How to extract intersection between two 3D shapes

I have a two 3D shapes, one defined by a patch object, the other by a simple analytical function (in my case a sphere):

[verts, faces, cindex] = teapotGeometry;
sphere_origin = [1 1 1];
sphere_radius = 1;
figure;
p = patch('Faces',faces,'Vertices',verts,'FaceVertexCData',cindex,'FaceColor','interp');
sph = drawSphere([sphere_origin sphere_radius]); % using matGeom (https://github.com/mattools/matGeom)

I'd like a way to slice the patch into 2 or more sub-objects that contains the part of the teapot outside the sphere, and the one that is inside.

My main problems are that I don't know:

1. How to find the exact intersection between the sphere and the 3D shape (not just the closest vertice, but the extrapolated one). (DONE: using surfaceintersection as @darova suggested)
2. How to add the faces to the extrapolated vertices in a way that conserve the integrity of the teapot if i were to plot only the sub-objects found.

I suppose the right way to start is to find the faces that are intersecting the sphere like this:

out_pnt = find(vecnorm(verts-sphere_origin,2,2)>=sphere_radius);
out_faces = any(ismember(faces,out_pnt),2);

But going from there to finding the exact set of points that define the intersection is really difficult for me right now.

Any part of the answer could really help me, thanks in advance.

[darova]

Please show the data. Maybe it's possible to find intersection using contour

For more complicated cases use surfaceIntersection

[hagege ruben]

Thanks for you'r quick response!

The code should run as is given that you installed matGeom

[darova]

Can you please just attach the data? I don't want to install anything

[hagege ruben]

Ok, so instead of using drawSphere you can do the following:

hold on;
[X,Y,Z] = sphere(32);
sph = surf(gca,X.*sphere_radius+sphere_origin(1),Y.*sphere_radius+sphere_origin(2),Z.*sphere_radius+sphere_origin(3));
view([135 0])
axis equal

[darova]

You shuold use surfaceIntersection

[hagege ruben]

For anyone who is interested in doing something similar, I tried the following:

tea.faces = faces;
tea.vertices = verts;
DT = delaunayTriangulation(Z(:).*sphere_radius+sphere_origin(3), Y(:).*sphere_radius+sphere_origin(2), X(:).*sphere_radius+sphere_origin(1));
[sphere.faces, sphere.vertices] = freeBoundary(DT);
[intersect, Surf] = SurfaceIntersection(tea,sphere);
patch('Faces',Surf.faces,'Vertices',Surf.vertices,'LineWidth',2)

It solved the first part of my problem, thank you very much!

Now do you know how I can "slice" the teapot so that I have the part outside of the sphere with a hole in the shape of the sphere and the part inside the sphere? (the two parts should touch each other)

[darova]

Im using older MATLAB version and don't have teapot. Can you show it? What are you trying to achieve?

[hagege ruben]

This is a matlab built-in, the file has been created in 2014 so you must have a very old version

I've attached the file, if you need help reproducing another step becasuse of the version of you'r matlab I'd be happy to help.

My goal is to divide the "teapot" (or any object really) into parts that are divided by the intersection of another object (sphere in this case).

[hagege ruben]

This seems like the function I need, too bad it's not available...

[Joseph Olson]

Seems like the inShape function is what you want!

https://www.mathworks.com/matlabcentral/answers/496500-intersection-volume-of-two-3d-alphashapes