## Description

The perspective cylindrical projection is a cylindrical map projection that can be constructed geometrically by projecting the globe onto a tangent (or secant) cylinder from the point on the equatorial plane opposite a given meridian. A special case of the projection is the central cylindrical or simple cylindrical projection, which projects the globe from its center.

The projection was used in oblique aspect for political and physical maps of the Soviet Union. It is available in ArcGIS Pro 2.6 and later and in ArcGIS Desktop 10.8.1 and later.

## Projection properties

The subsections below describe the perspective cylindrical projection properties.

### Graticule

In the normal aspect, the meridians are equally spaced straight lines. The parallels and both poles are straight lines, perpendicular to meridians and the same length as the projected equator. The spacing between the parallels increases from the equator to the poles. With some perspective ratios, the poles cannot be shown on the map. The graticule is symmetrical across the equator and the central meridian.

In the oblique aspect, the central meridian and the antimeridian lines are presented as three vertical lines: one in the middle and two on the left and right edges of the projection. The other meridians and all parallels are complex curves. The pole closest to the center of the map projects as a point on the middle vertical line. The other pole shows as a point on left and right edge of the projection. The graticule is symmetrical across the middle vertical line.

When the projection is centered on a pole, the opposite pole projects in the middle of the left and right projection edges. The central meridian and antimeridian lines are still presented with the same three vertical lines. The two meridians 90° away from the central meridian project as a horizontal straight line through the center of the projection. The equator projects as two vertical lines halfway between the center and the edge of the projection. The other meridians and parallels are complex curves. The graticule is symmetrical across the middle vertical and horizontal lines.

### Distortion

The perspective cylindrical projection is neither conformal nor equal-area. Shapes, areas, distances, directions, and angles are all generally distorted. The projection in normal aspect has correct scale and no distortion along the two standard parallels. Distortion increases away from the standard parallels, and it is extreme at the polar regions in the normal aspect. Along any given latitude, distortion values are constant. In any other aspect, there are two straight lines with accurate scale equidistant from and on each side of the central horizontal line. The distortion pattern is the same around the two lines as in normal aspect.

## Usage

Some variants of this projection in normal aspect can be used for general world maps not requiring accurate areas and when its phenomena changes with longitude, although its use is not recommended due to extreme distortion in polar regions. Some oblique variations of this projection were used for political and physical maps of the Soviet Union.

## Limitations

The perspective cylindrical projection is supported on spheres only. For an ellipsoid, the semimajor axis is used for the radius. Some distortion properties are not maintained when an ellipsoid is used. With some perspective ratios, the polar regions or area near oblique poles cannot be shown on the map.

## Parameters

Perspective cylindrical parameters are as follows:

- False Easting
- False Northing
- Central Meridian
- Pseudo Standard Parallel 1
- Latitude Of Origin
- Perspective Ratio, which represents the distance of the perspective point on the equatorial plane from the center of the globe, divided by the radius.

### Particular parameter cases

When the Perspective Ratio parameter is set to 0, the resulting projection is the central cylindrical projection with the perspective point in the center of the sphere or spheroid. The Braun and Gall stereographic projections can be created by setting the Perspective Ratio to 1 and the psuedo standard parallel to 0° and 45°, respectively.

## Sources

Bugayevskiy, L. M. and Snyder, J. P. (1995). Map Projections: A Reference Manual. London: Taylor & Francis.

Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections.Chicago and London: University of Chicago Press.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.