Geometric Method for Hermite Interpolation by a Class of PH Quintics

In this paper, geometric relationship among Bézier control points of PH(Pythagorean Hodograph) quintics is developed, which leading to a geometric method for Hermite interpolation by PH quintics. The resultant PH quintics are represented in a standard Bézier form. Additionally,according to the similarity to a Bézier curve of degree three with the same Hermite interpolation conditions, a geometric method for selecting the best curve in the resultant PH quintics is given as well.