[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.
Regards,
Mikael Rittri
Carmenta
Sweden
http://www.carmenta.com
-----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
Mikael:
Here are a few quick observations...
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