ELLIPSE region

Hi,

Looking more carefully about the ELLIPSE shape, the spherical ellipse seems to me to be perfectly defined -- why should it be ambiguous ? It seems to be effectively the intersection of the celestial sphere,
-- either with a cone having an elliptical section in the tangential

   plane with semi-axes tan(a) and tan(b)
-- or with a cylinder having an elliptical section with semi-axes

   sin(a) and sin(b)

The spherical ellipse is defined as the set of points M of the sphere having the sum of their distances to the 2 foci F and F' constant (MF + MF' = 2a). The limitations are: max(a,b) <=90deg; and the distance between the center of the ellipse and one focus F is given by

       cos(a) = cos(b).cos(c).

The fact that a point lies inside a spherical ellipse could be done by checking the sign of a quadratic formula applied on the cartesian coordinates (x,y,z) of that point, in a fashion similar to the planar ellipses.

Unless I missed something about this elliptical region ?

Cheers, Francois

Francois Ochsenbein       ------       Observatoire Astronomique de Strasbourg
   11, rue de l'Universite F-67000 STRASBOURG       Phone: +33-(0)390 24 24 29
Email: francois-at-astro.u-strasbg.fr   (France)         Fax: +33-(0)390 24 24 17
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