Abstract: By the advantages of computing arcs and representing offsets, study of phythagorean
hodograph curves is one of the hot topics in recent years. In this paper, G2 Hermite interpolation by
sextic PH curves is studied. Sextic PH curves can be classified into two types and the interpolation
problem can be resolved to get the control points with some free parameter in complex representation.
With the analysis of arc-length, bending energy and absolute rotation number, the better interpolation
curves are selected. Moreover, the sextic PH G2 Hermite interpolation is applied to approximate the 90°
and 67° arcs. The best approximating curves can solve C1 Hermite interpolation by the PH sextics. And
the best curves’ performance is better than the quintic G2 Hermite interpolation curves when
approximating the 90° arc, and is almost same as the latter’s best curve when approximating the 67° arc.

Key words: PH curve, G2 Hermite interpolation, arc