Iterative process for G2-multi degree reduction of Bézier curves

Abedallah Rababah; Stephen Mann

doi:10.1016/j.amc.2011.03.016

Iterative process for G²-multi degree reduction of Bézier curves

Abedallah Rababah, Stephen Mann

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

38 Citations (Scopus)

Abstract

In this paper, the issue of multi-degree reduction of Bézier curves with C¹ and G²-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method.

Original language	English
Pages (from-to)	8126-8133
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	217
Issue number	20
DOIs	https://doi.org/10.1016/j.amc.2011.03.016
Publication status	Published - Jun 15 2011
Externally published	Yes

Keywords

Bézier curves
G-continuity
Geometric continuity
Iterative methods
Multi-degree reduction

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.amc.2011.03.016

Cite this

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title = "Iterative process for G2-multi degree reduction of B{\'e}zier curves",

abstract = "In this paper, the issue of multi-degree reduction of B{\'e}zier curves with C1 and G2-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method.",

keywords = "B{\'e}zier curves, G-continuity, Geometric continuity, Iterative methods, Multi-degree reduction",

author = "Abedallah Rababah and Stephen Mann",

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N1 - Funding Information: The authors thank the referees for their valuable comments.This work was funded in part by the National Research Council of Canada.

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KW - Geometric continuity

KW - Iterative methods

KW - Multi-degree reduction

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