Function subdivide_hex

python/pymesh/meshutils/generate_box_mesh.py:226–283

Subdivide hex into 8**order sub-cells. Corner ordering: Edge orders: 7 _______ 6 ___2___ /: /| 7/: 6/| z 4 /______/ | /___1__/ | | | : 5| | | 11 | |10 | y | :... |.| 8

(corners, order)

    return mesh, hex_indices

def subdivide_hex(corners, order):
    """ Subdivide hex into 8**order sub-cells.
    Corner ordering:     Edge orders:
         7 _______ 6            ___2___
          /:     /|           7/:    6/|        z
       4 /______/ |           /___1__/ |        |
        |  :   5| |          | 11    | |10      |  y
        |  :... |.|         8|  :.3. |.|        | /
        | . 3   | /2         | 4    9| /        |/
        |_______|/           |_______|/5        /-------x
        0        1               0
    """
    if order == 0:
        return [corners]
    else:
        corners = np.array(corners)
        centroid = np.mean(corners, axis=0)

        faces = np.array([
            [0, 3, 2, 1], # bottom
            [4, 5, 6, 7], # top
            [1, 2, 6, 5], # right
            [0, 4, 7, 3], # left
            [0, 1, 5, 4], # front
            [7, 6, 2, 3], # back
            ])
        face_centers = np.array([np.mean(corners[face], axis=0)
            for face in faces])

        edge = np.array([
            [0, 1], [4, 5], [7, 6], [3, 2], # along X
            [0, 3], [1, 2], [5, 6], [4, 7], # along Y
            [0, 4], [1, 5], [2, 6], [3, 7], # along Z
            ])
        edge_centers = np.mean(corners[edge], axis=1)

        subcells = [
                [corners[0], edge_centers[0], face_centers[0], edge_centers[4],
                 edge_centers[8], face_centers[4], centroid, face_centers[3] ],
                [edge_centers[0], corners[1], edge_centers[5], face_centers[0],
                 face_centers[4], edge_centers[9], face_centers[2], centroid],
                [edge_centers[4], face_centers[0], edge_centers[3], corners[3],
                 face_centers[3], centroid, face_centers[5], edge_centers[11]],
                [face_centers[0], edge_centers[5], corners[2], edge_centers[3],
                 centroid, face_centers[2], edge_centers[10], face_centers[5]],

                [edge_centers[8], face_centers[4], centroid, face_centers[3],
                 corners[4], edge_centers[1], face_centers[1], edge_centers[7]],
                [face_centers[4], edge_centers[9], face_centers[2], centroid,
                 edge_centers[1], corners[5], edge_centers[6], face_centers[1]],
                [face_centers[3], centroid, face_centers[5], edge_centers[11],
                 edge_centers[7], face_centers[1], edge_centers[2], corners[7]],
                [centroid, face_centers[2], edge_centers[10], face_centers[5],
                 face_centers[1], edge_centers[6], corners[6], edge_centers[2]] ]
        subcell_corners = []
        for cell in subcells:
            subcell_corners += subdivide_hex(cell, order-1)
        return subcell_corners