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how can I find the radius of part of spherical surface

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I had an experiment that gave my part of spherical surface.
I didnt know where the (x,y,z) location of the surface and is radius? I want to find a way to determine the radius, and if there is some fit for spherical surface it will be the best option.

Answers (3)

Torsten
Torsten on 19 Dec 2017
Edited: Torsten on 19 Dec 2017
Use fminsearch to determine radius and center of the sphere which approximates your point cloud best (4 unknowns).
To this end, you will need to project your points onto the surface of a sphere suggested by fminsearch, calculate the distances between your points and their projections and sum them up. This will give you the function to minimize.
Best wishes
Torsten.
  2 Comments
Torsten
Torsten on 19 Dec 2017
Im not sure how to use fminsearch,
I have x y z there are my data (each of them are vector with n values) and the function I want to check is (x-x0)^2+(y-y0)^2+(z-z0)^2-R^2=0
but I dont understand how to use fmin for that
thanks a lot! Israel.
Torsten
Torsten on 19 Dec 2017
During the optimization process, fminsearch gives you 4 parameters: x0, y0, z0 and R.
With these parameters you will have to calculate the distances d_i of all your points (x_i,y_i,z_i) (i=1,...,N) from the sphere (x-x0)^2+(y-y0)^2+(z-z0)^2 = R^2.
The return parameter to fminsearch is then sum_{i=1}^{N} d_i, and fminsearch will try to minimize this sum.
Best wishes
Torsten.

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israel gabay
israel gabay on 19 Dec 2017
I still dont understand how to find with fmin the parameter (x0,y0,z0,R)
  1 Comment
Torsten
Torsten on 19 Dec 2017
You don't need to find them, fminsearch will do.
You only have to provide a starting guess for x0,y0,z0 and R.
Best wishes
Torsten.

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israel gabay
israel gabay on 19 Dec 2017
its good that fmin will find them but how I use this function I dont find the write syntax u can write please how I need to use this function exactly
Thanks again !
  3 Comments
Torsten
Torsten on 19 Dec 2017
This might be of help if the use of fminsearch is too difficult:
https://de.mathworks.com/help/vision/ref/pcfitsphere.html
Best wishes
Torsten.

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