Stereographic

images\sc_projections_stereographic.gif

 

An azimuthal, conformal, polyconic (general) perspective projection. Used most conveniently with a single hemisphere. Illustrated centered on -90 degrees longitude and 0 degrees latitude.

 

images\sc_projections_polar_stereographic.gif

 

The Polar Stereographic form of this projection (polar aspect) is provided as a separate projection within the azimuthal projections. It is illustrated above.

 

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

 

Commonly used in the polar aspect for topographic maps of polar regions. The Equatorial aspect was used regularly for maps of the Eastern and Western hemispheres in the 17th and 18th centuries. Oblique aspects are used to show paths of solar eclipses.

 

Recommended for conformal mapping of regions approximately circular in extent.

 

Limitations

 

The Stereographic projection must not be used to map the entire world’s surface at once: at least the point directly opposite to the projection origin must be excluded. This limitation arises because the Stereographic projection maps the point opposite the projection origin to infinity, causing numeric overflows. For example, if the North Pole is used as the projection origin, the South Pole and region immediately about the South Pole should not be included in the map.

 

Origin

 

Apparently developed in polar aspect by Egyptians and Greeks by the 2nd Century BC

 

Options

 

Specify the latitude origin and longitude origin to center the map projection to the area to be mapped. Specifying a non-Equatorial or non-polar origin causes an oblique projection.

 

Tech Tip

 

The top illustration, showing a partially clipped Africa and Europe, was created using a trick to clip Europe and Africa. A graticule from 0 longitude to 90 longitude and from -80 latitude to 80 latitude was created as lines. Areas were then created within the graticule and unioned together to form one large area. This was used with the Clip with (Subtract) transform to clip those portions of Europe and Africa within the graticule area. Other areas in Europe, Africa and Asia were simply selected and deleted free hand. The remaining, unclipped portions of Europe and Africa fit neatly within the 0 to -90 longitude graticule seen in the illustration.