How to use the compas.geometry.basic.normalize_vector function in compas

If the lines are parallel, the return value is [None, None].

    Examples
    --------
    >>>

    """
    a, b = l1
    c, d = l2

    ab = subtract_vectors(b, a)
    cd = subtract_vectors(d, c)

    n = cross_vectors(ab, cd)
    n1 = normalize_vector(cross_vectors(ab, n))
    n2 = normalize_vector(cross_vectors(cd, n))

    plane_1 = (a, n1)
    plane_2 = (c, n2)

    i1 = intersection_line_plane(l1, plane_2, tol=tol)
    i2 = intersection_line_plane(l2, plane_1, tol=tol)

    return i1, i2

>>> axis1 = normalize_vector([-0.043, -0.254, 0.617])
    >>> angle1 = 0.1
    >>> R = matrix_from_axis_and_angle(axis1, angle1)
    >>> axis2, angle2 = axis_and_angle_from_matrix(R)
    >>> allclose(axis1, axis2)
    True
    >>> allclose([angle1], [angle2])
    True

    """
    if not point:
        point = [0.0, 0.0, 0.0]

    axis = list(axis)
    if length_vector(axis):
        axis = normalize_vector(axis)

    sina = math.sin(angle)
    cosa = math.cos(angle)

    R = [[cosa, 0.0, 0.0], [0.0, cosa, 0.0], [0.0, 0.0, cosa]]

    outer_product = [[axis[i] * axis[j] *
                      (1.0 - cosa) for i in range(3)] for j in range(3)]
    R = [[R[i][j] + outer_product[i][j]
          for i in range(3)] for j in range(3)]

    axis = scale_vector(axis, sina)
    m = [[0.0, -axis[2], axis[1]],
         [axis[2], 0.0, -axis[0]],
         [-axis[1], axis[0], 0.0]]

Examples
    --------
    >>> xaxis = [1, 4, 5]
    >>> yaxis = [1, 0, -2]
    >>> xaxis, yaxis = correct_axes(xaxis, yaxis)
    >>> allclose(xaxis, [0.1543, 0.6172, 0.7715], tol=0.001)
    True
    >>> allclose(yaxis, [0.6929, 0.4891, -0.5298], tol=0.001)
    True
    """
    xaxis = normalize_vector(xaxis)
    yaxis = normalize_vector(yaxis)
    zaxis = cross_vectors(xaxis, yaxis)
    if not norm_vector(zaxis):
        raise ValueError("Xaxis and yaxis cannot span a plane.")
    yaxis = cross_vectors(normalize_vector(zaxis), xaxis)
    return xaxis, yaxis

def matrix_from_orthogonal_projection(point, normal):
    """Returns an orthogonal projection matrix to project onto a plane \
        defined by point and normal.

    Args:
        point(:obj:`list` of :obj:`float`)
        normal(:obj:`list` of :obj:`float`)

    Example:
        >>> point = [0, 0, 0]
        >>> normal = [0, 0, 1]
        >>> P = matrix_from_orthogonal_projection(point, normal)
    """
    T = identity_matrix(4)
    normal = normalize_vector(normal)

    for j in range(3):
        for i in range(3):
            T[i][j] -= normal[i] * normal[j]  # outer_product

    T[0][3], T[1][3], T[2][3] = scale_vector(
        normal, dot_vectors(point, normal))
    return T

Parameters
        ----------
        xaxis : :class:`Vector`
            The x-axis of the frame.
        yaxis : :class:`Vector`
            The y-axis of the frame.

        Examples
        --------
        >>> xaxis = [0.68, 0.68, 0.27]
        >>> yaxis = [-0.67, 0.73, -0.15]
        >>> R = Rotation.from_basis_vectors(xaxis, yaxis)

        """
        xaxis = normalize_vector(list(xaxis))
        yaxis = normalize_vector(list(yaxis))
        zaxis = cross_vectors(xaxis, yaxis)
        yaxis = cross_vectors(zaxis, xaxis)  # correction

        R = cls()
        R.matrix[0][0], R.matrix[1][0], R.matrix[2][0] = xaxis
        R.matrix[0][1], R.matrix[1][1], R.matrix[2][1] = yaxis
        R.matrix[0][2], R.matrix[1][2], R.matrix[2][2] = zaxis
        return R

Parameters
        ----------
        xaxis : :class:`Vector`
            The x-axis of the frame.
        yaxis : :class:`Vector`
            The y-axis of the frame.

        Examples
        --------
        >>> xaxis = [0.68, 0.68, 0.27]
        >>> yaxis = [-0.67, 0.73, -0.15]
        >>> R = Rotation.from_basis_vectors(xaxis, yaxis)

        """
        xaxis = normalize_vector(list(xaxis))
        yaxis = normalize_vector(list(yaxis))
        zaxis = cross_vectors(xaxis, yaxis)
        yaxis = cross_vectors(zaxis, xaxis)  # correction

        R = cls()
        R.matrix[0][0], R.matrix[1][0], R.matrix[2][0] = xaxis
        R.matrix[0][1], R.matrix[1][1], R.matrix[2][1] = yaxis
        R.matrix[0][2], R.matrix[1][2], R.matrix[2][2] = zaxis
        return R

def __init__(self, point, normal):
        super(Reflection, self).__init__()

        normal = normalize_vector((list(normal)))

        for i in range(3):
            for j in range(3):
                self.matrix[i][j] -= 2.0 * normal[i] * normal[j]

        for i in range(3):
            self.matrix[i][3] = 2 * dot_vectors(point, normal) *\
                normal[i]

as list of 3 numbers.
        normal (:obj:`list` of :obj:`float`): The normal of the shear plane
            as list of 3 numbers.

    Raises:
        ValueError: If direction and normal are not orthogonal.

    Example:
        >>> angle = 0.1
        >>> direction = [0.1, 0.2, 0.3]
        >>> point = [4, 3, 1]
        >>> normal = cross_vectors(direction, [1, 0.3, -0.1])
        >>> S = matrix_from_shear(angle, direction, point, normal)
    """

    normal = normalize_vector(normal)
    direction = normalize_vector(direction)

    if math.fabs(dot_vectors(normal, direction)) > _EPS:
        raise ValueError('Direction and normal vectors are not orthogonal')

    angle = math.tan(angle)
    M = [[1. if i == j else 0. for i in range(4)] for j in range(4)]

    for j in range(3):
        for i in range(3):
            M[i][j] += angle * direction[i] * normal[j]

    M[0][3], M[1][3], M[2][3] = scale_vector(
        direction, -angle * dot_vectors(point, normal))

    return M

def matrix_from_basis_vectors(xaxis, yaxis):
    """Creates a rotation matrix from basis vectors (= orthonormal vectors).

    Args:
        xaxis (:obj:`list` oof :obj:`float`): The x-axis of the frame.
        yaxis (:obj:`list` oof :obj:`float`): The y-axis of the frame.

    Example:
        >>> xaxis = [0.68, 0.68, 0.27]
        >>> yaxis = [-0.67, 0.73, -0.15]
        >>> R = matrix_from_basis_vectors(xaxis, yaxis)
    """
    xaxis = normalize_vector(list(xaxis))
    yaxis = normalize_vector(list(yaxis))
    zaxis = cross_vectors(xaxis, yaxis)
    yaxis = cross_vectors(zaxis, xaxis)  # correction

    R = identity_matrix(4)
    R[0][0], R[1][0], R[2][0] = xaxis
    R[0][1], R[1][1], R[2][1] = yaxis
    R[0][2], R[1][2], R[2][2] = zaxis
    return R

(:obj:`list` of :obj:`list` of :obj:`float`): The matrix.

    Example:
        >>> axis1 = normalize_vector([-0.043, -0.254, 0.617])
        >>> angle1 = 0.1
        >>> R = matrix_from_axis_and_angle(axis1, angle1)
        >>> axis2, angle2 = axis_and_angle_from_matrix(R)
        >>> allclose(axis1, axis2)
        True
        >>> allclose([angle1], [angle2])
        True
    """

    axis = list(axis)
    if length_vector(axis):
        axis = normalize_vector(axis)

    sina = math.sin(angle)
    cosa = math.cos(angle)

    R = [[cosa, 0.0, 0.0], [0.0, cosa, 0.0], [0.0, 0.0, cosa]]

    outer_product = [[axis[i] * axis[j] *
                      (1.0 - cosa) for i in range(3)] for j in range(3)]
    R = [[R[i][j] + outer_product[i][j]
          for i in range(3)] for j in range(3)]

    axis = scale_vector(axis, sina)
    m = [[0.0, -axis[2], axis[1]],
         [axis[2], 0.0, -axis[0]],
         [-axis[1], axis[0], 0.0]]