# Orthographic projection (cartography)

### From Wiki.GIS.com

**Orthographic projection** is a map projection of cartography. Like the Stereographic projection, Orthographic projection is a perspective projection, in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the Orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from deep space. The shapes and areas are distorted, particularly near the edges, but distances are preserved along parallels.

## [edit] History

The orthographic projection was called the "analemma" by the Greeks. The name was changed to "orthographic" in 1613 by François d'Aiguillon of Antwerp. Albrecht Dürer (1471 – 1528) prepared the first known polar and equatorial orthographic maps of the Earth.^{[1]} Photographs of the Earth and other planets has inspired renewed interest in the Orthographic projection in astronomy and planetary science.

## [edit] Mathematics

The formulas for the Orthographic projection are in terms of longitude () and latitude () on the sphere. Defining the radius of the sphere R and the center point and origin of the projection as (), the equations for the Orthographic projection onto the () plane reduce to the following:

Latitudes beyond the range of the map should be clipped by calculating the distance *c* form the center of the projection. This ensures that points on the opposite hemisphere are not plotted:

The point should be clipped from the map if cos(*c*) is negative.

For the inverse formulas for the sphere, to find given :

where

## [edit] References

- ↑ Keuning, Johannes.
*The History of Geographical Map projections until 1600:*Imago Mundi, v.12, p.1-24

- Weisstein, Eric W.,
*Orthographic Projection*From MathWorld--A Wolfram Web Resource. Accessed 17 August 2010.

- USGS Map Projections: A Working Manual, USGS Professional Paper 1395 (1987). A freely downloadable book with details on most projections, including formulas and sample calculations.