intersection of sphere and surface

Hi everyone!

I have an STL surface/skin imported. So I have a vertex, faces and normals matrix of that patch.

Now I've generated 4 spheres using the sphere function , and all of its nodes coordinates are grouped in a 4x3 cell array.

The spheres are strategically positioned under the surface in x and y axis. z is inittialy 0.

What I need is to impose an ascendent movement (in z axis) to the spheres until each one of them touches the surface at any point. At the moment the sphere touches the surface it must stop its moviment. Then, the output I need to get is the amplitude of each sphere movement, the amplitude can be calculated in the center of the sphere.

Its important to notice that the surface its a convex surface so the sphere can touch the surface a little "sideward".

Can somebody help me with this, please?