daan wrote:Ah, I think I see what you mean. You want to be able to specify a great circle emanating from a particular point and going in a particular direction
Yes, that’s it!
daan wrote:but Geocart’s metric lines syntax does not provide for this case. That’s unfortunate.
I guess something like this is very
so it’s perfectly understandable that it isn’t provided.
On an overlay projection, you can turn off drawing parallels and then set the projection center so that the overlay’s graticule’s north pole coincides with the point you care about.
That’s what I did now – however I still can’t get a result that’s 100% accurate (see below).
The calculation to find the proper latitudinal, longitudinal, and transversal rotations is a little complicated. The easiest I can describe it is that you need to find the Euler angles via a concatenation of 3 3x3 rotational matrices multiplied against the Euclidean 3-vector that represents the geographic point.
Better don’t even try
to elaborate on this – it would be completely lost on me! *laugh*
daan wrote:If you’re only going to do this one time, then the method you seem to have used is probably easiest.
While I might
repeat this now and then, I’ll certainly not be doing this on regular basis. So I’m better off with the »two-maps-solution«.
Now, as I’ve said, my current result isn’t completely accurate.
It’s good enough for my purposes, which is simply giving an idea of how the great circles emanating from a particular point change on a different projection. So I could
stop at this point…
… but it really bugs me that I can’t get this done properly and fail to see where at which point I’m doing something wrong.
So, here we go:
The point of interest is 7.22° E and 51.47° N (I’m using decimal degrees here for the ease of typing).
The underlying map is Wagner IX, centered to [0,0]. It includes the coastlines, the meridian at 7.22° E and the parallel at 51.47° N, both printed in red.
The map layered on top of the is of course again Wagner IX, with following settings:
Drawing of parallels turned off, meridian spacing: 30°;
prime meridian: 7.22° E;
origin of longitude spacing: 7.22° E.
Graticule color is set to blue.
Latitudinal: 38.53°E (= 90 - 51.47)
Longitudinal: 3.61°E (= 7.22 / 2)
If I compare this to the azimuthal projection, i.e. take a look where the blue lines intersect with the coastlines, this seems to be right:
However, the point where the blue lines converge is a little bit off the junction of the red meridian + parallel:
I’ve tried various combinations of the settings mentioned above, but none of them do the trick.
So, where’s my error in thinking?
In case this helps, here’s the zipped .geo3 file
with the two Wagner projections, and for reference, the azimuthal equidistant version
(again, with two maps overlaid).