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Geodesics (kind of).. by Unicorn 2003-04-24 00:51:10
Lines of lattitude are not geodesics (straight lines) on a sphere. Therefore you cannot form a "square" using lines of lat and lon.

This is not just a question of semantics. Consider a circle 100 kms in radius.
What shape is the enclosing box if the centre is 145 kms form a pole? How about 101 kms? How about if the pole lies inside the circle?
Without knowing what you are doing, its hard to say.
However, if you want the enclosing box size and shape to be independent of the circles location on the sphere, there is only one real interpretation of what the square is - it is formed by the four great circles (geodesics!) distance r from the centre. This is by definition invariant under rotation of the sphere (because it doesn't matter where on the sphere it is located).
So you can position the circle with centre at (lat,lon)=(0,0), work out the four corners, then apply an arbitrary 3D rotation matrix to move the centre wherever you like, and use exactly the same matrix to move the corners. This may involve rotating the square on the sphere, so that the sides are not lines of longititude. In general, they won't be anyway (consider a circle very near a pole). The rotation matrix that moves the centre will not be fully defined, and will still have one degree of freedom, corresponding to the ultimate orientation of the sqaure.

Hope this helped a little.. I'll keep on thinking about it though.
[ Reply ]
  Is this Jeopardy? by skeptic2003-04-24 01:23:42
    Here.. by Unicorn2006-11-19 12:55:59
      OK, now I get it by skeptic2003-04-24 03:37:09
        That's a tough one. by Tomo2003-04-24 04:40:12
          Whoops, longitude calcs don't need scaling. (n/t) by Tomo2003-04-24 04:41:07
  I think what we're looking for by Egaeus2003-04-24 13:48:04
  hhm.. by Unicorn2003-04-24 18:11:41
  oh.. and.. by Unicorn2003-04-24 18:12:26
    hehe. I noticed that by Egaeus2003-04-24 20:51:53

 

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