# Orthographic

## Description

The orthographic projection is an azimuthal perspective projection, projecting the Earth's surface from an infinite distance to a plane. It gives the illusion of a three-dimensional globe so it is often used as an inset map or for pictorial views of the Earth from space. This map projection is the same as the local projection but only supports spheres.

It is believed that the projection was developed by the Egyptians and the Greeks. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.1.1 and later.

## Projection properties

The subsections below describe the orthographic projection properties.

### Graticule

Orthographic is an azimuthal projection available in three aspects.

In the polar aspect, the meridians project as straight lines originating at the pole in the center. Angles between them are true. The parallels are shown as unequally spaced concentric circular arcs. Their spacing decreases with the distance from the center. All graticule line intersections are 90 degrees. The opposite pole cannot be projected. The graticule is symmetric across any meridian.

In the equatorial aspect, the equator and the central meridian are projected as two perpendicular straight lines. Two meridians, 90 degrees east and west of the central meridian, project as a circle and represent the edge of the projection. The other meridians are complex curves. Their spacing decreases away from the central meridian. All parallels are straight lines, perpendicular to the central meridian. Their spacing decreases away from the equator. Both poles project as points at the projection's edge. The graticule is symmetric across the equator and the central meridian.

In the oblique case, only the central meridian and antimeridian project as straight lines. The other meridians are semiellipses intersecting at the pole nearest to the center, which is projected as a point. The parallels are unequally spaced complete or partial ellipses and their spacing decreases away from the projection's center. The graticule is symmetric across the central meridian.

### Distortion

The orthographic projection is neither conformal nor equal-area. Shapes, areas, distances, directions, and angles are all generally distorted. Only the center of the map is free of distortion. Distortion values greatly increase radially from the origin.

## Usage

The oblique aspect of this projection can be used as an inset locator map or for pictorial views of the Earth from space.

## Variants

There are two variants available in ArcGIS:

• The orthographic variant uses the semimajor axis for the radius and equations for a sphere. It does not support the ellipsoid. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.1.1 and later.
• The orthographic auxiliary sphere variant uses sphere-based equations with a sphere specified by the Auxiliary Sphere Type parameter. It does not support the ellipsoid. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.3 and later.

## Limitations

The orthographic projection is limited to one hemisphere and cannot display the whole world. Neither variant supports an ellipsoid.

## Parameters

Orthographic parameters are as follows:

• False Easting
• False Northing
• Longitude Of Center
• Latitude Of Center

Orthographic auxiliary sphere parameters are as follows:

• False Easting
• False Northing
• Longitude Of Center
• Latitude Of Center
• Auxiliary Sphere Type, with values as follows:
• 0 = Use semimajor axis of the geographic coordinate system
• 1 = Use semiminor axis
• 2 = Calculate and use authalic radius
• 3 = Use authalic radius and convert geodetic latitudes to authalic latitudes
##### Note:

If the geographic coordinate system uses a sphere, the Auxiliary Sphere Type uses the radius of the sphere in all four cases.

## Sources

Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.

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.