Create 3D objects and save as image stack (tiff)

Hello,

Some context:

I am working with an algorithm that evaluates contact angles of a liquid on a surface. It requires a segmented image stack (.tiff) as an input.

To verify that the algorithm is working correctly, I want to input a segmented image stack of an artificial sphere (representing a droplet of liquid) on an artificial rectangular prism (representing the surface). Depending on where the intersection of the two is chosen, we can analytically determine the contact angle of the sphere, and see if algorithm outputs the expected result.

I am new to creating 3D objects in Matlab. I understand that I can create a sphere in matlab using the

sphere

function. But I am not sure how I can then create a rectangular prism and have it 'merge' with the sphere (see below).

So, two parts to my question. First, how can I generate the object I drew above? Second, how can I convert it as a stack of 2D images (.tiff format)?

Thanks in advance.

Chris