[Proj] Inverse Winkel Tripel and others

[support.mn at elisanet.fi]

"Gerald I. Evenden" <geraldi.evenden at gmail.com> kirjoitti: 
> After sleeping on the problem for a bit and enjoying the services of my new 
> toy introduced in the tmerc circus I am now of the opinion that GSL is 
> probably not needed in inversing inverseless projections.
> 
> However, libproj4 will need one or two tweeks to lib_proj.h and introduction 
> of a new support routine.  I suspect the changes will warrant a boost of the 
> release number from 4.3 to 4.4.  If the methods I now envision works, it will 
> still take some time to apply it to all the inverse-less projections; even 
> then some will probably remain inverse-less.  Worry about that later.
> 
> I will use Winkel Tripel as the first development/test case.
> 

Actually there is a very fast method to produce some inverse routine for
any projection (that can calculate forward). That is to calculate a
lookup table forward and then using that table backwards adding
some (maybe clever) interpolation?

If the error is a bit larger... it is anyway better than nothing at all.

Computers have very much memory nowadays so some extra tables
(generated on demand and request) would not be too costly. When
sombody initializes a projection he could also call an extra routine
that generates the interpolation tables etc. And those who don't need
them jsut don't generate any tables.

Tables and pre calculated values might also speed up the forward
routines in some cases? If that is required.

When a projection is initialized, there usually is a little time to spend
extra to do some precalculations. Assuming that the routine is fast
when calling it with the large point sets.

Regards: Janne.