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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 |