C1C1 Hermite interpolation with PH curves by boundary data modification

We show how to create a new class of infinitely many PH Hermite interpolants for a given ordinary C1C1 Hermite data-set, in a way that ameliorates the rapid shape transitions in PH quintic interpolants that occurs when boundary data has poor geometric compatibility. We first interpolate a Hermite data-set using two asymmetric PH cubics, each of which satisfies the data at one boundary. Then we selectively apply one of three shape improvement techniques to the interpolant, so as to eliminate rapid shape transitions and produce C1C1 PH curves with lower bending energy, at the expense of a small increase in arc-length.