On Jan 6, 7:09 pm, marcelo <[email protected]> wrote: > > Your example, (0,0; 87,0; 0,180), puts all three points on the same > great circle and therefore is not a spherical triangle.
Isn't it? I'm not sure who your "No" was directed to. There *are* three great circles there, I think: part of the Prime Meridian (0,0 to 87,0), part of the Equator (0,0 to 0,180), and part of an oblique great circle connecting 87,0 to 0,180. Using http://maps.forum.nu/gm_flight_path.html and points 85,0 to 0,180 which lie on the map, the line goes around the Pole, on the opposite side of the earth from the US [ie across Asia]. It doesn't follow the Meridian. That does describe a spherical triangle. Even if the northernmost point of the three was actually at the Pole, there would still be two great circles involved, the Meridian and the Equator, and a bilinear segment of a quarter of the Earth would result. The "centre of gravity" of those points on the surface wouldn't be at 30,60 though, which does show that the simplification of the arithmetic mean is a simplification which breaks down in boundary cases. (In fact because you only have two great circles involved, you can divide by 2 and get a point at 45,90, which does seem reasonable for the 3D solid surface). Andrew --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Google Maps API" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/Google-Maps-API?hl=en -~----------~----~----~----~------~----~------~--~---
