  By interpreting planar polynomial curves as complex-valued functions of a
real parameter, an inner product, norm, metric function, and the notion of
orthogonality may be defined for such curves. This approach is applied to the
complex pre-image polynomials that generate planar Pythagorean-hodograph (PH)
curves, to facilitate the implementation of bounded modifications of them that
preserve their PH nature. The problems of bounded modifications under the
constraint of fixed curve end points and end tangent directions, and of
increasing the arc length of a PH curve by a prescribed amount, are also
addressed.
