IBM Journal of Research and Development
The conformal map z→z2 of the hodograph plane
Computer Aided Geometric Design
The NURBS book
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Geometric Hermite interpolation
Computer Aided Geometric Design
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
Geometric Hermite interpolation with Tschirnhausen cubics
Journal of Computational and Applied Mathematics
Hermite interpolation with Tschirnhausen cubic spirals
Computer Aided Geometric Design
Optimal geometric Hermite interpolation of curves
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
On the local existence of the quadratic geometric Hermite interpolant
Computer Aided Geometric Design
Geometric Hermite curves with minimum strain energy
Computer Aided Geometric Design
An offset algorithm for polyline curves
Computers in Industry
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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.