Tobler hyperelliptical projection: Difference between revisions
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In the projection’s normal aspect,<ref>[http://www.csiss.org/map-projections/Pseudocylindrical/Hyperelliptical.pdf The Tobler Hyperelliptical Projection on the Center for Spatially Integrated Social Science's site]</ref> the [[circle of latitude|parallels]] of [[latitude]] are parallel [[straight line]]s whose spacing is calculated to provide the equal-area property; the [[Meridian (geography)|meridian]]s 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''|<sup>γ</sup> + ''b''|''y''|<sup>γ</sup> = 1 (with ''a'' dependent on longitude and ''b'' constant for a given map), known as ''[[superellipse]]s''<ref>[http://mathworld.wolfram.com/Superellipse.html "Superellipse" in MathWorld encyclopedia]</ref> or Lamé curves. When γ |
In the projection’s normal aspect,<ref>[http://www.csiss.org/map-projections/Pseudocylindrical/Hyperelliptical.pdf The Tobler Hyperelliptical Projection on the Center for Spatially Integrated Social Science's site]</ref> the [[circle of latitude|parallels]] of [[latitude]] are parallel [[straight line]]s whose spacing is calculated to provide the equal-area property; the [[Meridian (geography)|meridian]]s 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''|<sup>γ</sup> + ''b''|''y''|<sup>γ</sup> = 1 (with ''a'' dependent on longitude and ''b'' constant for a given map), known as ''[[superellipse]]s''<ref>[http://mathworld.wolfram.com/Superellipse.html "Superellipse" in MathWorld encyclopedia]</ref> 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 projection|Lambert cylindrical equal-area]], [[Gall–Peters projection|Gall–Peters]], or [[Behrmann projection]]). Values of γ that are favored by Tobler and others are generally greater than 2. |
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==References== |
==References== |
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Revision as of 18:15, 31 July 2013
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]
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.
References
- ^ 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.
{{cite journal}}:|pages=has extra text (help) - ^ The Tobler Hyperelliptical Projection on the Center for Spatially Integrated Social Science's site
- ^ "Superellipse" in MathWorld encyclopedia