How do you measure the volume of a mesh?

Question

Is there a function in blender to measure the volume of the mesh that you input in the geometry nodes? For example let's say I have a cube with the dimensions (10,10,10), then it should output 1000.0 because that is the volume of the cube.

Answer 1

Using Blender 3.4's topology nodes and recreating this answer will give you the volume of a mesh.

public float SignedVolumeOfTriangle(Vector p1, Vector p2, Vector p3) {
    var v321 = p3.X*p2.Y*p1.Z;
    var v231 = p2.X*p3.Y*p1.Z;
    var v312 = p3.X*p1.Y*p2.Z;
    var v132 = p1.X*p3.Y*p2.Z;
    var v213 = p2.X*p1.Y*p3.Z;
    var v123 = p1.X*p2.Y*p3.Z;
    return (1.0f/6.0f)*(-v321 + v231 + v312 - v132 - v213 + v123);
}
public float VolumeOfMesh(Mesh mesh) {
    var vols = from t in mesh.Triangles
               select SignedVolumeOfTriangle(t.P1, t.P2, t.P3);
    return Math.Abs(vols.Sum());
}

The above code recreated in nodes:

Apologies for the spaghetti, Blend file is attached so no one has to recreate it.

You can check the results by enabling and using the built-in "3D-Print Toolbox" addon.

Answer 2

There is at list a possibility of volume calculation but it’s painfully slow, you have to stop the calculation on the last frame so it’s not very practical, furthermore it doesn't work with moving objects.

It’s based on the buffer hack. At every frame it increment the Z position of a plane accordingly to the index and with a Mesh Boolean it calculate the surface of this cross section of the mesh. Then the mesh section is instanced and the surface is stored in a Store Attribute node.

At the end, after the buffer hack, a Statistic Attribute calculate the mean of all the surfaces (except the first and the last witch are those of tangent planes and cause problem with the boolean, any way there surfaces is equal to 0), multiply it by the height and this volume value is stored too.

You have to set the definition by setting the Start Frame and the End Frame with a Driver. I hope it will help somebody one day...

Answer 3

I think the @Valala's answer can be further simplified since it is actually simple vector algebraic operation that comes from the discrete geometry and windings. I created a simplified node group:

You can find the blend file here

The actual equation to calculate the volume is the following:

Let $p_1$, $p_2$, $p_3$ be the corners of the triangle. Given that you have $K$ triangles in the mesh then the volume of the mesh comes from the following equation:

$$\sum_{i=0}^K p_1\cdot(p_2\times p_3)$$

The corresponding computation in the blender source code is available in here. This can be computed with the blender's python API call calc_volume

Answer 4

You can use rigid body ops.

bpy.ops.rigidbody.object_add()
bpy.ops.rigidbody.mass_calculate(material='Custom', density=1) # density in kg/m^3
volume = ob.rigid_body.mass

https://blender.stackexchange.com/a/304033/72020