Pythagorean hodographs

  title={Pythagorean hodographs},
  author={Rida T. Farouki and Takis Sakkalis},
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… 

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