Theory of calculating sphere centres from surface co-ordinates

  • Context: Graduate 
  • Thread starter Thread starter broouk
  • Start date Start date
  • Tags Tags
    Sphere Surface Theory
Click For Summary
SUMMARY

The discussion focuses on calculating the center of a sphere from 35 surface coordinates using sets of four points and determinant equations, as outlined on the website by Paul Bourke. The method is confirmed to be effective, but the user seeks a deeper understanding of the underlying theory and whether this is the optimal approach. The importance of ensuring that no three points are collinear and that all four points are not coplanar is emphasized as a critical requirement for accurate calculations.

PREREQUISITES
  • Understanding of spherical geometry
  • Familiarity with determinant equations
  • Knowledge of coordinate systems in 3D space
  • Basic principles of linear algebra
NEXT STEPS
  • Research the mathematical theory behind sphere fitting algorithms
  • Explore alternative methods for sphere center calculation, such as least squares fitting
  • Study the implications of point collinearity and coplanarity on geometric calculations
  • Review textbooks on computational geometry for advanced techniques
USEFUL FOR

This discussion is beneficial for mathematicians, computer graphics developers, and engineers involved in 3D modeling or spatial analysis who require precise calculations of sphere centers from surface coordinates.

broouk
Messages
3
Reaction score
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.
 
Last edited by a moderator:
Physics news on Phys.org
I like how the author of that page requires that no three points be colinear, and that all four not be coplanar.
 

Similar threads

High School Hopf fibration, Bloch sphere and quantum rotations - interactive site
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Volumes of n-Spheres: Intuition & Calculations
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Calculating the surface area of a sphere using dA
  • · Replies 33 ·
2
Replies
33
Views
7K
Creating the geometry using MNCPX VisEd
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Help Re-Designing A Curve Using X Y Z Co-ordinates
  • · Replies 1 ·
Replies
1
Views
2K
High School Calc Excess Rad on Earth in Curved 3D Space | Feynman Lectures 6-2
  • · Replies 29 ·
Replies
29
Views
3K
Undergrad How to Calculate an Offset for Centre of Gravity using Weight and Distance?
  • · Replies 1 ·
Replies
1
Views
3K
Electric field a distance z from the center of a spherical surface
  • · Replies 26 ·
Replies
26
Views
6K
Graduate Rotating Sphere: Conceptual Question
  • · Replies 10 ·
Replies
10
Views
3K
How to calculate the dipole moment of the spherical shell?
  • · Replies 1 ·
Replies
1
Views
8K