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[[File:Bonne projection SW.jpg|450px|thumb|Bonne projection of the world, standard parallel at 45°N.]] | |||
[[File:Sylvanus map 1511.jpg|300px|thumb|World map by Bernard Sylvanus, 1511]] | |||
A '''Bonne projection''' is a pseudoconical equal-area [[map projection]], sometimes called a '''dépôt de la guerre''' or a '''Sylvanus'''{{citation needed|date=May 2012}} projection. Although named after [[Rigobert Bonne]] (1727–1795), the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696. Both Sylvano and Honter’s usages were approximate, however, and it is not clear they intended to be the same projection.<ref>''Flattening the Earth: Two Thousand Years of Map Projections'', John P. Snyder, 1993, pp.60-62, ISBN 0-226-76747-7</ref> | |||
The projection is: | |||
:<math>x = \rho \sin E\,</math> | |||
:<math>y = \cot \varphi_1 - \rho \cos E\,</math> | |||
where | |||
:<math>\rho = \cot \varphi_1 + \varphi_1 - \varphi\,</math> | |||
:<math>E = \frac {(\lambda - \lambda_0) \cos \varphi} {\rho}</math> | |||
and φ is the latitude, λ is the longitude, λ<sub>0</sub> is the longitude of the central meridian, and φ<sub>1</sub> is the standard parallel of the projection.<ref>[http://pubs.er.usgs.gov/usgspubs/pp/pp1395 ''Map Projections - A Working Manual''], [[United States Geological Survey|USGS]] Professional Paper 1395, John P. Snyder, 1987, pp.138-140</ref> | |||
Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. On the [[meridian (geography)|central meridian]] and the standard latitude shapes are not distorted. | |||
The inverse projection is given by: | |||
:<math>\varphi = \cot \varphi_1 + \varphi_1 - \rho\,</math> | |||
:<math>\lambda = \lambda_0 + \rho \{ \arctan [ x / ( \cot \varphi_1 - y)] \} / \cos \varphi</math> | |||
where | |||
:<math> \rho = </math>± <math>[ x^2 + ( \cot \varphi_1 - y)^2 ]^{1/2}</math> | |||
taking the sign of <math>\varphi_1</math>. | |||
Special cases of the Bonne projection include the [[sinusoidal projection]], when φ<sub>1</sub> is zero, and the [[Werner projection]], when φ<sub>1</sub> is π/2. The Bonne projection can be seen as an intermediate projection in the unwinding of a [[Werner projection]] into a [[Sinusoidal projection]]; an alternative intermediate would be a [[Bottomley projection]]<ref>[http://www.cybergeo.eu/index3977.html Between the Sinusoidal projection and the Werner: an alternative to the Bonne], Henry Bottomley 2002</ref> | |||
==See also== | |||
{{Portal|Atlas}} | |||
* [[List of map projections]] | |||
==References== | |||
<references/> | |||
==External links== | |||
*[http://www.cybergeo.eu/index3977.html Cybergeo article] | |||
*[http://exchange.manifold.net/manifold/manuals/5_userman/mfd50Bonne.htm Bonne Map Projection (manifold.net)] | |||
* [http://www.radicalcartography.net/?projectionref Table of examples and properties of all common projections], from radicalcartography.net | |||
* [http://www.uff.br/mapprojections/Bonne_en.html An interactive Java Applet to study the metric deformations of the Bonne Projection] | |||
* [http://mathworld.wolfram.com/BonneProjection.html Bonne Projection (wolfram.com)] | |||
{{Map Projections}} | |||
{{DEFAULTSORT:Bonne Projection}} | |||
[[Category:Cartographic projections]] | |||
[[Category:Equal-area projections]] | |||
{{Cartography-stub}} | |||
Revision as of 20:56, 28 October 2013
A Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre or a SylvanusPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. projection. Although named after Rigobert Bonne (1727–1795), the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696. Both Sylvano and Honter’s usages were approximate, however, and it is not clear they intended to be the same projection.[1]
The projection is:
where
and φ is the latitude, λ is the longitude, λ0 is the longitude of the central meridian, and φ1 is the standard parallel of the projection.[2]
Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. On the central meridian and the standard latitude shapes are not distorted.
The inverse projection is given by:
![{\displaystyle \lambda =\lambda _{0}+\rho \{\arctan[x/(\cot \varphi _{1}-y)]\}/\cos \varphi }](https://wikimedia.org/api/rest_v1/media/math/render/svg/7c782257558dc3f47bae6e8573c0c391336516fc)
where
- ±
![{\displaystyle [x^{2}+(\cot \varphi _{1}-y)^{2}]^{1/2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f60a7e95d22870a7196c1d0e0ced17d3ab7a5cc1)
taking the sign of .
Special cases of the Bonne projection include the sinusoidal projection, when φ1 is zero, and the Werner projection, when φ1 is π/2. The Bonne projection can be seen as an intermediate projection in the unwinding of a Werner projection into a Sinusoidal projection; an alternative intermediate would be a Bottomley projection[3]
See also
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References
- ↑ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp.60-62, ISBN 0-226-76747-7
- ↑ Map Projections - A Working Manual, USGS Professional Paper 1395, John P. Snyder, 1987, pp.138-140
- ↑ Between the Sinusoidal projection and the Werner: an alternative to the Bonne, Henry Bottomley 2002