Gnomonic projection map: how country sizes change

Gnomonic projection: key facts and what it does to country sizes

Distortion class: Neither equal-area nor conformal
Graticule type: Perspective azimuthal
Creator: Unknown; traditionally, though speculatively, attributed to Thales of Miletus
Year: 6th century BC
Area: Distorted: grows rapidly toward the edge of the view; moderate only within about 30° of the center
Shape: Reasonable only near the center; heavily stretched near the edge
Distances: Distorted; true only at the very center of the map
Angles and directions: Distorted; accurate only at the center. In return, every great circle is a straight line

When the gnomonic map opens, its center lies at 25°N over the Sahara, and the view reaches 80° from that point. Of the thirty Tissot indicatrices, ten fit inside it completely, and two more, at 30°N and 90° longitude, show only partly at the edge. Distortion depends only on distance from the center and grows faster away from the center than across. At a distance of 60° an ellipse is four times longer and twice as wide as the circle, so it covers eight times the area.

The ellipses at 30°N and 30° longitude are enlarged by only about 40%, those on the equator twofold, and those at 30°S, over southern Africa and the South Atlantic, almost tenfold. The most surprising are the two at 60°N, 90°E and 90°W. They lie almost 70° from the center, have about twenty times the area and stretch into long ovals pointing away from the middle of the map. At the very edge of the view the enlargement reaches about 190 times. Area doubles 37.5° from the center, quadruples at 51° and grows eightfold at 60°. A point 90° away would lie at infinity, which is why a gnomonic map can never show even a full hemisphere.

Add Poland: it lies about 31° from the center and is enlarged by more than half. Choose the “Europe” center in the panel and it lands almost on the central point, regaining its true shape. The “Pacific” center, or a point you pick on the map, moves this whole pattern of distortion elsewhere. In return, every great circle, the shortest route on the sphere, is a straight line here.

Full guide: Gnomonic projection Compare with another projection Quiz: name the projection

Gnomonic map: frequently asked questions

Why is the shortest path a straight line on the gnomonic map?

Every great circle, the shortest path on a sphere, is a straight segment here. That is the main virtue of this projection, paid for with enlarged areas: the farther from the center, the faster they grow.

Why can a gnomonic map never show a whole hemisphere?

A point 90° from the center would lie at infinity. On opening, the map is centered on 25°N over the Sahara and the view reaches 80° from that point. Of the thirty Tissot ellipses, ten fit in whole.

How much does the gnomonic map enlarge areas far from the center?

Area has doubled by 37.5° from the center, quadrupled by 51° and grown eightfold by 60°. At the very edge of the view enlargement reaches about 190 times, and the ellipses at 60°N, 90°E and 90°W have about twenty times the area.

How do I put Europe in the center of the gnomonic map?

Choose the Europe center in the panel. Poland, which lies about 31° from the default center and is enlarged by more than half there, lands almost on the central point and regains its true shape. The Pacific center moves the whole pattern of distortion elsewhere.