Re: area enclosed by a poylgon on a sphere

[Struan Gray <struan.gray(at)sljus.lu.se>]

Ronn Kling, ronn@rlkling.com writes: 

> I found out how to do this today.  For a spherical 
> triangle the solid angle subtended is the sum (in 
> radians) of the interior angles  - Pi.

    I'm sure you probably know this, but it's worth pointing out that
the 'interior angles' are those measured on the surface of the sphere,
and not the angles between chords joining the points.  That is, you
can't plug the  cartesian coordinates of your vertices into the
familiar vector formulea for angles and distances.  Instead, you have
to construct the two great circles which bound each vertex and
calculate the complement of the angle between their normal vectors. 
For small areas on a large sphere it makes no difference, but the case
of three points spaced equally around, and just north of, the equator
makes the distinction clear: one method gives you zero, the other
gives 2*pi.

    One of the public IDL libraries (idlastro I *think*) has useful
utility routines for great circle calculations.


Struan