Cousin Ricky <ric### [at] yahoocom> wrote:
> On 2023-12-10 10:13 (-4), Bald Eagle wrote:
> >
> > So, having looked into inversive geometry, stereographic projection, Mobius
> > transforms, etc. - I think I recall seeing some examples of slightly different
> > ways of projecting the sphere's surface onto a plane.
>
> I suspect that there are an infinite number of such projections.
>
> > Not having delved into this topic to any real extent, are there different image
> > maps that might not result in a correctly mapped sphere?
>
> It all depends on the projection algorithms.
>
> > Or is the main problem just the cylindrical vs uv-mapping in the scene?
>
> In this particular case, it's just cylindrical vs uv-mapping.  The
> images were created in the equidistant cylindrical projection, so that
> is what I had to work with.
>
> > Also just curious if the sphere got scaled to be an oblate spheroid.
>
> The sphere is not scaled.  To account for oblateness, I'd have to know
> whether the maps were prepared with geocentric or geodedic latitudes,
> and *then* I'd have to remember how I handled the difference 30 years
> ago when I worked on USAF satellites.  And then a function would have to
> be applied to distort the image map in the north-south orientation.
>
> My head is already starting to hurt.



Great endeavor !

Indeed, almost as many projection systems... (That's how these calculations are
called in the GIS field (Geographical Information Systems aka modern
cartography))...As there are countries,
(https://en.wikipedia.org/wiki/Map_projection) not even counting the vertical
projection systems.

Each country wants to minimize distortions in its area. The world's shape is
also not much more of a sphere than a potato can be (latitudes vs longitudes
lengths, or Himalayas vs japan's deep seas) so for instance in France use the
Lambert 93 projection. And it's already a good thing that all of the country is
normalized to use the same.

Just as much as the language that "won" for international exchanges is English,
The encoding UTF8...
The projection that did so is WGS84
(https://en.wikipedia.org/wiki/World_Geodetic_System#WGS84)
So that's what anything without specified system is expected to be using (GPS,
etc...).

The awesome free software QGIS can convert between projections.
the hard thing for non specialists is to know were to look for the projection
system of some data when not specified, before converting it and not tempering
too much to avoid corrupting it.

The first thing to do is to search for a file next to the graphical data such as
a TIFF image. it could for instance be a file with the same name but ending with
*.PRJ

the other thing to do whether you have that file around or not is to look at the
numbers for coordinates of one entity in your data : opening it, selecting it,
zooming to it, moving cursor around, whatever software will always show you some
couple or tuple of numbers.

The X and Y value of a point, for a given projection will always be comprised
within some bounding limits in the country accustomed to use it again, in e.g.

France is within:
0 000 000>X>1 300 000
6 000 000>Y>7 200 000
(not that it matters but all in meters)

In fact if you actually know where this point is supposed to be, and provided no
data corruption has occurred, you can identify the original projection of some
data by entering its coordinates in the below tool, and choosing the point that
comes up at its right place:
https://app.dogeo.fr/Projection/#/point-to-coords


That's all folks ! enjoy your open data !

Post a reply to this message