Linear independence of the blending functions of T-splines without multiple knots

Aizeng Wang; Gang Zhao; Yong Dong Li

doi:10.1016/j.eswa.2013.12.012

Linear independence of the blending functions of T-splines without multiple knots

Aizeng Wang
, Gang Zhao^*
, Yong Dong Li

^*Corresponding author for this work

School of Mechanical Engineering and Automation

Beihang University

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

8 Scopus citations

Abstract

The purpose of the present paper is to answer the following open question given by Sederberg's research team: are there T-splines with linearly dependent blending functions that do not have multiple knots? First, the mathematical properties of the blending functions of T-splines without multiple knots are analyzed. Then, the linear independence of them is proved, and meanwhile a necessary condition is deduced for the linear dependence of T-spline blending functions. Finally, the answer to the open question is obtained: there are no T-splines with linearly dependent blending functions that do not have multiple knots.

Original language	English
Pages (from-to)	3634-3639
Number of pages	6
Journal	Expert Systems with Applications
Volume	41
Issue number	8
DOIs	https://doi.org/10.1016/j.eswa.2013.12.012
State	Published - 15 Jun 2014

Keywords

B-splines
Blending function
CAGD
Linear independence
T-splines

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10.1016/j.eswa.2013.12.012

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title = "Linear independence of the blending functions of T-splines without multiple knots",

abstract = "The purpose of the present paper is to answer the following open question given by Sederberg's research team: are there T-splines with linearly dependent blending functions that do not have multiple knots? First, the mathematical properties of the blending functions of T-splines without multiple knots are analyzed. Then, the linear independence of them is proved, and meanwhile a necessary condition is deduced for the linear dependence of T-spline blending functions. Finally, the answer to the open question is obtained: there are no T-splines with linearly dependent blending functions that do not have multiple knots.",

keywords = "B-splines, Blending function, CAGD, Linear independence, T-splines",

author = "Aizeng Wang and Gang Zhao and Li, \{Yong Dong\}",

year = "2014",

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doi = "10.1016/j.eswa.2013.12.012",

language = "英语",

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journal = "Expert Systems with Applications",

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TY - JOUR

T1 - Linear independence of the blending functions of T-splines without multiple knots

AU - Wang, Aizeng

AU - Zhao, Gang

AU - Li, Yong Dong

PY - 2014/6/15

Y1 - 2014/6/15

N2 - The purpose of the present paper is to answer the following open question given by Sederberg's research team: are there T-splines with linearly dependent blending functions that do not have multiple knots? First, the mathematical properties of the blending functions of T-splines without multiple knots are analyzed. Then, the linear independence of them is proved, and meanwhile a necessary condition is deduced for the linear dependence of T-spline blending functions. Finally, the answer to the open question is obtained: there are no T-splines with linearly dependent blending functions that do not have multiple knots.

AB - The purpose of the present paper is to answer the following open question given by Sederberg's research team: are there T-splines with linearly dependent blending functions that do not have multiple knots? First, the mathematical properties of the blending functions of T-splines without multiple knots are analyzed. Then, the linear independence of them is proved, and meanwhile a necessary condition is deduced for the linear dependence of T-spline blending functions. Finally, the answer to the open question is obtained: there are no T-splines with linearly dependent blending functions that do not have multiple knots.

KW - B-splines

KW - Blending function

KW - CAGD

KW - Linear independence

KW - T-splines

UR - https://www.scopus.com/pages/publications/84891704541

U2 - 10.1016/j.eswa.2013.12.012

DO - 10.1016/j.eswa.2013.12.012

M3 - 文章

AN - SCOPUS:84891704541

SN - 0957-4174

VL - 41

SP - 3634

EP - 3639

JO - Expert Systems with Applications

JF - Expert Systems with Applications

IS - 8

ER -

Linear independence of the blending functions of T-splines without multiple knots

Abstract

Keywords

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