Calculating an elliptical surface and formulating this surface in 3d

  • Thread starter erencan144
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In summary, the conversation discusses finding the area of an elliptical surface formed by merging four points on the Earth's surface. The solution involves creating two spherical triangles and using standard formulas to calculate the area. The user also asks for further explanation and resources for solving the problem.
  • #1
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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  • #2
Put in a diagonal and you now have two spherical triangles. You should be able to get the answer from that.
 
  • #3
mathman said:
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?
 
  • #4
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.
 

FAQ: Calculating an elliptical surface and formulating this surface in 3d

1. What is an elliptical surface?

An elliptical surface is a three-dimensional shape that resembles a flattened circle. It is characterized by a center point and two axes, with the distance from the center to any point on the surface being equal to the sum of the distances from the two axes.

2. How is an elliptical surface calculated?

An elliptical surface can be calculated using the formula x^2/a^2 + y^2/b^2 = 1, where a is the length of the semi-major axis and b is the length of the semi-minor axis. This formula can be used to determine the coordinates of points on the surface.

3. What is the importance of formulating an elliptical surface in 3d?

Formulating an elliptical surface in 3d allows for a more accurate representation of the shape in a three-dimensional space. It also allows for more complex calculations and analysis of the surface, which can be useful in fields such as engineering, physics, and astronomy.

4. Are there any real-life applications of calculating and formulating an elliptical surface in 3d?

Yes, there are many real-life applications of this concept. For example, in architecture, elliptical shapes are often used in the design of buildings and structures. In astronomy, elliptical surfaces are used to model the orbits of celestial bodies. In medical imaging, elliptical surfaces are used to create three-dimensional images of organs and tissues in the body.

5. Can an elliptical surface be converted into a different shape in 3d?

Yes, an elliptical surface can be transformed into a different shape in 3d through a process called deformation. Deformation involves stretching, bending, or twisting the surface in various ways. This can be useful in creating more complex shapes or in simulating real-life scenarios in fields such as computer graphics and animation.

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