A simple verification of the implicitization formulae for Bézier curves (Q1324665)
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scientific article; zbMATH DE number 571729
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple verification of the implicitization formulae for Bézier curves |
scientific article; zbMATH DE number 571729 |
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A simple verification of the implicitization formulae for Bézier curves (English)
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6 November 1994
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It is well-known that any (planar) rational Bézier curve of ``degree'' \(n\) can be defined implicitly by a single equation of the form (1) \(\text{det} (F)=0\), where \(F\) is a certain explicitly known \((n \times n)\)- matrix. In the present paper the authors give a new and rather short proof (based on de-Casteljau's algorithm) of the fact that (1) is satisfied for each point on the Bézier curve.
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implicit definition
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rational Bézier curve
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de-Casteljau's algorithm
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