DALI 1.1 and Ellipse

[Francois Ochsenbein]

Well, the definition of the ellipse on a sphere is not ambiguous at all, it is defined as
the set of points on the sphere which have a constant sum of the (spherical) distances to
2 points (the foci) located on the sphere. Like the planar distance; one can define the
semi-major axis a, the semi-minor axis b, and if 2c = distance between the 2 foci, the
relation between the 3 distances is   cos a = cos b cos c (instead of the planar ellipse
relation a²=b²+c²).

Cheers,
François Ochsenbein

Le 09/05/2016 16:24, Arnold Rots a écrit :
> The current STC standard contains the following language in Section 4.5.1.3 on this subject:
>
>
>         Ellipse
>
> The Ellipse (2-dimensional) is similar to the Circle but has, in addition, a minor radius and a position angle. Position angles are measured following the definition in Section 4.4.1.2.5 and refer to the first axis. The definition of an ellipse in a Cartesian coordinate system is unambiguous, but this is not the case for spherical coordinates. In a spherical coordinate system the ellipse shall be defined as the intersection of an elliptical cone with the unit sphere, where the axes and position angle describe the geometry of the cone.
>
>
>
> Which is the second option you mention.
> Considering that we have agreed on that in the past, I would suggest that we stick with that.
>
> Cheers,
>
>   - Arnold
>
> -------------------------------------------------------------------------------------------------------------
> Arnold H. Rots Chandra X-ray Science Center
> Smithsonian Astrophysical Observatory tel:  +1 617 496 7701
> 60 Garden Street, MS 67   fax:  +1 617 495 7356
> Cambridge, MA 02138 arots at cfa.harvard.edu <mailto:arots at cfa.harvard.edu>
> USA http://hea-www.harvard.edu/~arots/ <http://hea-www.harvard.edu/%7Earots/>
> --------------------------------------------------------------------------------------------------------------
>
>
> On Mon, May 9, 2016 at 6:29 AM, Walter Landry <wlandry at caltech.edu <mailto:wlandry at caltech.edu>> wrote:
>
>     Hi Everyone,
>
>     I noticed the question in DALI 1.1 about whether we should add an
>     Ellipse type.  We already sort of support ellipses in our TAP service
>     because we have users that need it.  So it would be nice to add it to
>     the spec.
>
>     However, I think we might have a problem with how to define it.
>     pgSphere defines an ellipse as
>
>       If the center of any spherical ellipse is the North Pole, the
>       perpendicular projection into the x-y-plane gives an ellipse as in
>       two-dimensional space.
>
>     http://pgsphere.projects.pgfoundry.org/types.html#dt.sellipse
>
>     On the other hand, q3c and our tinyhtm-based service define an ellipse
>     as an intersection of an elliptical cone with the unit sphere.
>     Essentially, it is the difference between projecting an ellipse
>     perpendicularly or radially.
>
>     To distinguish between these two choices, we can look at how the two
>     implementations answer various questions about ellipses.
>
>     1) Does ellipse E CONTAIN point P?
>
>        This is expressible in closed form for both formulations.  If you
>        are feeling adventurous, you can write the expressions in ADQL.
>
>     2) Does an ellipse E1 INTERSECT or CONTAIN ellipse E2?
>
>        pgSphere uses an iterative algorithm.  It is not in closed form.
>        In contrast, I think (but have not implemented) that q3c/tinyhtm can
>        compute it by finding the null spaces of 3x3 matrices. This is, in
>        principle, expressible in closed form.  But for numerical
>        stability, you probably want to use something like QR or SVD.
>
>     3) Does a polygon intersect/overlap with ellipse E?
>
>        No one implements this.
>
>     Just to make things more complicated, we also use PostGIS, which does
>     not have ellipses at all.
>
>     Cheers,
>     Walter Landry
>
>

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Francois Ochsenbein   ---   Observatoire Astronomique de Strasbourg
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