[josm-dev] [off-topic] pecision of mouseclick in josm - may be not jsom-specific

[Sebastian Klein]

Frederik Ramm wrote:
> Hi,
> 
> Sebastian Klein wrote:
>> Good to know... I think we could get this value down to 0.642cm if use 
>> the full 64 bit and don't skip the range from 180*10^7 to 2^31 
>> (longitude) and from 85.1*10^7 to 2^31 (latitude).
> 
> But why stop there and allow ridiculous resolution at the poles? Given 
> that the earth has a surface of 510,072,000 square kilometres, if you 
> divide that surface in 2^64 almost-round shapes, then each of those only 
> has an area of 0.2765 square centimetres, allowing you to address each 
> place on the surface with 0.52cm precision!

Right, but how is it done in practice? You could map the sphere to a 
disk, without area distortion (e.g.[1]). Then cut the disk into pieces 
and rearrange them on a square.

Nice puzzle game... What's the minimum size of the square when you limit 
the number of straight cuts on the disk? Maybe it gets better if you 
allow arc shaped cuts, e.g. slice off crescents and shift them into a 
nice pattern... :)

Sebastian

[1] <http://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection>