Find volume of object given a triangular mesh

Question

I have an object defined by vertices and triangular faces.

verts = [[0.1, 1.,  1. ]  [1.,  1.,  0.1]  [1.,  0.1, 1. ]  [1.,  1.,  1.9]  [1.,  1.9, 1. ]
 [1.9, 1.,  1. ] ]

And triangular faces, which define the vertices composing each faces:

faces = [[ 2,  1,  0]  [ 0,  3,  2]  [ 1,  4,  0]  [ 0,  4,  3]  [ 5,  1,  2]  [ 3,  5,  2]
 [ 5,  4,  1]  [ 4,  5,  3]]

I can create a mesh using Poly3DCollection

from mpl_toolkits.mplot3d.art3d import Poly3DCollection
mesh = Poly3DCollection(verts[faces])

I can use mesh to plot the object in 3D. Is there a way in python to then find the volume of this object? Papers (here, here, and here) indicate it is possible. If not in python, are there methods in other languages that make this possible (i.e. that you know of). Thanks in advance!

mmont mmont · Accepted Answer · 2020-05-08T04:06:31

I solved this using meshplex

import meshplex
import numpy as np

verts = [[0.1, 1.,  1. ],  [1.,  1.,  0.1],  [1.,  0.1, 1. ],  [1.,  1.,  1.9],  [1.,  1.9, 1. ], [1.9, 1.,  1. ]]
faces = [[ 2,  1,  0],  [ 0,  3,  2],  [ 1,  4,  0],  [ 0,  4,  3],  [ 5,  1,  2],  [ 3,  5,  2], [ 5,  4,  1],  [ 4,  5,  3]]

mesh = meshplex.MeshTri(np.array(points), np.array(faces))

V = np.sum(mesh.cell_volumes)

print("Volume =", V)
# Volume = 5.6118446

Find volume of object given a triangular mesh

2 Answers