Calculating an elliptical surface and formulating this surface in 3d

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To calculate the area of an elliptical surface formed by connecting four points on a sphere, one must first determine the (x, y, z) coordinates of these points. The area can then be computed using a surface area integral. The discussion emphasizes the importance of accurately merging the points with the shortest curves to create the elliptical shape. Understanding the mathematical principles behind surface area calculations on a spherical surface is crucial for solving this problem. This approach provides a framework for formulating the elliptical surface in 3D coordinates.
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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
 
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Well you need to know the (x,y,z) coordinates first then just find the area using a surface area integral.
 

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