Reduced-knot nurbs representations of rational G1 composite Bézier curves

Barry Joe; Wenping Wang; Fuhua Cheng

doi:10.1016/0010-4485(94)90026-4

Reduced-knot nurbs representations of rational G¹ composite Bézier curves

Barry Joe, Wenping Wang, Fuhua Cheng

Computer Science

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

2 Scopus citations

Abstract

It is well known that a rational G¹ composite Bézier curve of degree n can be represented as a nurbs curve with knots of multiplicity n. An algorithm is presented that reduces the degree of multiplicity of some knots to n-1. This reduced-knot nurbs representation is based on the reparameterization of the Bézier curve segments.

Original language	English
Pages (from-to)	393-399
Number of pages	7
Journal	CAD Computer Aided Design
Volume	26
Issue number	5
DOIs	https://doi.org/10.1016/0010-4485(94)90026-4
State	Published - May 1994

Bibliographical note

Funding Information:
The research of B Joe was partially supported by a grant from the Natural Sciences and Engmeenng Research Council of Canada The research ofF Cheng was partially supported by IBM

Keywords

knot reduction
nurbs
rational Bézier curves
reparameterization

ASJC Scopus subject areas

Computer Science Applications
Computer Graphics and Computer-Aided Design
Industrial and Manufacturing Engineering

Access to Document

10.1016/0010-4485(94)90026-4

Cite this

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title = "Reduced-knot nurbs representations of rational G1 composite B{\'e}zier curves",

abstract = "It is well known that a rational G1 composite B{\'e}zier curve of degree n can be represented as a nurbs curve with knots of multiplicity n. An algorithm is presented that reduces the degree of multiplicity of some knots to n-1. This reduced-knot nurbs representation is based on the reparameterization of the B{\'e}zier curve segments.",

keywords = "knot reduction, nurbs, rational B{\'e}zier curves, reparameterization",

author = "Barry Joe and Wenping Wang and Fuhua Cheng",

note = "Funding Information: The research of B Joe was partially supported by a grant from the Natural Sciences and Engmeenng Research Council of Canada The research ofF Cheng was partially supported by IBM",

year = "1994",

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language = "English",

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T1 - Reduced-knot nurbs representations of rational G1 composite Bézier curves

AU - Joe, Barry

AU - Wang, Wenping

AU - Cheng, Fuhua

N1 - Funding Information: The research of B Joe was partially supported by a grant from the Natural Sciences and Engmeenng Research Council of Canada The research ofF Cheng was partially supported by IBM

PY - 1994/5

Y1 - 1994/5

N2 - It is well known that a rational G1 composite Bézier curve of degree n can be represented as a nurbs curve with knots of multiplicity n. An algorithm is presented that reduces the degree of multiplicity of some knots to n-1. This reduced-knot nurbs representation is based on the reparameterization of the Bézier curve segments.

AB - It is well known that a rational G1 composite Bézier curve of degree n can be represented as a nurbs curve with knots of multiplicity n. An algorithm is presented that reduces the degree of multiplicity of some knots to n-1. This reduced-knot nurbs representation is based on the reparameterization of the Bézier curve segments.

KW - knot reduction

KW - nurbs

KW - rational Bézier curves

KW - reparameterization

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