Stereographic projection

In cartography and geometry, the stereographic projection is a mapping that projects each point on a sphere onto a tangent plane along a straight line from the antipode of point of tangency, with one exception: the center of projection, antipodal to the point of tangency, is not projected to any point. Two remarkable properties of this projection were demonstrated mathematically by Hipparchus:

• This mapping is conformal, i.e. it preserves angles at which curves cross each other, and
• This mapping transforms circles on the surface of the sphere that do not pass through the center of projection, to circles in the plane.