Multi-degree Reduction of Bezier Curves with Constraints Using Dual Bernstein Basis Polynomials

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Bakhshesh, Davood | 2009

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40022 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi-Amiri, Nezameddin
Abstract:
Bezier curves are among important curves which are broadly used in different fields such as computer graphic, vector graphic and animation. Among softwares in which these curves are used nowadays are: Adobe, Inkscape, GIMP, Adobe Photoshop, and Illustrator. An important concept in drawing the Bezier curves is to plot these curveswith fewer numbers of control points (low degree). Many algorithms have been introduced to reduce the degree of bezier curves. Here we first describe Bezier curves and their properties. Our main concern here is implementation of a new algorithm for multi-degree reduction of Bezier curves which are constrainted. The algorithm has recently been proposed byWozny and Lewanowicz in [26]. The generated software code is written in C#.Net language. We will see that the degree of a Bezier curve with constraints could be reduced, with suitable approximation using dual Bernstein basis polynomials. The numerical results from the generated software are reporetd.
Keywords:
Bezier Curve ; Multi Degree Reduction ; Dual Bernstein Basis Polynomial ; Dual Discrete Bernstein Basis Polynomial

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