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 used for mapping the earth. It is named for Waldo R. Tobler, its inventor, who first described the family in 1973.

In the projection’s normal aspect, the parallels of latitude are parallel straight lines whose spacing is calculated to provide the equal-area property; the meridians of longitude (except for the central meridian, which is a straight line perpendicular to the lines representing parallels) 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 or Lamé curves. When γ=1 it becomes the Collignon projection; when γ=2 the projection becomes the Mollweide projection; the limiting case as γ→∞ is the Cylindrical equal-area projection (Lambert cylindrical equal-area, Gall–Peters, or Behrmann projection). Values of γ that are favored by Tobler and others are generally greater than 2.