pyblenderSDIC.meshes.TriangleMesh3D.compute_volume

TriangleMesh3D.compute_volume() → None

Compute the volume of the mesh.

The volume is computed as the sum of the signed volumes of each triangle. The result is stored in the volume attribute as a float.

The volume is compute by using the Green theorem for polyhedra. For each triangle, the signed volume is computed as:

\[V = \frac{1}{6} P_1 \cdot (P_2 \times P_3)\]

where \(P_1\), \(P_2\), and \(P_3\) are the vertices of the triangle and \(\cdot\) and \(\times\) are the dot and cross products, respectively. The total volume is the sum of the absolute values of the signed volumes of all triangles.

from pyblenderSDIC.mesh import TriangleMesh3D

# Create a TriangleMesh3D instance
mesh = TriangleMesh3D(vertices=..., triangles=...)

# Compute the volume of the mesh
mesh.compute_volume()

# The volume is now available in the `volume` attribute
mesh.volume

Warning

The volume can only be computed if the mesh is_watertight.

The volume is given as a signed value, which can be negative if the mesh is not oriented correctly.