Rectifying control polygon for planar Pythagorean hodograph curves

Soo Hyun Kim, Hwan Pyo Moon

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

A Bézier control polygon is not appropriate to control a Pythagorean hodograph curve since it has redundant degrees of freedom. So we propose an alternative, which is the rectifying control polygon. A rectifying control polygon of a PH curve has the same degrees of freedom as the PH curve. It interpolates the end points of the PH curve, but not the end tangents. Most of all, it has the same arc length as the PH curve. In this paper, we present the method to compute the rectifying control polygon from the Bézier control polygon of the PH curve. We also present the procedure to compute the PH curves from a given rectifying control polygon. For the development of these algorithms, we employ the Gauss–Legendre quadrature method and the Bernstein–Vandermonde linear system.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalComputer Aided Geometric Design
Volume54
DOIs
StatePublished - 1 May 2017

Keywords

  • Bernstein–Vandermonde matrix
  • Bézier control polygon
  • Gauss–Legendre quadrature
  • Pythagorean-hodograph curve
  • Rectifying control polygon

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