Page History: Transverse Mercator on the ellipsoid (TME)
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Page Revision: 2010/10/04 12:52
Radfearn's transformation formulae
TME is derived as a series by a complex transformation from the NME projection.
![Image](GetFile.aspx?File=/MWME/nme-to-tme.png)
The direct series for x and y
![Image](GetFile.aspx?File=/MWME/direct-series.png)
The inverse series for
![Image](GetFile.aspx?File=/MWME/f1.png)
and
![Image](GetFile.aspx?File=/MWME/f2.png)
![Image](GetFile.aspx?File=/MWME/inverse-series.png)
Direct
![Image](GetFile.aspx?File=/MWME/direct.png)
Inverse
![Image](GetFile.aspx?File=/MWME/inverse.png)
where
![Image](GetFile.aspx?File=/MWME/where.png)
Condition
1.
![Image](GetFile.aspx?File=/MWME/m1.png)
where the coefficients are given by
![Image](GetFile.aspx?File=/MWME/given.png)
If we use the numerical values for the Airy ellipsoid, then , in meteres,
![Image](GetFile.aspx?File=/MWME/m2.png)
2. Function
![Image](GetFile.aspx?File=/MWME/f3.png)
and
![Image](GetFile.aspx?File=/MWME/f4.png)
are defined in
![Image](GetFile.aspx?File=/MWME/vb.png)
3.
![Image](GetFile.aspx?File=/MWME/f2.png)
is measured on radians from central meridian
4. The subscripted terms in the inverse series are to be evaluated at the footpoint latitude
![Image](GetFile.aspx?File=/MWME/f5.png)
such that
![Image](GetFile.aspx?File=/MWME/f6.png)
Document
The MERCATOR projections