse
Mercator (UTM) projection systems to represent polar regions. Limitations The
Universal Polar Stereographic projection is used only from the North Pole to 84
degrees latitude North and from the South Pole to 80 degrees latitude South.
Scale True only where the central latitude crosses the central meridian or,
alternatively, along a circle concentric about the projection center (or a
parallel on the polar aspect). Scale is constant along any circle having its
center at the projection center, but scale increases moderately with distance
from the center within a hemisphere. Distortion Only the center or the circle
of true scale (if not the center) is free from all distortion. Areas grow
greater the farther from the center, albeit in a conformal manner. Usage
Employed in the UTM system to show North and South polar regions. Used from the
North Pole to latitude 84 degrees North and from the South Pole to latitude 80
degrees South. In Universal Polar Sterographic projections the scale is reduced
to 0.994, resulting in a standard parallel of about 81 degrees 07 minutes North
or South. Origin Apparently developed in polar aspect by Egyptians and Greeks
by the 2nd Century BC. Hipparchus was apparently the first Greek to use it and
is generally considered its inventor.
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