The gnomonic projection intersects rays from a sphere’s centre with a tangent plane. If is its unit normal and are tangent basis vectors, a direction maps to . It maps great circle arcs to straight lines and is singular at the tangent-plane horizon.
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Gnomonic projection is a type of map projection where the surface of the Earth is projected onto a plane from a point at the center of the Earth. This projection is characterized by its unique property that all great circle routes (the shortest path between two points on the surface of a sphere) are represented as straight lines.