Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics

Figure 5

Comparison of pairs of PH interpolants, satisfying the same 𝐶¹ Hermite data-set (0,2,𝑘(1+√−1),1+2√−1), when 𝑘=1,5,10,20: (a), (b), (c), and (d), respectively, show the Möbius transformations of the PH cubics 𝑀𝐶_𝑖 when 𝑘=1,5,10,20; and (a)′, (b)′, (c)′, and (d)′ show the correspoding PH quintics 𝑄_𝑖.