Matthias Julius schrieb: >> If you want to use the "normal" Web Mercator, OSM and Google use, >> it would be better to use spherical geometry ... it's more accurate >> than calculation into a projection and back to LatLon. > > The point is that things like the state of Wyoming only look > rectangular in spherical Mercator projection or similar.
Uhhh ... Spherical Mercator does _not_ preserve shape! That's because the scale increases from the Equator to the poles. Okay, on a sphere it might be easy to calculate the distortion... >> 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. >> I can do some calculations about accurancy the next week, perhaps >> sphere is enough ... but as soon as you work on big objects, you >> might run into problems. > > The question is: What is big? That's pretty easy to calculate: 1. calculate the geodetic distance between & angle two points on WGS84 2. calculate the distance of the distance & angle on other projections On a point, the error of angle and distance will grow. > When does the error become more than, say, 0.1 m? You were talking about angles, not about distances ;-) ID;LAT;LON 0;51.0;7.0 1;51.05:7.03 - geodetic distance on WGS84: 5947 m - Haversine formular (using 6371000 m): 5942 m Error: +/- 5 m ID;LAT;LON 0;51.0;7.0 1;51.20:7.20 - geodetic distance on WGS84: 26293 m - Haversine formular (using 6371000 m): 26260 m Error: +/- 33 m Didn't have time to do it with Mercator, perhaps you've got time for it. _______________________________________________ josm-dev mailing list [email protected] http://lists.openstreetmap.org/listinfo/josm-dev
