[Octave-patch-tracker] [patch #9958] [octave forge](mapping) gcxgc

[Philip Nienhuis]

Follow-up Comment #9, patch #9958 (project octave):

This condition at L.129:

:
  elseif (sind (rad2deg (vect(:, 1))) ==  sind (rad2deg (vect(:, 4))) &&
          sind (rad2deg (vect(:, 2))) == -sind (rad2deg (vect(:, 5))))
warning("gcxgc: Non-unique intersection.\n")


is too simple.
I think the only reliable way to detect coinciding great circles is to compare
the (Lat, Lon) values of their poles at the surface of the sphere (i.e., the
cross product of those polar axes).
Those can easily be deduced by the cross products of the input points and
inferred points e.g., a quarter of the circumference away on the great
circles. Or maybe directly from the given (Lat, Lon) points + azimuths, but I
couldn't find an expression for the latter on the web. (And TBH my own
spherical trig textbook is too thick :-) last time I seriously looked in it
was 45 years ago at high school when I did a navigation project for
geography.)


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