halffaces

halffaces(T)

Given a tet mesh with face tet T, returns all oriented halffaces as indices into the vertex array.

Parameters:

Name	Type	Description	Default
T	(m,4) numpy int array	tet index list of a tet mesh	required

Returns:

Name	Type	Description
hf	(m,4,3) numpy int array	halfface list as per above conventions

Notes

The ordering convention for halfedges is the following: [halfface opposite vertex 0, halfface opposite vertex 1, halfface opposite vertex 2, halfface opposite vertex 3]

Examples:

import gpytoolbox as gpy
v,f = gpy.regular_cube_mesh(4)
# Call to halffaces
hf = gpy.halffaces(v,f)
# hf is a three-dimensional array. To turn into a traditional 2D array, one can flatten the second dimension:
flat_hf = np.concatenate([hf[:,0,:],hf[:,1,:],hf[:,2,:],hf[:,3,:]], axis=0)

Source code in src/gpytoolbox/halffaces.py

def halffaces(T):
    """Given a tet mesh with face tet T, returns all oriented halffaces
    as indices into the vertex array.

    Parameters
    ----------
    T : (m,4) numpy int array
        tet index list of a tet mesh

    Returns
    -------
    hf : (m,4,3) numpy int array
        halfface list as per above conventions

    Notes
    -----
    The ordering convention for halfedges is the following:
        [halfface opposite vertex 0,
         halfface opposite vertex 1,
         halfface opposite vertex 2,
         halfface opposite vertex 3]

    Examples
    --------
    ```python
    import gpytoolbox as gpy
    v,f = gpy.regular_cube_mesh(4)
    # Call to halffaces
    hf = gpy.halffaces(v,f)
    # hf is a three-dimensional array. To turn into a traditional 2D array, one can flatten the second dimension:
    flat_hf = np.concatenate([hf[:,0,:],hf[:,1,:],hf[:,2,:],hf[:,3,:]], axis=0)
    ```

    """

    assert T.shape[0] > 0
    assert T.shape[1] == 4

    hf = np.block([[[T[:,1][:,None], T[:,2][:,None], T[:,3][:,None]]],
        [[T[:,3][:,None], T[:,2][:,None], T[:,0][:,None]]],
        [[T[:,3][:,None], T[:,0][:,None], T[:,1][:,None]]],
        [[T[:,1][:,None], T[:,0][:,None], T[:,2][:,None]]]]).transpose((1,0,2))
    return hf