diff options
Diffstat (limited to 'docs/source/operations/projections/tmerc.rst')
| -rw-r--r-- | docs/source/operations/projections/tmerc.rst | 15 |
1 files changed, 11 insertions, 4 deletions
diff --git a/docs/source/operations/projections/tmerc.rst b/docs/source/operations/projections/tmerc.rst index fd600001..a52e4059 100644 --- a/docs/source/operations/projections/tmerc.rst +++ b/docs/source/operations/projections/tmerc.rst @@ -28,7 +28,7 @@ The transverse Mercator projection in its various forms is the most widely used .. figure:: ./images/tmerc.png :width: 500 px :align: center - :alt: Transverse Mercator + :alt: Transverse Mercator proj-string: ``+proj=tmerc`` @@ -79,7 +79,9 @@ Parameters .. versionadded:: 6.0.0 - Use faster, less accurate algorithm for the Transverse Mercator. + Use the algorithm described in section "Elliptical Form" below. + It is faster than the default algorithm, but also diverges faster + as the distance from the central meridian increases. .. include:: ../options/lon_0.rst @@ -98,7 +100,7 @@ Parameters Mathematical definition ####################### -The formulas describing the Transverse Mercator are all taken from Evenden's [Evenden2005]_. +The formulas describing the Transverse Mercator below are quoted from Evenden's [Evenden2005]_. :math:`\phi_0` is the latitude of origin that match the center of the map. It can be set with ``+lat_0``. @@ -148,6 +150,11 @@ Inverse projection Elliptical form *************** +The formulas below describe the algorithm used when giving the +:option:`+approx` option. They are originally from :cite:`Snyder1987`, +but here quoted from :cite:`Evenden1995`. +The default algorithm is given by Poder and Engsager in :cite:`Poder1998` + Forward projection ================== @@ -169,7 +176,7 @@ Forward projection .. math:: - x &= k_0 \lambda \cos \phi \\ + x &= k_0 \lambda \cos \phi \\ &+ \frac{k_0 \lambda^3 \cos^3\phi}{3!}(1-t^2+\eta^2) \\ &+ \frac{k_0 \lambda^5 \cos^5\phi}{5!}(5-18t^2+t^4+14\eta^2-58t^2\eta^2) \\ &+\frac{k_0 \lambda^7 \cos^7\phi}{7!}(61-479t^2+179t^4-t^6) |