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

[Glynn Clements]

Mikael Rittri wrote:

> G> It's the reverse case which doesn't work. If you project a 
> G> rectangle which encloses the pole, the north and south edges 
> G> of the bounding box will be determined by the min/max 
> G> latitudes of the border points; the projection of the pole 
> G> will lie above or below the bounding box of the projected border.
> 
> But we would need the reverse case as well, because of "demand-driven
> geodata access" (or whatever it should be called).  When the user looks
> at a polar projection, the zoom level etc. of his window determines a 
> bounding rectangle which is defined in the polar projection.  The 
> geodata, on the other hand, are defined in lat/lon in a database, 
> which can be queried with a bounding lat/lon-rectangle.  That is, 
> the database returns only the polygons that intersect the lat/lon-
> rectangle of interest.  So we need to find a lat/lon-rectangle which 
> covers at least the polar rectangle --- that's the reverse case. 
> 
> Since I thought all GIS systems behave like this, I hoped the 
> fully general problem (including discontinuities) had been solved 
> (and published). 

I doubt it. Actually, I'm not sure that it's possible to derive a
mechanism which will work in the general case.

Also, you might do better asking in a forum which is concerned with
numerical methods generally. Essentially, you're looking for a
numerical method to compute the minima and maxima of f(x,y) for
arbitrary f where x and y are bounded. In that sense, the fact that f
is being used in a cartographic projection doesn't really help you.

OTOH, if you had an algebraic representation of the projection
function, you could (potentially) determine the maxima and minima
analytically. However, you can't realistically get this information
out of PROJ.

[I have examined the possibility of parsing the PROJ source code, but
it's just too messy, in the sense that it depends too heavily on
imperative constructs.]

I suspect that the most feasible approach is to specify a function to
compute the bounding box on a per-projection basis. Most projections
could use a generic algorithm based upon adaptive sampling, while a
few would need to handle special cases explicitly, using a
manually-derived analytical solution.

-- 
Glynn Clements <glynn.clements at virgin.net>