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 top illustration; that is, *α* = 0, *k* = 2.5, and *γ* = 1.183136.

## See also

## References

**^**Snyder, John P. (1993).*Flattening the Earth: 2000 Years of Map Projections*. Chicago: University of Chicago Press. p. 220.**^**The Tobler Hyperelliptical Projection on the Center for Spatially Integrated Social Science's site**^**"Superellipse" in MathWorld encyclopedia**^**Tobler, Waldo (1973). "The hyperelliptical and other new pseudocylindrical equal area map projections".*Journal of Geophysical Research*.**78**(11): 1753–1759. Bibcode:1973JGR....78.1753T. CiteSeerX 10.1.1.495.6424. doi:10.1029/JB078i011p01753.