Support Function of Pythagorean Hodograph Cubics and G1 Hermite Interpolation

The Tschirnhausen cubic represents all non-degenerate Pythagorean Hododgraph cubics. We determine its support function and represent it as a convolution of a centrally symmetrical curve and a curve with linear normals. We use the support function to parametrize the Tschirnhausen cubic by normals. This parametrization is then used to an elegant and complete solution of the G(1) Hermite interpolation by Pythagorean Hodograph cubics. We apply the resulting algorithm to various examples and extend it to the interpolation by offsets of PH cubics.