An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Geometric Hermite interpolation with Tschirnhausen cubics
Journal of Computational and Applied Mathematics
Construction and shape analysis of PH Hermite interpolants
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
Computer Aided Geometric Design
Characterization and construction of helical polynomial space curves
Journal of Computational and Applied Mathematics
A generalisation of the Pythagorean hodograph quintic spiral
Journal of Computational and Applied Mathematics
Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
Computer Aided Geometric Design
Journal of Symbolic Computation
Quintic space curves with rational rotation-minimizing frames
Computer Aided Geometric Design
Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
Journal of Symbolic Computation
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
Advances in Computational Mathematics
Computer Aided Geometric Design
Rational Pythagorean-hodograph space curves
Computer Aided Geometric Design
Computer Aided Geometric Design
A complete classification of quintic space curves with rational rotation-minimizing frames
Journal of Symbolic Computation
Geometric design using space curves with rational rotation-minimizing frames
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
On the approximation order of a space data-dependent PH quintic Hermite interpolation scheme
Computer Aided Geometric Design
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As observed by Farouki et al.[9], any set of C1 space boundary data (two points with associated first derivatives) can be interpolated by a Pythagorean hodograph (PH) curve of degree 5. In general there exists a two dimensional family of interpolants. In this paper we study the properties of this family in more detail. We introduce a geometrically invariant parameterization of the family of interpolants. This parameterization is used to identify a particular solution, which has the following properties. Firstly, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve. Secondly, it has the best possible approximation order (4). Thirdly, it is symmetric in the sense that the interpolant of the “reversed” set of boundary data is simply the “reversed” original interpolant. These observations lead to a fast and precise algorithm for converting any (possibly piecewise) analytical curve into a piecewise PH curve of degree 5 which is globally C1. Finally we exploit the rational frames associated with any space PH curve (the Euler-Rodrigues frame) in order to obtain a simple rational approximation of pipe surfaces with a piecewise analytical spine curve and we analyze its approximation order.