Equirectangular projection: Difference between revisions

Revision as of 18:19, 3 January 2021

Revision as of 19:21, 18 March 2021

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==Definition==

The forward projection transforms spherical coordinates into planar coordinates. The reverse projection transforms from the plane back onto the sphere. The formulae presume a [[Figure of the Earth|spherical model]] and use these definitions:

:*<math>\lambda</math> is the [[longitude]] of the ___location to project;

:*<math>\varphi</math> is the [[latitude]] of the ___location to project;

:*<math>\varphi_1</math> are the standard parallels (north and south of the equator) where the scale of the projection is true;

:*<math>\varphi_0</math> is the central parallel of the map;

:*<math>\lambda_0</math> is the central meridian of the map;

:*<math>x</math> is the horizontal coordinate of the projected ___location on the map;

:*<math>y</math> is the vertical coordinate of the projected ___location on the map;

:*<math>R</math> is the radius of the globe.

Longitude and latitude variables are defined here in terms of radians.

===Forward===

:<math>\begin{align}

x &= R (\lambda - \lambda_0) \cos \varphi_1\\

y &= R (\varphi - \varphi_0)

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===Reverse===

:<math>\begin{align}

\lambda &= \frac{x} {R \cos \varphi_1} + \lambda_0\\

\varphi &= \frac{y} {R} + \varphi_0