[GRASS-user] OFF-TOPIC - Earth Curvature in profiles

[Michael Perdue]

If I understand you correctly, you want to draw a topographic profile  
superimposed on an arc representing the curvature of the earth? What  
you want to do then is show the orthogonal distance of each sample  
from the chord defined by the start and end point of profile. You can  
try as follows but you'll have to work out the details;

1.) Plot a great circle line between your intended start and end points.
2.) Trace the path that the great circle line follows with r.profile  
and have it save the results to an xyz file. (the inability to sample  
along the great circle exactly will introduce some errors).
3.) Multiply z by 200 (note that to be technically correct you should  
change your sampled elevations from orthometric to ellipsoidal, but  
the magnitude of the errors introduced will likely be insignificant on  
the overall scale).
4.) Convert your xyz values to ECEF.
5.) Now, the vector between your start and end points in the ECEF  
coordinate system will represent a chord so a little trigonometry  
applied to the problem will allow you to calculate the orthogonal  
distance between the sample and the chord (ie, apply a rotation matrix  
so that the chord will be coincident with the x-axis of your plot).
6.) Plot your new values in any plotting software.

Clear as mud? The explanation is a little spartan, but it should get  
you started.

Cheers,

Mike


On 10-Jan-08, at 2:06 PM, Carlos Guâno Grohmann wrote:

> Sorry for the OT, but can anyone point me some reference (paper, web,
> etc) that explains how can I draw a topographic profile using the
> Earth´s curvature? I am thiking about the output of r.profile (ascii,
> distance from origin + elevation), in a section of about 3000 km, with
> a vertical exaggeration of about 200 times.
>
> tks!
>
> Carlos
>
> -- 
> +-----------------------------------------------------------+
>              Carlos Henrique Grohmann - Guano
>  Geologist M.Sc  - Doctorate Student at IGc-USP - Brazil
> Linux User #89721  - carlos dot grohmann at gmail dot com
> +-----------------------------------------------------------+
> _________________
> "Good morning, doctors. I have taken the liberty of removing Windows
> 95 from my hard drive."
> --The winning entry in a "What were HAL's first words" contest judged
> by 2001: A SPACE ODYSSEY creator Arthur C. Clarke
>
> Can't stop the signal.
> _______________________________________________
> grass-user mailing list
> grass-user at lists.osgeo.org
> http://lists.osgeo.org/mailman/listinfo/grass-user