Sinusoidal projection: Difference between revisions
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[[Image:Sinusoid-projection.jpg|thumb|384px|right|Sinusoidal projection of the [[Earth]].]] |
[[Image:Sinusoid-projection.jpg|thumb|384px|right|Sinusoidal projection of the [[Earth]].]] |
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The '''sinusoidal projection''' is a pseudocylindrical [[Map_projection#Equal-area|equal-area]] [[map projection]], sometimes called the ''' |
The '''sinusoidal projection''' is a pseudocylindrical [[Map_projection#Equal-area|equal-area]] [[map projection]], sometimes called the '''Sanson–Flamsteed''' or the '''Mercator equal-area projection'''. It is defined by: |
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:<math>x = \left(\lambda - \lambda_0\right) \cos \phi</math> |
:<math>x = \left(\lambda - \lambda_0\right) \cos \phi</math> |
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:<math>y = \phi\,</math> |
:<math>y = \phi\,</math> |
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where <math>\phi\,</math> is the latitude, <math>\lambda\,</math> is the longitude, and <math>\lambda_0\,</math> is the central meridian.<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. |
where <math>\phi\,</math> is the latitude, <math>\lambda\,</math> is the longitude, and <math>\lambda_0\,</math> is the central meridian.<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. 243–248</ref> |
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The north-south scale is the same everywhere at the central [[meridian (geography)|meridian]], and the east-west scale is throughout the map the same as that; correspondingly, on the map, as in reality, the length of each parallel is proportional to the cosine of the latitude; thus the shape of the map for the whole earth is the area between two symmetric rotated cosine curves. The true distance between two points on the same meridian corresponds to the distance on the map between the two parallels, which is smaller than the distance between the two points on the map. There is no distortion on the central meridian or the [[equator]]. |
The north-south scale is the same everywhere at the central [[meridian (geography)|meridian]], and the east-west scale is throughout the map the same as that; correspondingly, on the map, as in reality, the length of each parallel is proportional to the cosine of the latitude; thus the shape of the map for the whole earth is the area between two symmetric rotated cosine curves. The true distance between two points on the same meridian corresponds to the distance on the map between the two parallels, which is smaller than the distance between the two points on the map. There is no distortion on the central meridian or the [[equator]]. |
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[[Image:Usgs map sinousidal equal area.PNG|350px|thumb|right|center|A sinusoidal projection shows relative sizes accurately, but distorts shapes and directions. Distortion can be reduced by "interrupting" the map.]] |
[[Image:Usgs map sinousidal equal area.PNG|350px|thumb|right|center|A sinusoidal projection shows relative sizes accurately, but distorts shapes and directions. Distortion can be reduced by "interrupting" the map.]] |
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[[Image:Tissot_indicatrix_world_map_sinusoidal_proj.svg|thumb|right|350px|The sinusoidal projection with [[Tissot's |
[[Image:Tissot_indicatrix_world_map_sinusoidal_proj.svg|thumb|right|350px|The sinusoidal projection with [[Tissot's indicatrix]] of deformation]] |
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Similar projections which wrap the east and west parts of the sinusoidal projection around the [[north pole]] are the [[Werner projection|Werner]] and the intermediate [[Bonne projection|Bonne]] and [[Bottomley projection]]s. |
Similar projections which wrap the east and west parts of the sinusoidal projection around the [[north pole]] are the [[Werner projection|Werner]] and the intermediate [[Bonne projection|Bonne]] and [[Bottomley projection]]s. |
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[[Category:Equal-area projections]] |
[[Category:Equal-area projections]] |
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[[Category:Equidistant projections]] |
[[Category:Equidistant projections]] |
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{{Cartography-stub}} |
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[[ca:Projecció sinusoidal]] |
[[ca:Projecció sinusoidal]] |
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Revision as of 23:16, 5 June 2011
The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson–Flamsteed or the Mercator equal-area projection. It is defined by:
where is the latitude, is the longitude, and is the central meridian.[1]
The north-south scale is the same everywhere at the central meridian, and the east-west scale is throughout the map the same as that; correspondingly, on the map, as in reality, the length of each parallel is proportional to the cosine of the latitude; thus the shape of the map for the whole earth is the area between two symmetric rotated cosine curves. The true distance between two points on the same meridian corresponds to the distance on the map between the two parallels, which is smaller than the distance between the two points on the map. There is no distortion on the central meridian or the equator.
Similar projections which wrap the east and west parts of the sinusoidal projection around the north pole are the Werner and the intermediate Bonne and Bottomley projections.
References
- ^ Map Projections—A Working Manual, USGS Professional Paper 1395, John P. Snyder, 1987, pp. 243–248
External links
- Cybergeo article
- Table of examples and properties of all common projections, from radicalcartography.net