Planar C~1 Hermite interpolation with PH cuts of degree (1,3) of Laurent series

摘要

We show how to find four generic interpolants to a C~1 Hermite data-set in the complex representation, using Pythagorean-hodograph curves generated as cuts of degree (1,3) of Laurent series. The developed numerical experiments have shown that two of these interpolants are simple curves and that these (at least) have stable shape, in the sense that their topologies persist when the direction of the velocity at each end-point changes. Our curves are fair, but have different shapes to those of other interpolants. Unlike existing methods, our technique allows regular PH interpolants to be found for special collinear C~1 Hermite data-sets.