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Diffstat (limited to 'docs/source/operations/projections/merc.rst')
| -rw-r--r-- | docs/source/operations/projections/merc.rst | 13 |
1 files changed, 7 insertions, 6 deletions
diff --git a/docs/source/operations/projections/merc.rst b/docs/source/operations/projections/merc.rst index 62aa5bc9..c474009f 100644 --- a/docs/source/operations/projections/merc.rst +++ b/docs/source/operations/projections/merc.rst @@ -6,9 +6,10 @@ Mercator The Mercator projection is a cylindrical map projection that origins from the 15th century. It is widely recognized as the first regularly used map projection. -The projection has the property that a rhumb line, a course of constant -heading, projects to a straight line. This makes it suitable for -navigational purposes. +It is a conformal projection in which the equator projects to a straight +line at constant scale. The projection has the property that a rhumb +line, a course of constant heading, projects to a straight line. This +makes it suitable for navigational purposes. +---------------------+----------------------------------------------------------+ @@ -99,7 +100,7 @@ Forward projection .. math:: - \psi &= \log \tan \biggl(\frac{\pi}{4} + \frac{\phi}{2} \biggr)\\ + \psi &= \ln \tan \biggl(\frac{\pi}{4} + \frac{\phi}{2} \biggr)\\ &= \sinh^{-1}\tan\phi The quantity :math:`\psi` is the isometric latitude. @@ -143,9 +144,9 @@ Forward projection .. math:: - \psi &= \log\tan\biggl(\frac\pi4 + \frac{\phi}2\biggr) + \psi &= \ln\tan\biggl(\frac\pi4 + \frac{\phi}2\biggr) -\frac12 e - \log \biggl(\frac{1 + e \sin\phi}{1 - e \sin\phi}\biggr)\\ + \ln \biggl(\frac{1 + e \sin\phi}{1 - e \sin\phi}\biggr)\\ &= \sinh^{-1}\tan\phi - e \tanh^{-1}(e \sin\phi) |