Gnomonic projection

Under gnomonic projection every great circle on the sphere is projected to a straight line in the plane (a great circle is a geodesic on the sphere, the shortest path between any two points, analogous to a straight line on the plane).

It is commonly used as a geographic map projection, and can be convenient in navigation because great-circle courses are plotted as straight lines.

Rectilinear photographic lenses make a perspective projection of the world onto an image plane; this can be thought of as a gnomonic projection of the image sphere (an abstract sphere indicating the direction of each ray passing through a camera modeled as a pinhole).

The gnomonic projection of the 3-sphere of unit quaternions, points of which represent 3-dimensional rotations, results in Rodrigues vectors.

[2] The path of the shadow-tip or light-spot in a nodus-based sundial traces out the same hyperbolae formed by parallels on a gnomonic map.

They are also used by navies in plotting direction finding bearings, since radio signals travel along great circles.

In astronomy, gnomic projection star charts of the celestial sphere can be used by observers to accurately plot the straight line path of a meteor trail.