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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def transform(curve, tf):
 """Transforms the curve by the homogeneous transformation matrix tf"""

    def to_point(p):
        return np.array([[p.real], [p.imag], [1.0]])

    def to_vector(z):
        return np.array([[z.real], [z.imag], [0.0]])

    def to_complex(v):
        return v.item(0) + 1j * v.item(1)

    if isinstance(curve, Path):
        return Path(*[transform(segment, tf) for segment in curve])
    elif is_bezier_segment(curve):
        return bpoints2bezier([to_complex(tf.dot(to_point(p)))
                               for p in curve.bpoints()])
    elif isinstance(curve, Arc):
        new_start = to_complex(tf.dot(to_point(curve.start)))
        new_end = to_complex(tf.dot(to_point(curve.end)))
        new_radius = to_complex(tf.dot(to_vector(curve.radius)))
        return Arc(new_start, radius=new_radius, rotation=curve.rotation,
                   large_arc=curve.large_arc, sweep=curve.sweep, end=new_end)
    else:
        raise TypeError("Input `curve` should be a Path, Line, "
                        "QuadraticBezier, CubicBezier, or Arc object.")