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| [[File:Cassini projection SW.jpg|thumb|Cassini projection of the world]] | | Jayson Berryhill is how I'm called [http://www.seekavideo.com/playlist/2199/video/ psychic readings online] and my wife doesn't like it at all. For years he's been living in Mississippi and he doesn't plan on altering it. One of the very very best things in the world for him is doing ballet and he'll be starting some thing else along with it. My working day job is an invoicing officer but I've already utilized for an additional one.<br><br>Feel free to surf to my page - good [http://www.khuplaza.com/dent/14869889 cheap psychic readings] ([http://checkmates.co.za/index.php?do=/profile-56347/info/ my website]) |
| The '''Cassini projection''' is a [[map projection]] described by [[César-François Cassini de Thury]] in 1745.<ref>''Flattening the Earth: Two Thousand Years of Map Projections'', John P. Snyder, 1993, pp. 74–76, ISBN 0-226-76747-7.</ref> It is the [[:wikt:transverse|transverse]] aspect of the [[equirectangular projection]], in that the globe is first rotated so the central meridian becomes the "equator", and then the normal equirectangular projection is applied. Composing these operations:
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| :<math>x = \arcsin(\cos(\phi)\sin(\lambda))\,</math>
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| :<math>y = \arctan\left(\frac{\tan(\phi)}{\cos(\lambda)}\right)</math>
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| where <math>\lambda</math> is the longitude from the central meridian and <math>\phi</math> is the latitude. When programming these equations, the [[inverse tangent]] function used is actually the [[atan2]] function, with the first argument <math>\sin(\phi)</math> and the second <math>\cos(\phi)\cos(\lambda)</math>.
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| The use of the Cassini projection has largely been superseded by the [[Transverse Mercator]] projection, at least with central mapping agencies.
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| ==Distortions==
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| Things along the central meridian, and at right angles to it, are not distorted. Elsewhere, the distortion is largely in a north-south direction, and varies by the square of the distance from the central meridian. As such, the greater the longitudinal extent of the area, the worse the distortion becomes.
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| Due to this, the Cassini projection works best on long, narrow areas, and worst on wide areas.
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://www.radicalcartography.net/?projectionref Table of examples and properties of all common projections], from radicalcartography.net
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| * [http://www.ordnancesurvey.co.uk/oswebsite/freefun/geofacts/geo1164.html Ordnance Survey GeoFacts on the Cassini Projection]
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| {{Map Projections}}
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| {{DEFAULTSORT:Cassini Projection}}
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| [[Category:Cartographic projections]]
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| {{Cartography-stub}}
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