It is demonstrated that the ideal projection according to the Airy criterion for an arbitrary mapping area is one in which two functions, one associated with the sum of the extremal scales and the other with the difference between the azimuth of the main direction on the surface and the grid azimuth of the main direction on the plane, are conjugate harmonic functions. At the boundary of the region, one of the extremal scale factors of the ideal projection equals unity, and the Tissot’s indicatrixes are oriented either along the normals or tangents to the boundary. The fundamental properties of the resulting ideal projection are examined.