Polynomial approximation of rational Bézier curves with constraints

Polynomial approximation of rational Bézier curves with constraints

We present an efficient method to solve the problem of the constrained least squares approximation of the rational Bézier curve by the polynomial Bézier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials, and exploits their recursive properties. Examples are given,...

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Veröffentlicht in:Numerical algorithms 2012-04, Vol.59 (4), p.607-622
Hauptverfasser: Lewanowicz, Stanisław, Woźny, Paweł, Keller, Paweł
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algorithms
Approximation
Computer Science
Constraints
Curves
Mathematical analysis
Numeric Computing
Numerical Analysis
Original Paper
Polynomials
Theory of Computation
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Beschreibung
Zusammenfassung:We present an efficient method to solve the problem of the constrained least squares approximation of the rational Bézier curve by the polynomial Bézier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials, and exploits their recursive properties. Examples are given, showing the effectiveness of the algorithm.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-011-9507-0