Unbalanced Hermite Interpolation with Tschirnhausen Cubics.

A method for constructing a cubic Pythagorean hodograph (PH) curve (called a Tschirnhausen cubic curve as well) satisfying unbalanced Hermite interpolation conditions is presented. The resultant curve interpolates two given end points, and has a given vector as the tangent vector at the starting point. The generation method is based on complex number calculation. Resultant curves are represented in a Bézier form. Our result shows that there are two Tschirnhausen cubic curves fulfilling the unbalanced Hermite interpolation conditions. An explicit formula for calculating the absolute rotation number is provided to select the better curve from the two Tschirnhausen cubic curves. Examples are given as well to illustrate the method proposed in this paper. Keywords: Hermite; Pythagorean hodograph; Absolute rotation number. [ABSTRACT FROM AUTHOR]