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The Mathematics of Cartography

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Eric Marsh
Homebuilder or Craftsman
49
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#1 Posted: 9/8/2010 22:46:30

Can anyone here point me at some references to the mathematics of cartography? I'm playing with digitized sectional charts and because they are not "flat" i.e. the lines of latitude and longitude curve/converge I'm finding it a little challenging calculating geo-coordinates for a given pixel. Suggestions anyone?

Thanks,

Eric



Jon Wanzer
Vintage Aircraft Association MemberWarbirds of America MemberHomebuilder or Craftsman
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#2 Posted: 9/9/2010 11:49:06

Greetings Eric,

The simplest solution for a few reference points is to use Google Earth to determine the coordinates for a particular spot on earth. If you are looking at mapping a large number of points and depending on your application, a variety of GIS software applications are available and would be the route to take. 

As for the math, interpreting the coordinate is a matter spacing between perpendicular reference points, as close to perpendicular as possible anyway, with curving references. Its the same as it would be with a paper map, which while flat still has  curving reference points, hence the plethora of compass rose references on a sectional chart. There is also the matter of scale/resolution.

With a little more about the application you have in mind I could provide more useful information.

~Jon



FlyBoyJon ✈ Aviator, builder, and tool junkie ✈ jon@FlyBoyJon.comwww.FlyBoyJon.com
Eric Marsh
Homebuilder or Craftsman
49
Posts
7
#3 Posted: 9/9/2010 15:57:50 Modified: 9/9/2010 16:54:08

I'm trying to calculate the latitude and longitude for any pixel on a chart. I think I'm getting closer to the solution though. The charts are using a Lambert conforming conic projection. I found a formula for that at  http://mathworld.wolfram.com/LambertConformalConicProjection.html now I just need to code it, plug in some numbers and see if it works.


goggles

 



Jon Wanzer
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#4 Posted: 9/10/2010 11:07:00

Greetings Eric,

Is this an academic pursuit or for a specific application?

~Jon



FlyBoyJon ✈ Aviator, builder, and tool junkie ✈ jon@FlyBoyJon.comwww.FlyBoyJon.com
Eric Marsh
Homebuilder or Craftsman
49
Posts
7
#5 Posted: 9/10/2010 11:16:01 Modified: 9/10/2010 11:16:31

I'm planning on building an iPhone/iPad app and putting out on the iTunes app store. It's going to be very simple and inexpensive.

The map viewer is working great - it is very fast, does zooms and all that. But before I release it I think I need to integrate GPS.

 


 



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Bill Owens
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#6 Posted: 9/11/2010 13:37:52

Eric:

 

If you can find the IEEE Transactions on Aerospace and Electronic Systems, Vol 30, Number 3 (July 1994) in a local university library there is an article with all the mathematics of the ECEF (Earth-Centered Earth-Fixed) coordinates to geodetic coordinates defined.  The article is on page 957 and entitled, "Conversion of Earth Centered Earth Fixed Coordinates to Geodetic Coordinates."

If there isn't a library handy, you can Google for Eurocontrol's WGS 84 Implementation Manual that can be downloaded as a .pdf file.  It has Helmert's formula and other useful transformations given in Appendix E.

 

Hope this helps.  I do the transformations at work and its all to easy to make a mistake (watch for incorrect signs in your implementation of the equations)!




Eric Marsh
Homebuilder or Craftsman
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#7 Posted: 9/12/2010 09:56:41

Bill, thanks for the tip. I'll look it over. There's more to this than it would seem at first glimpse. I'm looking at Proj.4 and it seems promising.



Ron Natalie
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#8 Posted: 9/13/2010 16:56:53

Those charts are all in GEOTIFF encoding.    Just about everybody uses a piece of free code called  PROJ4 to map between the image X/Y to Lat/Lon.