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| author | Charles Karney <charles.karney@sri.com> | 2020-10-22 13:53:45 -0400 |
|---|---|---|
| committer | Charles Karney <charles.karney@sri.com> | 2020-10-22 13:53:45 -0400 |
| commit | 5b72015b0aaca836ee0e8bf1f2da193574fe8ab1 (patch) | |
| tree | 17d2d1f291d9ed7b31218340715ef3f806b5bde2 /docs | |
| parent | 02ef4ed32e15ea386ad3285e72e1bb7e4c188f05 (diff) | |
| download | PROJ-5b72015b0aaca836ee0e8bf1f2da193574fe8ab1.tar.gz PROJ-5b72015b0aaca836ee0e8bf1f2da193574fe8ab1.zip | |
merc.rst: revert to ln instead of log.
Also define merc (resp. tmerc) as the conformal projection in which the
equator (resp. a chosen meridan} projects to a straight line at constant
scale.
Diffstat (limited to 'docs')
| -rw-r--r-- | docs/source/operations/projections/merc.rst | 13 | ||||
| -rw-r--r-- | docs/source/operations/projections/tmerc.rst | 2 |
2 files changed, 9 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) diff --git a/docs/source/operations/projections/tmerc.rst b/docs/source/operations/projections/tmerc.rst index 3b2a0190..7fed3846 100644 --- a/docs/source/operations/projections/tmerc.rst +++ b/docs/source/operations/projections/tmerc.rst @@ -5,6 +5,8 @@ Transverse Mercator ******************************************************************************** The transverse Mercator projection in its various forms is the most widely used projected coordinate system for world topographical and offshore mapping. +It is a conformal projection in which a chosen meridian projects to a +straight line at constant scale. +---------------------+----------------------------------------------------------+ | **Classification** | Transverse and oblique cylindrical | |