On Sat, Jan 9, 2010 at 10:50 AM, Patrick Kilian <[email protected]> wrote:
> Hi all, > > > And, thinking about it a bit, I guess the proper rule is that (10, > > 10) -> (30, 30) passes through (20, 20), since it's completely > > unrealistic to assume that the basic renderers will do otherwise. > And this is where you are wrong. On zoomlevel 0 (one tile for the whole > earth) (10,10) ends up on (135.11, 135.15) and (30,30) ends up on > (149.33, 150.38). > Thanks for this. I'll have to look into it further. > > And what that also means is that a straight line on earth which is > > more than a certain length is not properly represented by a way with > > two points. > THAT depends on your definition of "straight line". > I suppose, but it'd have to be a pretty contrived definition of "straight line" to be equivalent to Spherical Mercator, would it not? > One thing I can't quite get my mind wrapped around is whether or not > > a geodesic is what we'd call a straight line on the earth. If we put > > a few million (?) rulers end-to-end as best we could, would that > > form a geodesic, and if not, what would it form? I'm fairly certain > > it wouldn't pass (10, 10) -> (30, 30) through (20, 20), since 20 > > degrees of longitude does not (generally) equal 20 degrees of > > latitude in length. But I'm not sure if it'd be a geodesic or not. > > I'd love for someone to answer that question and provide a link or > > source to back up their answer. > Well. There isn't one single definition of "straight line" here. Right. My definition, for the purpose of the mind experiment, was the thing I'd get if I placed a bunch of rulers end to end as best as I could. The answer might be "what you end up with depends on which errors you make when trying [and failing] at placing the rulers end to end". I don't know. Another mind experiment would be to question what I would get if I placed a bunch of rulers end to end and connected them with hinges so that they could bend vertically but not horizontally. I think that's what's meant by "straight" when we call a road "straight". May or may not be equivalent to "the shortest distance between two points using a path which lies on the surface of the earth". If I had to guess (and it'd be a fairly random guess relying solely on what I remember from when I held a string up to a globe), I'd say the two lines wouldn't coincide. So don't stop assuming that is a > simple topic, everybody was just a lazy bum or that you know it all (tm). > Never assumed any of that. Just the opposite, in fact. It's not a simple topic, and I don't know it all - that's exactly why I'm posting on this list. And not everyone is a lazy bum.
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