Calculating an elliptical surface and formulating this surface in 3d

[erencan144]

Hello.
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

picture 2

http://img836.imageshack.us/img836/3679/world2u.png

 

[mathman]

Put in a diagonal and you now have two spherical triangles. You should be able to get the answer from that.

 

[erencan144]

Put in a diagonal and you now have two spherical triangles. You should be able to get the answer from that.

Could you explain little bit more, please?

 

[mathman]

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.