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The Guyou hemisphere-in-a-square projection is a conformal
The Guyou hemisphere-in-a-square projection is a conformal map projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longit ...
for the hemisphere. It is an oblique aspect of the Peirce quincuncial projection
The Peirce quincuncial projection is the conformal map projection from the sphere to an unfolded square dihedron, developed by Charles Sanders Peirce in 1879. Each octant projects onto an isosceles right triangle, and these are arranged into a ...
.
History
The projection was developed by of France in 1887.Formal description
The projection can be computed as an oblique aspect of the Peirce quincuncial projection by rotating the axis 45 degrees. It can also be computed by rotating the coordinates −45 degrees before computing the stereographic projection; this projection is then remapped into a square whose coordinates are then rotated 45 degrees. The projection is conformal except for the four corners of each hemisphere’s square. Like other conformal polygonal projections, the Guyou is aSchwarz–Christoffel mapping In complex analysis, a Schwarz–Christoffel mapping is a conformal map of the upper half-plane or the complex unit disk onto the interior of a simple polygon. Such a map is guaranteed to exist by the Riemann mapping theorem (stated by Bernhard ...
.
Properties
Its properties are very similar to those of the Peirce quincuncial: * 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 thePeirce quincuncial projection
The Peirce quincuncial projection is the conformal map projection from the sphere to an unfolded square dihedron, developed by Charles Sanders Peirce in 1879. Each octant projects onto an isosceles right triangle, and these are arranged into a ...
are different aspects of the same underlying Schwarz–Christoffel mapping. Such mappings are transformations of half a stereographic projection.
See also
* List of map projectionsReferences
{{Map projections Map projections Conformal projections