Module talk:Location map/data/NATO: Difference between revisions

Revision as of 00:45, 7 July 2024

Revision as of 12:14, 2 October 2024

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{{WikiProject Maps}}

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== Formulae after cropping ==

I find it difficult to understand the vertical stretch factor 575/324 in the formula for y introduced in [https://en.wikipedia.org/w/index.php?title=Module:Location_map/data/NATO&diff=prev&oldid=1212692713 this edit].

If I am not mistaken [[:File:NATO Territory Map.svg]] is a derivative of [[:File:North Atlantic Ocean laea ___location map.svg]] by cropping the lower border at 324/575 = 56.3478260869565%.

Imho this operation on a map with [[Lambert azimuthal equal-area projection]] cannot be compensated for by adding some vertical stretch factor but it requires the correction of the parameters <math>px_0</math>, <math>py_0</math>, <math>dx</math> and <math>dy</math>.

The upper right corner of the map remains at lat = 71.02192702284165 N; lon = 38.61651360858501 E and the projection center remains at lat = 35 N; lon = 35 W. The projection of the upper right corner remains at

:<math>X_{UR} =0.97716044 \text{; } Y_{UR} =0.82614817</math>

However, the lower left corner moves to approximately lat = 14.35 N; lon = 96.55 W. Conversion of the lower left corner with the <code>proj</code> tool:

:

proj +proj=laea +lat_0=35 +lon_0=-35 +a=1 -f %.8f

-96.55 14.35

'''-0.97701214 -0.07076885'''

:<math>X_{LL} =-0.97701214 \text{; } Y_{LL} =-0.07076885</math>

From these values the projection parameters can be computed as:

:<math>px_0 = -100 \frac{X_{LL}}{X_{UR}-X_{LL}} = -100 \frac{-0.97701214}{0.97716044 - -0.97701214} = 49.9962</math>

:<math>py_0 = 100 \times \left(1+ \frac{Y_{LL}}{Y_{UR}-Y_{LL}}\right) = 100 \times \left(1+ \frac{-0.07076885}{0.82614817 - -0.07076885}\right) = 92.1098</math>

:<math>dx = \frac 1 {X_{UR}-X_{LL}} = \frac 1 {0.97716044 - -0.97701214} = 0.5117</math>

:<math>dy = \frac 1 {Y_{UR}-Y_{LL}} = \frac 1 {0.82614817 - -0.07076885} = 1.1149</math>

[[User:Spischot|Spischot]] ([[User talk:Spischot|talk]]) 12:14, 2 October 2024 (UTC)