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Peirce quincuncial projection

Conformal map projection / From Wikipedia, the free encyclopedia

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The Peirce quincuncial projection is the conformal map projection from the sphere to an unfolded square dihedron, developed by Charles Sanders Peirce in 1879.[1] Each octant projects onto an isosceles right triangle, and these are arranged into a square. The name quincuncial refers to this arrangement: the north pole at the center and quarters of the south pole in the corners form a quincunx pattern like the pips on the five face of a traditional die. The projection has the distinctive property that it forms a seamless square tiling of the plane, conformal except at four singular points along the equator.

Peirce quincuncial projection of the world. The red equator is a square whose corners are the only four points on the map at which the projection fails to be conformal.
The Peirce quincuncial projection with Tissot's indicatrix of deformation.

Typically the projection is square and oriented such that the north pole lies at the center, but an oblique aspect in a rectangle was proposed by Émile Guyou in 1887, and a transverse aspect was proposed by Oscar Adams in 1925.

The projection has seen use in digital photography for portraying spherical panoramas.