Gnomonic

Description

This azimuthal projection uses the center of the earth as its perspective point. All great circles are straight lines, regardless of the aspect. This is a useful projection for navigation because great circles highlight routes with the shortest distance.

Projection method

This is a planar perspective projection viewed from the center of the globe. The projection can be any aspect.

Point of tangency

A single point anywhere on the globe.

Polar aspect—North Pole or South Pole.

Equatorial aspect—any point along the equator.

Oblique aspect—any other point.

Linear graticules

All meridians and the equator.

Properties

Shape

Increasingly distorted from the center; moderate distortion within 30 degrees of the center point.

Area

Distortion increases with distance from the center; moderate distortion within a 30 degree radius of the center.

Direction

Accurate from the center.

Distance

No line has an accurate scale, and the amount of distortion increases with distance from the center.

Scalar distortion for polar aspect

Degrees from center (°)	Meridian distortion (%)	Latitude distortion (%)
15.0	7.2	3.5
30.0	33.3	15.5
45.0	100.0	41.4
60.0	300.0	100.0

Scalar distortion for polar aspect

Limitations

This projection is limited by its perspective point and cannot project a line that is 90° or more from the center point; this means that the equatorial aspect cannot project the poles, and the polar aspects cannot project the equator.

A radius of 30° produces moderate distortion, as indicated in the table above. This projection should not be used more than about 60° from the center.

Uses and applications

All aspects—routes of navigation for sea and air.

Polar aspect—navigational maps of polar regions.

Equatorial aspect—navigational maps of Africa and the tropical region of South America.

Parameters

Desktop

• False Easting
• False Northing
• Longitude of Center
• Latitude of Center

Note:

Supported on spheres only.

Gnomonic Auxiliary Sphere (Desktop version 9.3 and later)

• False Easting
• False Northing
• Longitude of Center
• Latitude of Center
• Auxiliary Sphere Type

Note:

The Auxiliary Sphere Type parameter accepts 0 (use semimajor axis or radius of the geographic coordinate system), 1 (use semiminor axis or radius), 2 (calculate and use authalic radius), or 3 (use authalic radius and convert geodetic latitudes to authalic latitudes).

Workstation

• Radius of the sphere of reference
• Longitude of center of projection
• Latitude of center of projection
• False Easting (meters)
• False Northing (meters)

Note:

Supported on spheres only.