Martin wrote:

> Projections are non-linear operations. But there is a few linear
> operations performed before and after the non-linear ones.
[...]
> Those linear parts can be removed from the projection code and inserted
> into affine transforms to be applied before and after the projection.
> Because the projections are often used together with affine transforms
> anyway (for unit conversions, for swapping the order of
> (latitude,longitude) axes, for rendering to screen, etc.), it does not
> introduce any additional cost. 

An interesting approach and certainly a good idea. I have two questions here.

1. Will this result in an API change or will the combinations of the affine 
transformations be done "behind the changes" from my point of view as an 
developer using GeoAPI interfaces to getting conversions done?

2. You write
> Because TransverseMercator depends only on Earth's excentricty,
> projecting c oordinates from a UTM zone to an other UTM zone on
> the same datum (a quite common operation when we are at the
> border of 2 UTM zones) can now be easily calculated as an
> affine transform.

You are surely deeper in that matter than me, but somehow the idea that that a 
conversion of coordinates between two UTM stripes is a matter of a affine 
transform contradicts my picture and understanding of those projections:
Two neighbouring stripes are parallel on equator and their central meridans 
converge towards the poles. Imho this means that while on the equator no 
rotation is needed (for a coordinate conversion) the rotation becomes stronger 
towards the poles. How does this fit to the idea of having ONE affine 
transform? Locally maybe, but I doubt this is what you mean.

Where is my error in understanding here?
-- 
Matthias Basler
matthiasbas...@earthflight.org


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