Double stereographic

Description

The double stereographic projection is a planar perspective projection, viewed from the point on the globe opposite the point of tangency. Points are transformed from the spheroid to a Gaussian conformal sphere before being projected to the plane with the stereographic projection. This projection is conformal and used for large-scale coordinate systems in the Canadian provinces of New Brunswick and Prince Edward Island, and in the Netherlands.

The projection is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0.1 and later.

Projection properties

The subsections below describe the double stereographic projection properties.

Graticule

Double stereographic is an azimuthal projection.

In the polar aspect, the meridians project as straight lines originating at the pole. Angles between them are true. The parallels are shown as concentric circular arcs. Their spacing rapidly increases with distance from the pole. All graticule line intersections are 90 degrees. The opposite pole cannot be shown.

In the equatorial aspect, the equator and central meridian are projected as two perpendicular straight lines. Other meridians and parallels are unequally spaced curves, concave toward the central meridian and poles, respectively.

In the oblique case, only the parallel with the opposite sign to the latitude of origin and the central meridian are straight lines. The other parallels are concave toward the poles on either side of the straight parallel. Other meridians are circular arcs intersecting at the poles. The antipodal point of the projection's center cannot be shown in any aspect.

Distortion

Double stereographic is a conformal map projection. It maintains true directions only from the center of the map. Angles and shapes are maintained at infinitesimal scale everywhere. The circular arc with no scale distortion can be specified with the scale factor parameter. Area, distance, and scale distortions rapidly grow with the distance from the standard parallel.

Usage

The double stereographic projection is appropriate for mapping the polar regions at large scales. It is used for large-scale coordinate systems in New Brunswick, Prince Edward Island, and the Netherlands.

Limitations

Double stereographic is limited to showing only about three-fourths of the planet. The antipodal point of the projection's center cannot be shown in any aspect, which means that in polar aspect, the opposite pole cannot be projected and shown on the map. Due to enormous distortion, projection is normally limited to one hemisphere.

Parameters

Double stereographic parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Scale Factor
• Latitude Of Origin

Sources

Thomas D. B., Mephan, M. P. and Steeves, R. R. (1977). The stereographic double projection. Technical report no. 46. Fredericton: University of New Brunswick, Department of Geodesy and Geomatics Engineering.