Tobler hyperelliptical projection

Tobler hyperelliptical projection of the world, α = 0, γ = 1.18314, k = 2.5

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]

Overview

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. Except for the straight central meridian, the meridians of longitude are curves of the form a|x|^γ + b|y|^γ = 1 (with a dependent on longitude and b constant for a given map), known as superellipses^[3] or Lamé curves. When γ=1 the projection degenerates to the Collignon projection; when γ=2 the projection becomes the Mollweide projection; the limiting case as γ→∞ is the cylindrical equal-area projection.^[4] Values of γ that are favored by Tobler and others are generally greater than 2.

See also

• List of map projections

References