IBM Journal of Research and Development
The conformal map z→z2 of the hodograph plane
Computer Aided Geometric Design
A metric for parametric approximation
Proceedings of the international conference on Curves and surfaces in geometric design
Hermite interpolation with Tschirnhausen cubic spirals
Computer Aided Geometric Design
Construction and shape analysis of PH Hermite interpolants
Computer Aided Geometric Design
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
Computer Aided Geometric Design
Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants
Computer Aided Geometric Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
Computer Aided Geometric Design
G1 Hermite interpolation by PH cubics revisited
Computer Aided Geometric Design
An approach to geometric interpolation by Pythagorean-hodograph curves
Advances in Computational Mathematics
Planar C1 Hermite interpolation with uniform and non-uniform TC-biarcs
Computer Aided Geometric Design
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In this paper the C^1 Hermite interpolation problem by spatial Pythagorean-hodograph cubic biarcs is presented and a general algorithm to construct such interpolants is described. Each PH cubic segment interpolates C^1 data at one point and they are then joined together with a C^1 continuity at some unknown common point sharing some unknown tangent vector. Biarcs are expressed in a closed form with three shape parameters. Two of them are selected based on asymptotic approximation order, while the remaining one can be computed by minimizing the length of the biarc or by minimizing the elastic bending energy. The final interpolating spline curve is globally C^1 continuous, it can be constructed locally and it exists for arbitrary Hermite data configurations.