[Proj] Little sphere projection

Carlo A. Bertelli (Charta s.r.l.) carlo.bertelli at gmail.com
Wed Aug 10 02:00:07 EST 2011

Everything you say it's true and very interesting.
We may think that the representation I'm looking for is a cartogram,
maybe, but in a peculiar way. It's mostly a "perspective" on the data.
It should show the "urban" view of this otherwise small scale
behaviour. But it risks to be off-topic.
Cartograms usually show a change in the *features* themselves, I'm
looking for an uneven scale for the map, which is not a perspective,
but a projection.
In my first idea it is truly what Clifford Mugnier calls a "radar"
view. Near things are enlarged, far thing become smaller in a
non-linear way.
This could lead to another "projection" (I think someone has already
worked on it), a normal (laplacian) projection that is very near
(statistically) to what is suggested by Mikael Rittri with Escher's
Balcony. As he implicitely says, this could be fairly easy to
approximate, but it's difficult to apply as this should really be
treated as a cartogram that is tied to each abbey and not to urban
space in comparison to the countryside. This is not easy to decide.
I think the idea of a spherical (globular?) projection is the most
practical, and I need it to be a projection and not a cartogram
because there are also other layers that should be re-projected
(roads, rivers, hillshading). But, as I said before, I cannot find a
projection supported by proj which could be used in this case. A
suggestion is gratefully accepted about the type and parameters I
should use for centering it on a town and to adjust the size of the
"spheroid" to the area of the phenomena.
Thank you to everyone, you have enhanced my understanding of the
problem. I think I can work out a cartogram on the size of farms, but
in this case built possessions (points) and localized financial
annuities are too much a complex issue for a cartogram.

On Tue, Aug 9, 2011 at 1:33 PM, Jan Hartmann <j.l.h.hartmann at uva.nl> wrote:
> Are these the kind of maps you mean:
> http://www-personal.umich.edu/~mejn/cartograms/
> These are "cartograms", distorted maps on the basis of some sort of density
> distributions. There is a complete book with hundreds of examples:
> http://www.amazon.com/Atlas-Real-World-Daniel-Dorling/dp/0500514259
> The authors have made available the software
> (http://www-personal.umich.edu/~mejn/cart/). I got it working some time ago,
> but you need to know a bit about low-level compiling. Alternatively, there
> is a tool for ArcGIS
> (http://blogs.esri.com/Info/blogs/gisedcom/archive/2009/10/16/exploring-data-using-cartograms-within-arcgis-desktop.aspx).
> Cartograms are real fun, so I hope you can do something with them for your
> subject.
> Cheers,
> Jan
> On 08/09/11 13:02, Mikael Rittri wrote:
> 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?
> c

Carlo A. Bertelli
   Charta servizi e sistemi per il territorio e la storia ambientale srl
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