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Pseudocylindrical equal-area map projection From Wikipedia, the free encyclopedia
The Tobler hyperelliptical projection is a family of equal-area pseudocylindrical projections that may be used for world maps. Waldo R. Tobler introduced the construction in 1973 as the hyperelliptical projection, now usually known as the Tobler hyperelliptical projection.[1]
As with any pseudocylindrical projection, in the projection’s normal aspect,[2] the parallels of latitude are parallel, straight lines. Their spacing is calculated to provide the equal-area property. The projection blends the cylindrical equal-area projection, which has straight, vertical meridians, with meridians that follow a particular kind of curve known as superellipses[3] or Lamé curves or sometimes as hyperellipses. A hyperellipse is described by , where and are free parameters. Tobler's hyperelliptical projection is given as:
where is the longitude, is the latitude, and is the relative weight given to the cylindrical equal-area projection. For a purely cylindrical equal-area, ; for a projection with pure hyperellipses for meridians, ; and for weighted combinations, .
When and the projection degenerates to the Collignon projection; when , , and the projection becomes the Mollweide projection.[4] Tobler favored the parameterization shown with the top illustration; that is, , , and .
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