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volume

volume(V, T)

Computes a vector containing the volumes of all tetrahedra in a mesh

Parameters:

Name Type Description Default
V numpy double array

Matrix of mesh vertex position coordinates

 required
T numpy double array

Matrix of mesh tetrahedra indices into V

 required

Returns:

Name Type Description
vols numpy double array

Vector of per-tetrahedron volumes

See Also

doublearea

Examples:

v = np.array([[0.0,0.0,0.0],
                [1.0,0.0,0.0],
                [0.0,1.0,0.0],
                [0.0,0.0,1.0]
                ])
# This tet is properly oriented
t = np.array([[0,1,2,3]])
vols = gpytoolbox.volume(v,t)
# This volume should be 1/6
Source code in src/gpytoolbox/volume.py 
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def volume(V,T):
    """Computes a vector containing the volumes of all tetrahedra in a mesh

    Parameters
    ----------
    V : numpy double array
        Matrix of mesh vertex position coordinates
    T : numpy double array
        Matrix of mesh tetrahedra indices into V

    Returns
    -------
    vols : numpy double array
        Vector of per-tetrahedron volumes

    See Also
    --------
    doublearea

    Examples
    --------
    ```python
    v = np.array([[0.0,0.0,0.0],
                    [1.0,0.0,0.0],
                    [0.0,1.0,0.0],
                    [0.0,0.0,1.0]
                    ])
    # This tet is properly oriented
    t = np.array([[0,1,2,3]])
    vols = gpytoolbox.volume(v,t)
    # This volume should be 1/6
    ```
    """


    # Dimension:
    a = V[T[:,0],:]
    b = V[T[:,1],:]
    c = V[T[:,2],:]
    d = V[T[:,3],:]

    vols = -np.sum(np.multiply(a-d,np.cross(b-c,c-d,axis=1)),axis=1)/6.

    return vols