How to calculate volume by Dilation (ball 3 structural element)?

Hello everyone,

I have 3d center coordinates and radii of an object which is made up of poly-disperse spheres (as shown in the figure). I want to compute the total volume of the object by Dilation (ball3) in order to calculate the open pores porosity. How can I perform this in MATLAB, any advice would be highly appreciated.

Answer 1

[Joost]

I am not sure if I understand your question correctly, but I think that what you need to do is:

1. Compute the sum of the volume of all individual spheres (4/3 * pi * r^3)
2. Subtract the overlapping volume of all permutations of 2 individual spheres. The volume of the overlap of spheres is nicely described at: Sphere-sphere Intersection.