Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics

Table 1

Comparison of arc-length and bending energy for the interpolants of Figure 5.

𝑘=1	𝑀𝐶1	𝑀𝐶2	𝑀𝐶3	𝑀𝐶4	𝑄1	𝑄2	𝑄3	𝑄4
arc-length	3.03	2.19	3.10	2.29	2.34	2.16	2.34	2.16
BE	45.0	5.5	72.8	6.8	149	3106	273	5.3
𝑘=5	𝑀𝐶1	𝑀𝐶2	𝑀𝐶3	𝑀𝐶4	𝑄1	𝑄2	𝑄3	𝑄4
arc-length	2.93	2.28	4.50	2.31	3.05	2.40	3.05	2.40
BE	50.2	6.5	20.9	5.7	36.1	762	47.3	10.0
𝑘=10	𝑀𝐶1	𝑀𝐶2	𝑀𝐶3	𝑀𝐶4	𝑄1	𝑄2	𝑄3	𝑄4
arc-length	2.89	2.31	5.47	2.36	4.42	3.02	4.42	3.02
BE	54.03	8.2	16.6	7.5	14.4	345.9	19.3	36.9
𝑘=20	𝑀𝐶1	𝑀𝐶2	𝑀𝐶3	𝑀𝐶4	𝑄1	𝑄2	𝑄3	𝑄4
arc-length	2.85	2.34	6.13	2.40	7.91	5.39	7.91	5.39
BE	60.1	11.9	17.7	11.3	8.0	136	10.7	97.9