Curve design with rational Pythagorean-hodograph curves

Helmut Pottmann

doi:10.1007/BF03028365

Curve design with rational Pythagorean-hodograph curves

Helmut Pottmann^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

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 a G² piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation and G² Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail.

Original language	English (US)
Pages (from-to)	147-170
Number of pages	24
Journal	Advances in Computational Mathematics
Volume	3
Issue number	1-2
DOIs	https://doi.org/10.1007/BF03028365
State	Published - Jan 1995
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/BF03028365

Cite this

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title = "Curve design with rational Pythagorean-hodograph curves",

abstract = "The dual B{\'e}zier 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 a G2 piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation and G2 Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail.",

keywords = "Rational curve, curve approximation, dual B{\'e}zier representation, geometric Hermite interpolation, hodograph, offset curve",

author = "Helmut Pottmann",

year = "1995",

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AB - 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 a G2 piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation and G2 Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail.

KW - Rational curve

KW - curve approximation

KW - dual Bézier representation

KW - geometric Hermite interpolation

KW - hodograph

KW - offset curve

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Curve design with rational Pythagorean-hodograph curves

Abstract

Keywords

ASJC Scopus subject areas

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