Calculating an elliptical surface and formulating this surface in 3d

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SUMMARY

The discussion centers on calculating the area of an elliptical surface formed by connecting four points on a sphere's surface. The user seeks a method to merge these points using the shortest curves, resulting in a 3D elliptical surface. To achieve this, one must first determine the (x, y, z) coordinates of the points and then apply surface area integrals to compute the area of the elliptical surface.

PREREQUISITES
  • Understanding of spherical coordinates and their conversion to Cartesian coordinates (x, y, z).
  • Knowledge of surface area integrals in multivariable calculus.
  • Familiarity with the concept of geodesics on a sphere.
  • Basic skills in 3D modeling or computational geometry.
NEXT STEPS
  • Study the principles of spherical coordinates and their applications in 3D space.
  • Learn about surface area integrals and how to apply them to elliptical surfaces.
  • Research geodesic calculations on spherical surfaces to understand shortest paths.
  • Explore 3D modeling software or libraries that can visualize elliptical surfaces, such as Blender or Three.js.
USEFUL FOR

This discussion is beneficial for mathematicians, 3D modelers, and engineers involved in geographic information systems (GIS) or any field requiring the calculation of areas on curved surfaces.

erencan144
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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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