[Proj] Re: Global Gauss-Kruger and libproj4---the final story

[Gerald I. Evenden]

On Thursday 28 August 2008 5:30:30 pm strebe at aol.com wrote:
> >The only context that I use the term "interruption" in discussing
> >cartographic projections are in cases like Goode's world maps or
> >"orange peal" charts often using the sinusoidal projection.  Please
> >define what *you* mean by interruptions.
>
> An interruption is any location where two points of infinitesimal
> separation on the globe are mapped to two points having finite separation
> on the plane. This happens somewhere on all projections. All along an
> interruption, the projection formulæ are no longer a function; they are
> multivalue.

Let's see.  tan(x) has two values at x=90 degrees: +inf and -inf.  So it is no 
longer a function, eh?

I can't find any such distinction for the definition of a "function."  Please 
give reference.

Even if your questionable definition were true, it merely verifies that 
proj_fwd() is a function because it only  returns one value.  It is defined 
that way in the documentation.

In terms of interruptions applying to all projections I presume you are 
referring to the del-lon=180 condition.  In many projection software this is 
not a break and the map merely repeats on in the x direction.  As far as I am 
aware it is always the graphic programmers job to handle this condition and 
not the projection routine: when at the map edge recall the function with the 
sign of the lon term reversed.

BTW: you are the first person I have ever heard that refers to the wrap-around 
condition of longitude as an interruption if, indeed, that is what you are 
referring to.

If there are other examples, other than projections commonly recognized as 
interrupted (for example Goode) *please* name them.

> Regards,
> -- daan Strebe

-- 
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist