STC Request for change: STC box definition needs clarification.

[Alberto Micol]

Tom McGlynn wrote:
> 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.
>
To clarify this point:  the BOX definition in STC is open to 
interpretation given that
"parallel to the axes" has a clear (unique) meaning in 2d cartesian 
geometry, but not so
when on a sphere.

According to you, Tom, "parallel" means "instantaneously parallel" 
(parallel to the equator
only in that very point). Examining this definition:

there are infintie circles for that point (box center) that are 
instantaneously parallel to the equator;

among those, there are two noticeable ones: the only one which is a 
great circle (your choice),
and the only one which is not only instantaneously but even "fully" 
parallel to the equator:
the small circle of equal latitude (aka _the_ parallel).

As I explained in a previous email, the only choice that really makes 
sense close to the  poles
is Tom's choice, not mine. Tom's choice has invariant behaviour wrt 
where the box centre is.
And this makes it ideal.

It would be better if the STC BOX definition could be made unambiguous 
on this point
so to avoid people like me taking the wrong choice.
For example, it could be said that the cross arms (and not only the box 
sides)
are lying on great circles.

(How to express this such that it is equally valid on a 2d cartesian
reference system is an art which Arnold masters)

(Whether box should become something completely different (ra and dec boxes)
is obviously beyond this little point of mine).

Thanks,
Alberto