A Direct Relation between Bezier and Polynomial Representation

Mohamed IMINE; Hiroshi NAGAHASHI; Takeshi AGUI

A Direct Relation between Bezier and Polynomial Representation

Mohamed IMINE, Hiroshi NAGAHASHI, Takeshi AGUI

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In this paper, a new explicit transformation method between Bezier and polynomial representation is proposed. An expression is given to approximate (n + 1) Bezier control points by another of (m + 1), and to perform simple and sufficiently good approximation without any additional transformation, such as Chebyshev polynomial. A criterion of reduction is then deduced in order to know if the given number of control points of a Bezier curve is reducible without error on the curve or not. Also an error estimation is given only in terms of control points. This method, unlike previous works, is more transparent because it is given in form of explicit expressions. Finally, we discuss some applications of this method to curve-fitting, order decreasing and increasing number of control points.

Publication: IEICE TRANSACTIONS on Information Vol.E79-D No.9 pp.1279-1285

Publication Date: 1996/09/25

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Type of Manuscript: PAPER

Category: Image Processing,Computer Graphics and Pattern Recognition

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Mohamed IMINE, Hiroshi NAGAHASHI, Takeshi AGUI, "A Direct Relation between Bezier and Polynomial Representation" in IEICE TRANSACTIONS on Information, vol. E79-D, no. 9, pp. 1279-1285, September 1996, doi: .
Abstract: In this paper, a new explicit transformation method between Bezier and polynomial representation is proposed. An expression is given to approximate (n + 1) Bezier control points by another of (m + 1), and to perform simple and sufficiently good approximation without any additional transformation, such as Chebyshev polynomial. A criterion of reduction is then deduced in order to know if the given number of control points of a Bezier curve is reducible without error on the curve or not. Also an error estimation is given only in terms of control points. This method, unlike previous works, is more transparent because it is given in form of explicit expressions. Finally, we discuss some applications of this method to curve-fitting, order decreasing and increasing number of control points.
URL: https://globals.ieice.org/en_transactions/information/10.1587/e79-d_9_1279/_p

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@ARTICLE{e79-d_9_1279,
author={Mohamed IMINE, Hiroshi NAGAHASHI, Takeshi AGUI, },
journal={IEICE TRANSACTIONS on Information},
title={A Direct Relation between Bezier and Polynomial Representation},
year={1996},
volume={E79-D},
number={9},
pages={1279-1285},
abstract={In this paper, a new explicit transformation method between Bezier and polynomial representation is proposed. An expression is given to approximate (n + 1) Bezier control points by another of (m + 1), and to perform simple and sufficiently good approximation without any additional transformation, such as Chebyshev polynomial. A criterion of reduction is then deduced in order to know if the given number of control points of a Bezier curve is reducible without error on the curve or not. Also an error estimation is given only in terms of control points. This method, unlike previous works, is more transparent because it is given in form of explicit expressions. Finally, we discuss some applications of this method to curve-fitting, order decreasing and increasing number of control points.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - A Direct Relation between Bezier and Polynomial Representation
T2 - IEICE TRANSACTIONS on Information
SP - 1279
EP - 1285
AU - Mohamed IMINE
AU - Hiroshi NAGAHASHI
AU - Takeshi AGUI
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 9
JA - IEICE TRANSACTIONS on Information
Y1 - September 1996
AB - In this paper, a new explicit transformation method between Bezier and polynomial representation is proposed. An expression is given to approximate (n + 1) Bezier control points by another of (m + 1), and to perform simple and sufficiently good approximation without any additional transformation, such as Chebyshev polynomial. A criterion of reduction is then deduced in order to know if the given number of control points of a Bezier curve is reducible without error on the curve or not. Also an error estimation is given only in terms of control points. This method, unlike previous works, is more transparent because it is given in form of explicit expressions. Finally, we discuss some applications of this method to curve-fitting, order decreasing and increasing number of control points.
ER -