Draw the sphere to find the radius of the sphere

I want to fit a 3D sphere, and my goal is to find the radius of the sphere. Knowing the coordinates of some points on the sphere (x,y,z,), which function should I use to quickly draw a sphere and know its radius?

[DGM]

See also:

https://www.mathworks.com/matlabcentral/answers/1891700-how-can-i-convert-a-series-of-2d-images-grayscale-into-a-3d-image

Answer 1

[John D'Errico]

Estimation of the sphere parameters is not too difficult. First, since you have shown no data, I'll make some up.

XYZ = randn(50,3); XYZ = XYZ./sqrt(sum(XYZ.^2,2));
XYZ = 2.5*XYZ + [1 3 5] + randn(size(XYZ))/20;
plot3(XYZ(:,1),XYZ(:,2),XYZ(:,3),'o')
axis equal
grid on
box on
xlabel 'X'
ylabel 'Y'
zlabel 'Z'

The result should be a sphere of radius 2.5, centered at the point [1 3 5].

You can use the tool I attached called spherefit.

[C,R] = spherefit(XYZ)

C = 1×3

0.9925 3.0094 5.0107

R = 2.5086

As you can see, the code recovered the original parameters well enough. Now, to plot the sphere...

fimplicit3(@(x,y,z) (x - C(1)).^2 + (y - C(2)).^2 + (z - C(3)).^2 - R.^2)
hold on
plot3(XYZ(:,1),XYZ(:,2),XYZ(:,3),'ro')
axis equal
grid on
box on
xlabel 'X'
ylabel 'Y'
zlabel 'Z'
hold off

I could have built a surface directly, perhaps using meshgrid. But fimplicit3 is just too easy.

[Sterne_17]

Sir thank you very much. @John D'Errico

My attachment contains the code from my project and the input image, which is a sphere in laser scan. Running the program generated an image of a segment of the outline of the sphere in the pixel coordinate system and a segment of the outline of the sphere in the 3D coordinate system. I want to draw a sphere using the points on the outline of the sphere.

I want you to help me to see if I can select the points on the outline of the sphere in the 3D coordinate system to draw the sphere?

[John D'Errico]

That is a completely different question, significantly different from what you asked and I answered. You will first need to use image processing tools, identifying the pixels on that perimeter. But then you still cannot easily convert a picture of the outline of a sphere into a sphere, since the picture lacks depth information. Anyway, I don't do image processing.

[Sterne_17]

I already know the coordinates (x,y,z) of several scatter points on the sphere in space, and I think I just need to bring their coordinates into the code you showed. I was wondering how to bring in the coordinates of these points? @John D'Errico

XYZ = randn(50,3); XYZ = XYZ./sqrt(sum(XYZ.^2,2));
XYZ = 2.5*XYZ + [1 3 5] + randn(size(XYZ))/20;
plot3(XYZ(:,1),XYZ(:,2),XYZ(:,3),'o')
axis equal
grid on
box on
xlabel 'X'
ylabel 'Y'
zlabel 'Z'