Approximate merging of B-spline curves via knot adjustment and constrained optimization

Chiew Lan Tai; Shi Min Hu; Qi Xing Huang

doi:10.1016/S0010-4485(02)00176-8

Approximate merging of B-spline curves via knot adjustment and constrained optimization

Chiew Lan Tai, Shi Min Hu^*, Qi Xing Huang

^*Corresponding author for this work

Department of Computer Science and Engineering

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

42 Citations (Scopus)

Abstract

This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of merging curves to pass through some target points is also discussed.

Original language	English
Pages (from-to)	893-899
Number of pages	7
Journal	CAD Computer Aided Design
Volume	35
Issue number	10
DOIs	https://doi.org/10.1016/S0010-4485(02)00176-8
Publication status	Published - 1 Sept 2003

Keywords

B-spline curves
Constrained optimization
Knot adjustment
Merging

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10.1016/S0010-4485(02)00176-8

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abstract = "This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of merging curves to pass through some target points is also discussed.",

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T1 - Approximate merging of B-spline curves via knot adjustment and constrained optimization

AU - Tai, Chiew Lan

AU - Hu, Shi Min

AU - Huang, Qi Xing

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Y1 - 2003/9/1

N2 - This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of merging curves to pass through some target points is also discussed.

AB - This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of merging curves to pass through some target points is also discussed.

KW - B-spline curves

KW - Constrained optimization

KW - Knot adjustment

KW - Merging

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EP - 899

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

IS - 10

ER -

Approximate merging of B-spline curves via knot adjustment and constrained optimization

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Keywords

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