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Calculating an elliptical surface and formulating this surface in 3d

  1. Jul 13, 2011 #1
    Let's think that we have a sphere that shown in the picture above. The user will select 4 different point the earth's surface. Then I must merge this points with shortest curves, then I got a surface. (Like picture 2) Because of the world's surface, our area is elliptical. How can I calculate the area of this elliptical surface and formulating this elliptical surface in 3d coordinates (x,y,z).

    I would be very grateful, if you tell me how can I deal with this problem.

    Sorry for poor English.

    picture 1

    http://img705.imageshack.us/img705/6263/worldre.png [Broken]

    picture 2

    http://img836.imageshack.us/img836/3679/world2u.png [Broken]
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jul 13, 2011 #2


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    Put in a diagonal and you now have two spherical triangles. You should be able to get the answer from that.
  4. Jul 14, 2011 #3
    Could you explain little bit more, please?
  5. Jul 14, 2011 #4


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    Connect diagonally opposite points by an arc of a great circle to get two spherical triangles.
    There are standard formulas to get the area of a spherical triangle as a function of the side lengths. Look up "spherical triangles" on Google or Bing.