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Gnomonic projection

Azimuthal gnomonic map projection / From Wikipedia, the free encyclopedia

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A gnomonic map projection is a map projection which displays all great circles as straight lines, resulting in any straight line segment on a gnomonic map showing a geodesic, the shortest route between the segment's two endpoints. This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the sphere passes through the point on the surface and then on to the plane. No distortion occurs at the tangent point, but distortion increases rapidly away from it. Less than half of the sphere can be projected onto a finite map.[1] Consequently, a rectilinear photographic lens, which is based on the gnomonic principle, cannot image more than 180 degrees.

Gnomonic projection of a portion of the north hemisphere centered on the geographic North Pole
The gnomonic projection with Tissot's indicatrix of deformation