[Proj] Little sphere projection

[Mikael Rittri]

Carlo Bertelli wrote:

> My idea is analysing each town cluster using a little sphere
> (or ellipsoid) centered on the town whith an emisphere that 
> only covers the space of the region, so to show larger distances 
> in town (so to distinguish any abbey) and reduced distances far 
> from the town center. 

If I understand you right, you want your map to be distorted
in the same way as M. C. Escher's Balcony,

http://www.worldofescher.com/gallery/A3.html

where the central balcony is shown in a large (detailed) scale,
but surrounding areas are shown in much smaller scale.  

In Escher's print, the scale has stabilized when you get to the
print edges, but that's not necessary. 

I haven't seen such map projections used for cartography, except
for patriotic joke maps, where one's beloved home town or country
is shown in a much larger scale than the rest of the world. But
maybe such projections are used for statistical or economic maps,
as you suggest.  I doubt there is anything appropriate in Proj.4, 
though. 

One could make a new kind of azimuthal map projection for this
purpose.  The azimuth (direction) from the town center could be
preserved (because, why not?).  The true distance from the town 
center could be represented by a shorter map distance.  The
mathematical function that converts true distance to map distance
should have slope 1 for short distances, but gradually get lower
slope.  Something like arctan or tanh, perhaps.  

Best regards,

Mikael Rittri
Carmenta
Sweden
http://www.carmenta.com

-----Original Message-----
From: proj-bounces at lists.maptools.org [mailto:proj-bounces at lists.maptools.org] On Behalf Of Carlo A. Bertelli (Charta s.r.l.)
Sent: den 7 augusti 2011 23:17
To: proj at lists.maptools.org
Subject: [Proj] Little sphere projection

Hello,
I'm trying a simplistic approach to a topological representation. I'm mapping the possessions belonging to a group of abbeys in a regional space. Il works well at a small scale, but when the abbeys are clustered in major towns, the representation ties properties to the cluster and not to the single abbey. The fact is that towns (and
clustering) play a significant role in this story (yes this happens in the 18th century), asks for a better representation.
My idea is analysing each town cluster using a little sphere (or
ellipsoid) centered on the town whith an emisphere that only covers the space of the region, so to show larger distances in town (so to distinguish any abbey) and reduced distances far from the town center.
I think it should not be impossible to craft ad hoc projections, but I have no idea on how to do it. Could someone help me?
TIA
c
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