Cycles upon cycles: an anecdotal history of higher curves in science and engineering
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Planar spirals that match G2 Hermite data
Computer Aided Geometric Design
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Planar G2 Hermite interpolation with some fair, C-shaped curves
Journal of Computational and Applied Mathematics
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
G2 curve design with a pair of Pythagorean Hodograph quintic spiral segments
Computer Aided Geometric Design
Rational hypersurfaces with rational convolutions
Computer Aided Geometric Design
Curves and surfaces represented by polynomial support functions
Theoretical Computer Science
Transition between concentric or tangent circles with a single segment of G2 PH quintic curve
Computer Aided Geometric Design
On rationally supported surfaces
Computer Aided Geometric Design
G2 cubic transition between two circles with shape control
Journal of Computational and Applied Mathematics
Journal of Symbolic Computation
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
An involute spiral that matches G2 Hermite data in the plane
Computer Aided Geometric Design
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
Computer Aided Geometric Design
On convolutions of algebraic curves
Journal of Symbolic Computation
Hermite interpolation by hypocycloids and epicycloids with rational offsets
Computer Aided Geometric Design
G2 Hermite interpolation with circular precision
Computer-Aided Design
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Reparameterization of curves and surfaces with respect to their convolution
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Planar C1 Hermite interpolation with uniform and non-uniform TC-biarcs
Computer Aided Geometric Design
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It was recently proved in [27] that all rational hypocycloids and epicycloids are Pythagorean hodograph curves, i.e., rational curves with rational offsets. In this paper, we extend the discussion to a more general class of curves represented by trigonometric polynomial support functions. We show that these curves are offsets to translated convolutions of scaled and rotated hypocycloids and epicycloids. Using this result, we formulate a new and very simple G 2 Hermite interpolation algorithm based on solving a small system of linear equations. The efficiency of the designed method is then presented on several examples. In particular, we show how to approximate general trochoids, which, as we prove, are not Pythagorean hodograph curves in general.