[Proj] Projecting a rectangle to another coord. system?

[Mikael Rittri]

Thanks for all replies. 

Ed wrote: 
>Glynn's response is right on the mark.  But are you asking a 
>really general question, or do you have specific values for A 
>and B?  If A and B come from a relatively limited list (rather 
>than needing to support ANY arbitrary projection) the job, and 
>Glynn says, can be made much simpler or even trivial.

I meant to be really general (hoping to find a published 
algorithm for the most general case.) 
   The company where I work sells a toolkit (www.SpatialAce.com) 
for building GIS systems.  Currently, the toolkit supports about 
nine (families of) projections, so we have special methods to 
project a rectangle from projection A to a rectangle in 
longitude/latitude, and then to projection B.  As you say, 
for most of the projections (but not all), projecting to 
or from a long/lat rectangle is almost trivial.  

But if, in the future, we would like to provide many more 
projections, it would probably be worthwhile to implement
a general solution that works for any pair of projections.  
And it must handle discontinuities well, since you never 
know what an end user might do... 

By the way, I disagree with Glynn's final sentence:

>There are cases where this approach can fail, i.e. where the 
>projection of an interior point lies far outside of the 
>projected border (e.g. projecting from a polar projection 
>to a cylindrical one).  However, these cases tend not to occur 
>in practice, as the level of distortion tends to make the resulting 
>data too inaccurate to be of any practical use.

Although I agree that data stored in a polar projection should not
be viewed in a cylindrical one, I think that one may have geodata
stored in longitude/latitude, which should be viewed in a polar 
projection. 

Again, thanks for all replies,
	Mikael Rittri (Mikael.Rittri at carmenta.se, www.carmenta.se)