Boxes and Polygons in ADQL/STC. Questions and recommendation.

[Alberto Micol]

On 23 Oct 2009, at 21:19, Arnold Rots wrote:

> 4.5.1.5 Box
> A Box is a special case of a Polygon, defined purely for  
> convenience. It is
> specified by a center position and size (in both coordinates)  
> defining a cross
> centered on the center position and with arms extending, parallel to  
> the
> coordinate axes at the center position, for half the respective  
> sizes on either side.
> The box’s sides are line segments or great circles intersecting the  
> arms of the
> cross in its end points at right angles with the arms.

My trouble is with the sentence that  the arms extend "parallel to the  
coordinate axes".
"Parallel" to the equator cannot be a great circle unless it is the  
equator itself. Hence:
Does that mean that the I should measure the size of the "horizontal"  
arm along
the small circle parallel to the equator?
If this is correct, then a size of 180 deg is an hemisphere if and  
only if the centre is placed
on the equator.

I appreciate some help, thanks!

Then, regarding the usefulness of a BOX made of great circle arcs:
that is useful because to find if a point is inside or outside such BOX
it is just matter to compute the scalar product of the vector  
representing the point
and the 4 vectors representing the half-spaces of the 4 box sides.

Of course this means that it will no longer be possible to use (ra,  
dec) as we are used to,
as in:  ra BETWEEN this AND that AND dec BETWEEN d0 AND d1
and instead we have to go to a vectorial representation of the sky  
coordinates.

That seems mathematically handy and quite fast for any database, but  
places the
burden on data providers that will have to change the way they store  
coordinates.

(It's a bit late here in Central Europe, I hope I got my math and  
reasoning right!)

Alberto