I want to define a custom CRS for a very special, technical use-case. For that I use a WGS84-World-Mercator as base definition, here are the
proj4 parameters taken von QGIS:
+proj=merc +lon_0=0 +k=1 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs
For my custom CRS, I wish to have positive coordinates for any point in the world and all coordinates should be within the range of 0 and 1. The coordinate origin should be in the north-west corner of the Mercator.
To scale all coordinates within the range
[0, 1], I use the parameter
+to_meter=40075016.68557849 while leaving the scale factor
k_0=1 and removing the metric
+proj=merc +lon_0=0 +k_0=1 +to_meter=40075016.68557849 +x_0=0 +y_0=0 +datum=WGS84 +no_defs
So far, so good, now the tricky part: How to create a coordinate origin at the north-west corner (North Pole)? Taking pen and paper, I found the solution is setting
lon_0=-180, like that:
+proj=merc +lon_0=-180 +lat_0=90 +k_0=1 +to_meter=40075016.68557849 +x_0=0 +y_0=0 +datum=WGS84 +no_defs
However, that creates weird results:
+lat_0=90basicly does nothing to whatever value it gets set. Why?
+lon_0=-180does behave like setting it to plus +180°, but I explicitly want the negative value from a mathematical view.
I know that plus and minus 180° are the same meridian on the map, but technically the difference with the minus is important for me.
How to create a CRS with coordinate origin at the north-west corner of the Mercator projection and only positive coordinates throught out the whole map? Is inverting the y-axis the issue here? Is chosing a World Mercator as base the wrong approach?