Measuring complex 3D mesh volumes in Blender

Question

How can I obtain the volume of complex objects, in such a way that it can be used in a driver?

Example:

Answer 1

Yes you can have a change in volume of a selected object drive another object's property. In this example, I am using the change in volume of the selected object (Cube) for driving the Y position of the sphere.

import bpy
import bmesh

bpy.app.handlers.depsgraph_update_post.clear()

obj = bpy.context.active_object
me = obj.data
bm = bmesh.new()

def drive_property(volume):
    bpy.data.objects["Sphere"].location.y = volume / 2

def update_volume():
    bm.clear()
    bm.from_mesh(me)
    bm.transform(obj.matrix_world)
    bmesh.ops.triangulate(bm, faces=bm.faces)

    volume = 0
    for f in bm.faces:
        v1 = f.verts[0].co
        v2 = f.verts[1].co
        v3 = f.verts[2].co
        volume += v1.dot(v2.cross(v3)) / 6

    print("Volume:", volume)
    drive_property(volume)

def on_depsgraph_update(scene):
    depsgraph = bpy.context.evaluated_depsgraph_get()
    for update in depsgraph.updates:
        if update.id.name == "Cube":
            update_volume()

bpy.app.handlers.depsgraph_update_post.append(on_depsgraph_update)

Answer 2

Here's an answer that is almost in every way worse than the ingenious mathematical answer by Harry

✅ Good aspects of this answer:

• actually using a driver, which doesn't require running Python outside of sandbox mode (no security warnings)
• works with internal faces
• updates more immediately (not counting huge CPU lag) while editing the mesh in Edit Mode
• maybe it's more accurate for some geometries but I wasn't able to find an example
• you can use it to get a confirmation Harry's answer is correct even though the latter seems way too simple to be.

(sphere is Harry's answer, cylinder is mine)

❌ Bad aspects:

• doesn't work with internal holes like when using Solidify modifier
• slow as hell
• probably still less accurate than Harry's answer, despite the huge number of samples
• for the most part, needs the mesh to be watertight (but works with Susanne)
• maybe some more, again I didn't test thoroughly

Instructions

1. ⭾ Tab to edit the default cube.
2. MA Merge all vertices at center.
3. Keep the vertex selected, ⭾ Tab to Object Mode.
4. ⬆ ShiftA, E, P Add an empty.
5. ⬆ Shift$\color{green}{█}\color{#888}{0█}$ click the single-vert "cube", so it becomes active but the empty stays selected.
6. ✲ CtrlP, V Parent the empty to the vertex.
7. Add the following geonodes setup to the single-vert "cube":

8. $\color{#888}{█0}\color{green}{█}$ right-click a field of choice, Add Driver.
9. In the popup window set the target object as the empty.
10. Default settings should work, but since Harry divides the result by 2, you may also want to change the formula to var / 2.