Interpolation of G¹ Hermite data by C¹ cubic-like sparse Pythagorean hodograph splines

Provided that they are in appropriate configurations (tight data), given planar G¹ Hermite data generate a unique cubic Pythagorean hodograph (PH) spline curve interpolant. On a given associated knot-vector, the corresponding spline function cannot be C¹, save for exceptional cases. By contrast, we show that replacing cubic spaces by cubic-like sparse spaces makes it possible to produce infinitely many C¹ PH spline functions interpolating any given tight G¹ Hermite data. Such cubic-like sparse spaces involve the constants and monomials of consecutive degrees, and they have long been used for design purposes. Only lately they were investigated in view of producing PH curves and associated G¹ PH spline interpolants with some flexibility. The present work strongly relies on these recent results.