Function intersect_volume_volume

python/visualization.py:183–237

(volume1: Volume, volume2: Volume)

# Volumes must be a line, plane, or rectangular prism
# (since they are volume objects)
def intersect_volume_volume(volume1: Volume, volume2: Volume) -> List[Vector3]:
    # volume1 ............... [volume]
    # volume2 ............... [volume]

    # Represent the volumes by an "upper" and "lower" coordinate
    U1 = [
        volume1.center.x + volume1.size.x / 2,
        volume1.center.y + volume1.size.y / 2,
        volume1.center.z + volume1.size.z / 2,
    ]
    L1 = [
        volume1.center.x - volume1.size.x / 2,
        volume1.center.y - volume1.size.y / 2,
        volume1.center.z - volume1.size.z / 2,
    ]

    U2 = [
        volume2.center.x + volume2.size.x / 2,
        volume2.center.y + volume2.size.y / 2,
        volume2.center.z + volume2.size.z / 2,
    ]
    L2 = [
        volume2.center.x - volume2.size.x / 2,
        volume2.center.y - volume2.size.y / 2,
        volume2.center.z - volume2.size.z / 2,
    ]

    # Evaluate intersection
    U = np.min([U1, U2], axis=0)
    L = np.max([L1, L2], axis=0)

    # For single points we have to check manually
    if np.all(U - L == 0):
        if (not volume1.pt_in_volume(Vector3(*U))) or (
            not volume2.pt_in_volume(Vector3(*U))
        ):
            return []

    # Check for two volumes that don't intersect
    if np.any(U - L < 0):
        return []

    # Pull all possible vertices
    vertices = []
    for x_vals in [L[0], U[0]]:
        for y_vals in [L[1], U[1]]:
            for z_vals in [L[2], U[2]]:
                vertices.append(Vector3(x_vals, y_vals, z_vals))

    # Remove any duplicate points caused by coplanar lines
    vertices = [
        vertices[i] for i, x in enumerate(vertices) if x not in vertices[i + 1 :]
    ]

    return vertices


# All of the 2D plotting routines need an output plane over which to plot.