[josm-dev] Geometric calculations and projections

[Anthony]

On Thu, Dec 17, 2009 at 5:40 PM, Anthony <osm at inbox.org> wrote:

>
>   >> Spherical geometry allows you to calculate _directly_ on the sphere
>>  >> without using a projection ... you simple use LatLon in radian
>>  >> degrees.
>>  >
>>  > True, but it's not really trivial.
>>
>> A rectangle with 89.55°, 90.1°, 89.89°, 90,01° is no rectangle.
>>
>
> What's the definition of "rectangle" in non-euclidean geometry anyway?
>

Here we go: http://www.math.ucdavis.edu/~xqwang/math141/hw7.pdf

Turns out Wyoming isn't even a polygon (*), let alone a rectangle.

In fact, there apparently are no rectangles on spheres (which probably holds
for bumpy oblate spheroids aside from some small exceptions due to the
"bumpy" part).

http://www.math.washington.edu/~king/coursedir/m444a04/notes/10-11-Def-of-Rectangle.html

(*) In reality.  In some projections it is, of course, a polygon.