[Gdal-dev] Projected vs Geographic Coordinate Systems

[Peter Morgan]

Hi everyone
I would like to add some additional information to the discussion.

In normal mapping/cartography as implied with a cylindrical or conic 
section the center of projection, COP, is the center of the Earth. The 
aim was to project the Earth onto a surface that could be "laid flat". 
When we use raw longitudes and latitudes we imply a special form of 
these projections and we normally don't care about the distortions. 
These  projections have many useful characteristics. Some have equal 
area, useful for comparative studies especially density or yields. 
Others are conformal where angular relationships are maintained. Yes we 
can compute distances and perform a host of geo-statical functions from 
a longitude and latitude tuple on the ellipsoid but it is much simpler 
in say a UTM projection especially if the area is of limited extent. 
There are lots of Cartographic references available for this 
information. Two highly recommended references are:
*Richardus*, P. & *Adler*, R K. (1972). Map Projections for Geodesists, 
Cartographers & Geographers. London. North-Holland Publishing Company  
(Old but good introductory text. Details all the basic cartographic theory.)
*Snyder*, J.P. (1987). Map Projections - A Working Manual. U.S. 
Geological Survey Professional Paper 1395, United States Government 
Printing Office, Washington D.C..  (Very good, very detailed with examples.)
The references in Snyder will provide you with more detail should you 
want this info.

The  GMT package, like most GIS suites, implements most of the common 
projections. One of the features of the GMT package is the ease of 
generating a projection . The documentation is especially useful here 
and it gives visual examples of the projections without the need to go 
in the projection mathematics. See
 http://gmt.soest.hawaii.edu/

Computer Graphics is all about projections. In this case it is from a 
three dimensional (usually Cartesian) space to a flat image space, our 
screens. The COP in most of these cases is external to the body being 
projected. It is the COP that moves around the body or in the case of 
fly throughs that moves on a trajectory that simulates travel. A very 
good coverage of projection theory is given in
*Foley*, J.D., *van Dam*, A.*,  Feiner*, S.K., and* Hughes*, J.F. 
(1990), Computer Graphics, Principles and Practice, 2nd Ed, Addison Wesley.
This is quite old as well. Apologies for not knowing the current crop of 
texts.

The azimuthal class of cartographic projections are consistent with 
computer graphics perspective projections. The often used perspective 
projection is consistent with both vision and the camera.

It is often more convenient to transform geographic 
coordinates(longitude, latitude and height) to plane coordinates such as 
UTM coordinates  or a simple Mercator and then to employ computer 
graphics principles of projection on these transformed values. There are 
many reasons for this with speed and complexity issues dominating.

Hope this might provide a starting point for continued enjoyment and 
understanding.
cheers peter


Simon Perkins wrote:
> Frank Warmerdam wrote:
>>> I guess I've just been spoiled by playing with Google Earth too 
>>> much... :)
>>
>> To the best of my knowledge Google Earth has one display project
>> (some sort of Mercator) and it reprojects everything to that.  That
>> approach is fine too if you are willing to reproject everything - either
>> in advance or on the fly.  Many apps will allow you to do this too if 
>> you
>> want.
>
> I think that google maps does everything in Mercator, but google earth
> allows you to view the entire globe, spin it around and view the poles,
> so my feeling is it must be doing something more cunning.
>
> According to wikipedia, GE uses a geographic coordinate system
> internally, and projects everything to a general perspective projection
> for display. I would guess though that it just texture maps
> (non-rectangular) geographic tiles onto a 3D sphere and then lets OpenGL
> take care of displaying things. Although it is possible to view the
> poles in GE, there is definitely weird stuff happening there - there
> appear to be very narrow triangular tiles. Anyway, it's all pretty 
> cool...
>
> http://en.wikipedia.org/wiki/Google_earth
>
>
> Cheers,
>
> Sy
>
>
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