Sinusoidal projection: Difference between revisions
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en>Chienlit ==See also== {{Portal|Atlas}} * List of map projections |
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[[File:Bottomley projection SW.JPG|450px|thumb|Bottomley projection of the world with standard parallel at 30°N.]] | |||
The Bottomley map projection is an [[map projection#Equal-area|equal area map projection]] | |||
defined as: | |||
:<math>x = \frac{\rho \sin E }{ \sin \phi_1} \,</math> | |||
:<math>y = \tfrac{\pi}{2} - \rho \cos E \,</math> | |||
where | |||
:<math>\rho = \tfrac{\pi}{2} - \phi\,</math> | |||
:<math>E = \frac {\lambda \sin \phi_1 \sin \rho} {\rho}</math> | |||
and φ is the latitude, λ is the longitude from the central meridian, and φ<sub>1</sub> is the given parallel of the projection which determines its shape, all in radians. | |||
Parallels (i.e. lines of latitude) are concentric [[ellipse|elliptical]] arcs of constant [[eccentricity (mathematics)|eccentricity]], centred on the [[north pole]]. On the central [[meridian (geography)|meridian]], shapes are not distorted, but elsewhere they are. Different projections can be produced by altering the eccentricity of the arcs, making it vary between the [[sinusoidal projection]] and the [[Werner projection]]. | |||
It was introduced by [[Henry Bottomley]] as an alternative to the [[Bonne projection]] to reduce the extent of extreme distortion at the edges and give a more satisfying overall shape. | |||
==See also== | |||
{{Portal|Atlas}} | |||
* [[List of map projections]] | |||
==External links== | |||
*[http://www.cybergeo.eu/index3977.html Cybergeo article] | |||
{{Map Projections}} | |||
[[Category:Cartographic projections]] | |||
[[Category:Equal-area projections]] | |||
{{Cartography-stub}} |
Revision as of 02:43, 22 December 2013
The Bottomley map projection is an equal area map projection defined as:
where
and φ is the latitude, λ is the longitude from the central meridian, and φ1 is the given parallel of the projection which determines its shape, all in radians.
Parallels (i.e. lines of latitude) are concentric elliptical arcs of constant eccentricity, centred on the north pole. On the central meridian, shapes are not distorted, but elsewhere they are. Different projections can be produced by altering the eccentricity of the arcs, making it vary between the sinusoidal projection and the Werner projection.
It was introduced by Henry Bottomley as an alternative to the Bonne projection to reduce the extent of extreme distortion at the edges and give a more satisfying overall shape.
See also
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