Tobler hyperelliptical projection

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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.[1]

Overview[edit]

In the projection’s normal aspect,[2] 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[3] 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.

See also[edit]

References[edit]

  1. ^ Tobler, Waldo (1973). "The hyperelliptical and other new pseudocylindrical equal area map projections". Journal of Geophysical Research 78 (11): pp. 1753–1759. Bibcode:1973JGR....78.1753T. doi:10.1029/JB078i011p01753. 
  2. ^ The Tobler Hyperelliptical Projection on the Center for Spatially Integrated Social Science's site
  3. ^ "Superellipse" in MathWorld encyclopedia