Compute 3D volume and intersection of 3D objects from point cloud data.

Hello everyone!

Currently, I am running a project that scans two 3D point cloud from two different objects (A and B). My aim is to transfer this point cloud (available in MATLAB workspace, i.e. x,y,z) into a 3D volume. Next step would be to determine whether the object B is partly inside object A, or not (point-wise check for object B is fine as well). If an intersection is detected, the location shall be returned. I can also increase the point density for the data.

I tried already several approaches, but was not successful so far ...

For the first problem, I found the DelaunayTri(x,y,z)-function to be helpful. In case of the TriScatteredInterp(x,y,z,e)-function I do not understand how to obtain the e-vector.
For the second problem, I found a function in MATLAB FEX called inpolyhedron(), which allows to determine whether specific points are located into a volume. However, the volume is specified by an isosurface. If I use TRI = DelaunayTri([x y z]), and rename the struct according to the notation (TRI.vertices=TRI.X; TRI.faces=TRI.Triangulation) and put it into the inpolyhedron-function, I always get a reshape-error. Moreover, I tried to create the isosurface using an array, but the differences in z-coordinate in my data are smaller than 1 (which requires me to multiply all coordinates accordingly, resulting in a huge set of data in the array). Any ideas?

Thanks for any support! Alternative solutions are also welcomed :)
Hay

NB: I also can provide STL datasets for both objects, if this is more helpful than point cloud data