Planar C1C1 Hermite interpolation with PH cuts of degree (1,3)(1,3) of Laurent series

• We introduce a new class of PH curves, PH cuts of degree (1,3)(1,3) of Laurent series.
• We show how to find PH skew cut interpolants to a C1C1 Hermite data-set.
• We show that two of these interpolants are short, simple curves with stable shape.
• Our curves are fair with different shapes to those of other interpolants.
• We can obtain regular PH interpolants for collinear C1C1 Hermite data-sets.

We show how to find four generic interpolants to a C1C1 Hermite data-set in the complex representation, using Pythagorean-hodograph curves generated as cuts of degree  (1,3)(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 C1C1 Hermite data-sets.