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from lib.kits.basic import *
def compute_mesh_volume(
verts: Union[torch.Tensor, np.ndarray],
faces: Union[torch.Tensor, np.ndarray],
) -> torch.Tensor:
'''
Computes the volume of a mesh object through triangles.
References:
1. https://github.com/muelea/shapy/blob/a5daa70ce619cbd2a218cebbe63ae3a4c0b771fd/mesh-mesh-intersection/body_measurements/body_measurements.py#L201-L215
2. https://stackoverflow.com/questions/1406029/how-to-calculate-the-volume-of-a-3d-mesh-object-the-surface-of-which-is-made-up
### Args
- verts: `torch.Tensor` or `np.ndarray`, shape = ((...B,) V, C=3)
- faces: `torch.Tensor` or `np.ndarray`, shape = (T, K=3) where T = #triangles
### Returns
- volume: `torch.Tensor`, shape = (...B,) or (,), in m^3.
'''
faces = to_numpy(faces)
# Get triangles' xyz.
batch_shape = verts.shape[:-2]
V = verts.shape[-2]
verts = verts.reshape(-1, V, 3) # (B', V, C=3)
tris = verts[:, faces] # (B', T, K=3, C=3)
tris = tris.reshape(*batch_shape, -1, 3, 3) # (..., T, K=3, C=3)
x = tris[..., 0] # (..., T, K=3)
y = tris[..., 1] # (..., T, K=3)
z = tris[..., 2] # (..., T, K=3)
volume = (
-x[..., 2] * y[..., 1] * z[..., 0] +
x[..., 1] * y[..., 2] * z[..., 0] +
x[..., 2] * y[..., 0] * z[..., 1] -
x[..., 0] * y[..., 2] * z[..., 1] -
x[..., 1] * y[..., 0] * z[..., 2] +
x[..., 0] * y[..., 1] * z[..., 2]
).sum(dim=-1).abs() / 6.0
return volume |