Guyou hemisphere-in-a-square projection

History

Formal description

Properties

• Each hemisphere is represented as a square, the sphere as a rectangle of aspect ratio 2:1.
• The part where the exaggeration of scale amounts to double that at the centre of each square is only 9% of the area of the sphere, against 13% for the Mercator and 50% for the stereographic
• The curvature of lines representing great circles is, in every case, very slight, over the greater part of their length.
• It is conformal everywhere except at the corners of the square that corresponds to each hemisphere, where two meridians change direction abruptly twice each; the Equator is represented by a horizontal line.
• It can be tessellated in all directions.

  Related projections

• The Adams hemisphere-in-a-square projection and the Peirce quincuncial projection are different aspects of the same underlying Schwarz–Christoffel mapping. Such mappings are transformations of half a stereographic projection.