Advances in Computational Mathematics

, Volume 3, Issue 1, pp 147-170

First online:

Curve design with rational Pythagorean-hodograph curves

  • Helmut PottmannAffiliated withInstitut für Geometrie, Technische Universität Wien

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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 aG 2 piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation andG 2 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