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I want to calculate the cavity volume on the inside of an 3D object. The object is modeled as a triangular mesh and is hollow. A good example for what I want to calculate is the volume of a ventricular cavity for a human heart.

I have looked at calculating the volume of a mesh according to the answer and paper from this thread; however, it seems to be only calculating the volume of the mesh. Depending on how my model is created the hollow/cavity of the model would not be calculated from this method. For example if my model is layered with an inner and outer surface, as seen in the image, would I be able to calculate the volume in red? I have thought of trying to find just the outer volume(World Space Volume) and subtracting the mesh volume from it to get the cavity volume, but have so far been unsuccessful.

Maybe I am misunderstanding the paper and previous thread, but believe this cavity calculation is a separate problem. As well, the method would need to be able to handle overhangs and inner objects that may cause complications. Let me know whether I am thinking about the previous thread/paper incorrectly or if there is an alternate method to look at.

Casey
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  • You would use the 3D version of the [shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula). This would calculate the volume of tetrahedra. One fixed 3D point is chosen. That point is connected to each of the triangles to form a tetrahedron. Note that the triangles need a consistent orientation (e.g. all clockwise when seen from the outside of the volume) and the triangles should form a closed volume. If you have an outer and an inner surface, you first calculate the volume using the outer surface and then subtract the volume using the inner surface. – JohanC Nov 06 '21 at 00:16
  • Does this answer your question? [How to calculate the volume of a 3D mesh object the surface of which is made up triangles](https://stackoverflow.com/questions/1406029/how-to-calculate-the-volume-of-a-3d-mesh-object-the-surface-of-which-is-made-up) – JohanC Nov 06 '21 at 00:16
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    @JohanC: If the body has a cavity, and the orientation of the triangles is consistent (e.g. all clockwise when seen from outside the volume (and remember that inside the cavity is outside the volume)), then there's no need to calculate the volume of the two surfaces separately and subtract; you can just treat them as one surface. – Beta Nov 06 '21 at 19:56

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