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Curve design with rational Pythagorean-hodograph curves

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Abstract

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.

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  1. Institut für Geometrie, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    Helmut Pottmann

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  1. Helmut Pottmann
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Pottmann, H. Curve design with rational Pythagorean-hodograph curves. Adv Comput Math 3, 147–170 (1995). https://doi.org/10.1007/BF03028365

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  • DOI: https://doi.org/10.1007/BF03028365

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