Advances in Computational Mathematics

, Volume 3, Issue 1–2, pp 147–170

Curve design with rational Pythagorean-hodograph curves

  • Helmut Pottmann


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 curve hodograph offset curve dual Bézier representation geometric Hermite interpolation curve approximation 


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Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

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

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