# Pythagorean hodographs

@inproceedings{Farouki1990PythagoreanH, title={Pythagorean hodographs}, author={Rida T. Farouki and Takis Sakkalis}, year={1990} }

The hdograph of a plane parametric curve r(t) = (x(t), y(t)f is the locus described by the first parametric derivative r' (t) = (x ' (t), y ' (t)) of that curve. A polynomial parametric curve is said to have a Pythagorean hodograph if there exists a polynomial a(t) such that x t 2 (t) + y " (t) " Pythagorean triple. " Although Pythagorean-hodograph curves have fewer degrees of freedom than general polynomial curves of the same degree, they exhibit remarkably attractive properties for practical…

## 413 Citations

Pythagorean-hodograph space curves

- MathematicsAdv. Comput. Math.
- 1994

A characterization for allcubic Pythagoreanhodograph space curves is derived, in terms of constraints on the Bézier control polygon, and it is shown that such curves correspond geometrically to a family of non-circular helices.

Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3

- MathematicsJ. Comput. Appl. Math.
- 2012

PYTHAGOREAN-HODOGRAPH CUBICS AND GEOMETRIC HERMITE INTERPOLATION

- Mathematics
- 2012

In this paper, we present the geometric Hermite interpolation for planar Pythagorean-hodograph cubics for some general Hermite data. curve ro(t) = r(t) + dn(t) at a xed distance d from a given…

Hermite interpolation by Pythagorean hodograph quintics

- Mathematics
- 1995

The Pythagorean hodograph (PH) curves are polynomial parametric curves {x(t),y(t)} whose hodograph (derivative) components satisfy the Pythagorean condition x' 2 (t) + y' 2 (t) = σ 2 (t) for some…

Pythagorean-Hodograph B-Spline Curves

- Mathematics
- 2016

We introduce the new class of planar Pythagorean-Hodograph (PH) B-Spline curves. They can be seen as a generalization of the well-known class of planar Pythagorean-Hodograph (PH) B\'ezier curves,…

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