Theory of calculating sphere centres from surface co-ordinates

In summary, The conversation discusses the process of calculating the center point of a sphere using sets of 4 points and determinant equations. The speaker is interested in understanding the theory behind the calculation and is seeking recommendations for resources to learn more. They also mention a link to a website with information on the topic."
  • #1
broouk
3
0
I have 35 x, y, z co-ordinates on a sphere surface and I need to calculate the sphere centre point. I am currently using sets of 4 points and determinant equations as shown at http://local.wasp.uwa.edu.au/pbourke~/geometry/spherefrom4/
This method works fine but I want to know the theory behind how the calculation works and also if this is the best method to use. Any help/recommended textbooks/websites would be much appreciated.
 
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  • #3
I like how the author of that page requires that no three points be colinear, and that all four not be coplanar.
 

1. What is the theory of calculating sphere centres from surface co-ordinates?

The theory of calculating sphere centres from surface co-ordinates is a mathematical method used to determine the exact center point of a sphere based on the known coordinates of points on its surface. This is useful in various fields such as geometry, physics, and astronomy.

2. How does the theory of calculating sphere centres work?

This theory works by using the Pythagorean theorem to find the distance between the known surface points and the potential center point. By applying this method to multiple surface points, the final calculated center point will be the one that satisfies the distance criteria for all points.

3. What are the applications of this theory?

The theory of calculating sphere centres has various applications in different fields. It is used in surveying and mapping to determine the center point of a spherical object, in astronomy to locate the center of a planet or star, and in physics to analyze the distribution of mass in a spherical object.

4. Are there any limitations to this theory?

One limitation of this theory is that it assumes the surface points are accurately measured, which may not always be the case. Additionally, it only works for perfectly spherical objects and may not be applicable to irregularly shaped objects.

5. Can this theory be applied to determine the center of the Earth?

Yes, the theory of calculating sphere centres can be applied to determine the center of the Earth. In fact, this method has been used by scientists and geologists to estimate the Earth's center point based on seismic data and other surface measurements.

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