# Volume of overlapping ellipsoids

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MaryD on 29 Mar 2020
Edited: John D'Errico on 29 Mar 2020
I'm creating program that fills given 3D object with ellipsoids. How can I calculate filled volume if ellipsoids can overlap ? Parts of ellipsoids can be outside of the volume i'm filling. Each ellipsoid have same size and is not rotated. 3D object is created from a point cloud with 'trisurf' function, ellipsoids are create by 'ellipsoid' function.

John D'Errico on 29 Mar 2020
Edited: John D'Errico on 29 Mar 2020
The simple solution is just to fill a 3-d array with voxels that are inside each ellipsoid. So, if a voxel is already filled, then you can't fill it twice.
Then count the number of fillled voxels at tha end. You can probably get a bit more accurate by trying to count partially fixed voxels, thus around the perimeter of an ellipsoid.
The entire result will be more accurate if you increase the size of the 3-d array, and only as good as the resolution of that array.