Advances in Computational Mathematics

, Volume 3, Issue 1, pp 147–170

Curve design with rational Pythagorean-hodograph curves

  • Helmut Pottmann

DOI: 10.1007/BF03028365

Cite this article as:
Pottmann, H. Adv Comput Math (1995) 3: 147. doi:10.1007/BF03028365


The dual Bézier representation offers a simple and efficient constructive approach to rational curves with rational offsets (rational PH curves). Based on the dual form, we develop geometric algorithms for approximating a given curve with aG2 piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation andG2 Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail.


Rational curvehodographoffset curvedual Bézier representationgeometric Hermite interpolationcurve approximation

Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • Helmut Pottmann
    • 1
  1. 1.Institut für GeometrieTechnische Universität WienWienAustria