Uniform B-spline curve interpolation with prescribed tangent and curvature vectors

Shoichi Okaniwa; Ahmad Nasri; Hongwei Lin; Abdulwahed Abbas; Yuki Kineri; Takashi Maekawa

doi:10.1109/TVCG.2011.262

Uniform B-spline curve interpolation with prescribed tangent and curvature vectors

Shoichi Okaniwa^*, Ahmad Nasri, Hongwei Lin, Abdulwahed Abbas, Yuki Kineri, Takashi Maekawa

^*Corresponding author for this work

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

45 Citations (Scopus)

Abstract

This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints. To satisfy these constraints, knot insertion is used to generate additional control points which are progressively repositioned using corresponding geometric rules. Compared to existing schemes, our approach is capable of handling plane as well as space curves, has local control, and avoids the solution of the typical linear system. The effectiveness of the proposed algorithm is illustrated through several comparative examples. Applications of the method in NC machining and shape design are also outlined.

Original language	English
Article number	6035703
Pages (from-to)	1474-1487
Number of pages	14
Journal	IEEE Transactions on Visualization and Computer Graphics
Volume	18
Issue number	9
DOIs	https://doi.org/10.1109/TVCG.2011.262
Publication status	Published - 2012
Externally published	Yes

Keywords

B-spline curve
curvature vector
interpolation
parametric curve
tangent

ASJC Scopus subject areas

Software
Signal Processing
Computer Vision and Pattern Recognition
Computer Graphics and Computer-Aided Design

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10.1109/TVCG.2011.262

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title = "Uniform B-spline curve interpolation with prescribed tangent and curvature vectors",

abstract = "This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints. To satisfy these constraints, knot insertion is used to generate additional control points which are progressively repositioned using corresponding geometric rules. Compared to existing schemes, our approach is capable of handling plane as well as space curves, has local control, and avoids the solution of the typical linear system. The effectiveness of the proposed algorithm is illustrated through several comparative examples. Applications of the method in NC machining and shape design are also outlined.",

keywords = "B-spline curve, curvature vector, interpolation, parametric curve, tangent",

author = "Shoichi Okaniwa and Ahmad Nasri and Hongwei Lin and Abdulwahed Abbas and Yuki Kineri and Takashi Maekawa",

note = "Funding Information: The authors would like to thank Malcolm Sabin and Takahiko Rachi for their constructive comments. This work is supported from the Japan Society for the Promotion of Funding Information: Science, Grants-in-Aid for Scientific Research under the grant number 20560127. Ahmad Nasri is supported in part by a grant from URB and Lebanese National Council for Scientific Research 2009-2011. Hongwei Lin is supported by Natural Science Foundation of China (Nos. 60970150, 60933008), and Zhejiang Provincial Natural Science Foundation (No. Y1090416).",

year = "2012",

doi = "10.1109/TVCG.2011.262",

language = "English",

volume = "18",

pages = "1474--1487",

journal = "IEEE Transactions on Visualization and Computer Graphics",

issn = "1077-2626",

publisher = "IEEE Computer Society",

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T1 - Uniform B-spline curve interpolation with prescribed tangent and curvature vectors

AU - Okaniwa, Shoichi

AU - Nasri, Ahmad

AU - Lin, Hongwei

AU - Abbas, Abdulwahed

AU - Kineri, Yuki

AU - Maekawa, Takashi

N1 - Funding Information: The authors would like to thank Malcolm Sabin and Takahiko Rachi for their constructive comments. This work is supported from the Japan Society for the Promotion of Funding Information: Science, Grants-in-Aid for Scientific Research under the grant number 20560127. Ahmad Nasri is supported in part by a grant from URB and Lebanese National Council for Scientific Research 2009-2011. Hongwei Lin is supported by Natural Science Foundation of China (Nos. 60970150, 60933008), and Zhejiang Provincial Natural Science Foundation (No. Y1090416).

PY - 2012

Y1 - 2012

N2 - This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints. To satisfy these constraints, knot insertion is used to generate additional control points which are progressively repositioned using corresponding geometric rules. Compared to existing schemes, our approach is capable of handling plane as well as space curves, has local control, and avoids the solution of the typical linear system. The effectiveness of the proposed algorithm is illustrated through several comparative examples. Applications of the method in NC machining and shape design are also outlined.

AB - This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints. To satisfy these constraints, knot insertion is used to generate additional control points which are progressively repositioned using corresponding geometric rules. Compared to existing schemes, our approach is capable of handling plane as well as space curves, has local control, and avoids the solution of the typical linear system. The effectiveness of the proposed algorithm is illustrated through several comparative examples. Applications of the method in NC machining and shape design are also outlined.

KW - B-spline curve

KW - curvature vector

KW - interpolation

KW - parametric curve

KW - tangent

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DO - 10.1109/TVCG.2011.262

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JO - IEEE Transactions on Visualization and Computer Graphics

JF - IEEE Transactions on Visualization and Computer Graphics

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M1 - 6035703

ER -

Uniform B-spline curve interpolation with prescribed tangent and curvature vectors

Abstract

Keywords

ASJC Scopus subject areas

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