how can I find the radius of part of spherical surface

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.

Answer 1

[Torsten]

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.

[Torsten]

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]

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.

Answer 2

[israel gabay]

I still dont understand how to find with fmin the parameter (x0,y0,z0,R)

[Torsten]

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.

Answer 3

[israel gabay]

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 !

[Torsten]

Here are some examples:

https://de.mathworks.com/help/matlab/ref/fminsearch.html

And please don't open new answers ever time - only comment on the answer given.

Best wishes

Torsten.

[Torsten]

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.

[israel gabay]

Thanks!

I will try to use the 2 option.