C~2 Hermite interpolation by Pythagorean-hodograph quintic triarcs

摘要

In this paper, the problem of C~2 Hermite interpolation by triarcs composed of Pythagorean-hodograph (PH) quintics is considered. The main idea is to join three arcs of PH quintics at two unknown points - the first curve interpolates given C~2 Hermite data at one side, the third one interpolates the same type of given data at the other side and the middle arc is joined together with C~2 continuity to the first and the third arc. For any set of C~2 planar boundary data (two points with associated first and second derivatives) we construct four possible interpolants. The best possible approximation order is 4. Analogously, for a set of C~2 spatial boundary data we find a six-dimensional family of interpolating quintic PH triarcs. The results are confirmed by several examples.