Approximate implicitization of planar curves by piecewise rational approximation of the distance function

Mohamed Shalaby; Bert Jüttler; Josef Schicho

doi:10.1007/s00200-006-0025-6

Approximate implicitization of planar curves by piecewise rational approximation of the distance function

Mohamed Shalaby, Bert Jüttler, Josef Schicho^*

^*Corresponding author for this work

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

Abstract

We present an approximate implicitization method for planar curves. The computed implicit representation is a piecewise rational approximation of the distance function to the given parametric curve. The proposed method consists of four main steps: quadratic B-spline approximation of the given parametric curve, data reduction, segments-wise implicitization, multiplying with suitable polynomial factors. These segments are joined such that the collection generate a global C ^r spline function which approximates the distance function, for r=0, 1.

Original language	English (US)
Pages (from-to)	71-89
Number of pages	19
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	18
Issue number	1-2
DOIs	https://doi.org/10.1007/s00200-006-0025-6
State	Published - Feb 2007
Externally published	Yes

Keywords

Approximate implicitization
Distance function

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1007/s00200-006-0025-6

Cite this

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abstract = "We present an approximate implicitization method for planar curves. The computed implicit representation is a piecewise rational approximation of the distance function to the given parametric curve. The proposed method consists of four main steps: quadratic B-spline approximation of the given parametric curve, data reduction, segments-wise implicitization, multiplying with suitable polynomial factors. These segments are joined such that the collection generate a global C r spline function which approximates the distance function, for r=0, 1.",

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AU - Schicho, Josef

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N2 - We present an approximate implicitization method for planar curves. The computed implicit representation is a piecewise rational approximation of the distance function to the given parametric curve. The proposed method consists of four main steps: quadratic B-spline approximation of the given parametric curve, data reduction, segments-wise implicitization, multiplying with suitable polynomial factors. These segments are joined such that the collection generate a global C r spline function which approximates the distance function, for r=0, 1.

AB - We present an approximate implicitization method for planar curves. The computed implicit representation is a piecewise rational approximation of the distance function to the given parametric curve. The proposed method consists of four main steps: quadratic B-spline approximation of the given parametric curve, data reduction, segments-wise implicitization, multiplying with suitable polynomial factors. These segments are joined such that the collection generate a global C r spline function which approximates the distance function, for r=0, 1.

KW - Approximate implicitization

KW - Distance function

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DO - 10.1007/s00200-006-0025-6

M3 - Article

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ER -

Approximate implicitization of planar curves by piecewise rational approximation of the distance function

Abstract

Keywords

ASJC Scopus subject areas

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