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:<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)
:After spending some more time thinking I do now consider the vertical stretching by factor 575/324 as correct. All positions in the upper 324/575 part of the original map (y between 0% and 56.3...%) are strechteched out to extend vertically over all (0% - 100%) of the new, cropped map.
:How does this relate to my computation of the new factors above?
:The formula for
::<math>y = \frac{575}{324} \times ((100 - 48.0905) - 62.8332 \times \dotsb)</math>
:can be simplified as
::<math>y = \frac{575}{324} \times (51.9095 - 62.8332 \times \dotsb)</math>
::<math>= \frac{575 \times 51.9095}{324} - \frac{575 \times 62.8332}{324} \times \dotsb</math>
::<math>= 92.1234 - 111.5096 \times \dotsb</math>
:so the projection parameters are actually
::vertical projection center <math>py_0 = 92.1234</math>
::vertical scaling <math>dy = 1.115096</math>
:which are pretty close to my computation above. The diviation of 0.015% was caused by my approximation of the new lower left corner. [[User:Spischot|Spischot]] ([[User talk:Spischot|talk]]) 09:40, 3 October 2024 (UTC)
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