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. The projection blends the cylindrical equal-area projection with meridians of longitude that follow a particular kind of curve known as superellipses^[3] or Lamé curves or sometimes as hyperellipses. The curve is described by x^k + y^k = γ^k. The relative weight of the cylindrical equal-area projection is given as α, ranging from all cylindrical equal-area with α = 1 to all hyperellipses with α = 0.

When α = 0 and k = 1 the projection degenerates to the Collignon projection; when α = 0, k = 2, and γ ≈ 1.2731 the projection becomes the Mollweide projection.^[4] Tobler favored the parameterization shown with the illustration; that is, α = 0, k = 2.5, and γ = 1.183136.

See also

• List of map projections

References