[Proj] Intersection test for two geodesics goes wrong for very long distances

Mikael Rittri Mikael.Rittri at carmenta.com
Thu Feb 7 08:45:44 EST 2013

Thanks, Charles!

> (5) I've only thought about the intersection problem in the simple case
> where the end points and the intersection point all lie in a single
> [shd]emi-ellipsoid (for f small).  In that case, the ellipsoidal
> gnomonic projection allows you to find the intersection point in a few
> iterations (I think the convergence is quadratic, a la Newton).

Yes, that's a nice application of your accurate gnomonic.

> [shd]emi-ellipsoid 


> (6) I suspect that solving the general problem will end up being fairly
> complicated.

I was afraid of that. 
I suppose you are familiar with the article 

    L. E. Sjöberg,
    Intersections on the sphere and ellipsoid,
    Journal of Geodesy (2002) 76: 115-120.

He writes: "each of the problems of intersection ... is solved without any limitation of arc length." I tried to read it, but the math was beyond me.

Anyway, maybe I will write a program that searches for the worst case
(longest permissible lines) for Carmenta's intersection method. 


Mikael Rittri

-----Original Message-----
From: Charles Karney [mailto:charles.karney at sri.com] 
Sent: Tuesday, February 05, 2013 5:11 PM
To: Mikael Rittri
Cc: proj at lists.maptools.org
Subject: Re: Intersection test for two geodesics goes wrong for very long distances


Here are a few quick observations...

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