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

[Tom McGlynn]

Alberto Micol wrote:
> 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!
>
>   
Hi Alberto,

I understood this to mean that the horizontal arm goes along great 
circle which has an apex (highest latitude, or lowest
if the point is in the southern hemisphere) at the point.  So the great 
circle is 'parallel' to the equator but only
instantaneously at that point  However I wouldn't mind one of the 
experts chiming in here.

> 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.
>
>   

My problem is that as far as I can see, the problem that the astronomers 
want to answer will be phrased
in terms of limits on RA and Dec so that even though it might be 
mathematically handy it's not necessarily relevant
to the problems we want to solve.   In any case there's nothing special 
about the box here.  It's true for any
(convex?) polygon isn't it?

Tom

P.S.  I think I've gotten the equations for the vertices of a box 
(assuming my interpretation above is correct).  The derivation
was pretty easy once I abandoned trying to do things using pure geometry 
and attacked it using the centers of the great circles and
analytic geometry.  I'll try to post it somewhere tomorrow.


>   
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