Constrained C1 piecewise bicubic Bézier surface interpolation

Caiming Zhang; Fuhua Cheng; B. A. Barsky

doi:10.1109/GMAP.2000.838248

Constrained C¹ piecewise bicubic Bézier surface interpolation

Caiming Zhang
, Fuhua Cheng
, B. A. Barsky

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The construction of a C¹ piecewise bicubic Bézier surface that interpolates a set of data points and lies on the same side of a given plane as the data points is presented. The main tasks in this construction process are the adjustment of the tangent vectors and the determination of the twist vectors at the data points. The tangent vectors are modified by decreasing their magnitudes. The twist vectors are first set by an energy minimization process and then filtered through a modification process to ensure the constructed surface lies on one side of the given plane. The technique for determining the twist vectors has an interpolation precision of cubic polynomials.

Original language	English
Title of host publication	Proceedings - Geometric Modeling and Processing 2000
Subtitle of host publication	Theory and Applications
Editors	Ralph Martin
Pages	162-171
Number of pages	10
ISBN (Electronic)	0769505627, 9780769505626
DOIs	https://doi.org/10.1109/GMAP.2000.838248
State	Published - 2000
Event	Geometric Modeling and Processing 2000, GMP 2000 - Hong Kong, China Duration: Apr 11 2000 → Apr 12 2000

Publication series

Name	Proceedings - Geometric Modeling and Processing 2000: Theory and Applications

Conference

Conference	Geometric Modeling and Processing 2000, GMP 2000
Country/Territory	China
City	Hong Kong
Period	4/11/00 → 4/12/00

Bibliographical note

Publisher Copyright:
© 2000 IEEE.

Funding

The financial support of Ford Motor Company through a URP grant and the consulting support of Drs. Paul Stewart and Yifan Chen of the Ford Research Lab are deeply appreciated.

Funders
Ford Motor Company

Keywords

constraint
energy
parametric interpolation
polynomial curve/surface

ASJC Scopus subject areas

Computational Mathematics
Geometry and Topology
Modeling and Simulation

Access to Document

10.1109/GMAP.2000.838248

Cite this

@inproceedings{e8472d0551c0414f8596955f458fe776,

title = "Constrained C1 piecewise bicubic B{\'e}zier surface interpolation",

abstract = "The construction of a C1 piecewise bicubic B{\'e}zier surface that interpolates a set of data points and lies on the same side of a given plane as the data points is presented. The main tasks in this construction process are the adjustment of the tangent vectors and the determination of the twist vectors at the data points. The tangent vectors are modified by decreasing their magnitudes. The twist vectors are first set by an energy minimization process and then filtered through a modification process to ensure the constructed surface lies on one side of the given plane. The technique for determining the twist vectors has an interpolation precision of cubic polynomials.",

keywords = "constraint, energy, parametric interpolation, polynomial curve/surface",

author = "Caiming Zhang and Fuhua Cheng and Barsky, \{B. A.\}",

note = "Publisher Copyright: {\textcopyright} 2000 IEEE.; Geometric Modeling and Processing 2000, GMP 2000 ; Conference date: 11-04-2000 Through 12-04-2000",

year = "2000",

doi = "10.1109/GMAP.2000.838248",

language = "English",

series = "Proceedings - Geometric Modeling and Processing 2000: Theory and Applications",

pages = "162--171",

editor = "Ralph Martin",

booktitle = "Proceedings - Geometric Modeling and Processing 2000",

}

Zhang, C, Cheng, F & Barsky, BA 2000, Constrained C¹ piecewise bicubic Bézier surface interpolation. in R Martin (ed.), Proceedings - Geometric Modeling and Processing 2000: Theory and Applications., 838248, Proceedings - Geometric Modeling and Processing 2000: Theory and Applications, pp. 162-171, Geometric Modeling and Processing 2000, GMP 2000, Hong Kong, China, 4/11/00. https://doi.org/10.1109/GMAP.2000.838248

Constrained C¹ piecewise bicubic Bézier surface interpolation. / Zhang, Caiming; Cheng, Fuhua; Barsky, B. A.
Proceedings - Geometric Modeling and Processing 2000: Theory and Applications. ed. / Ralph Martin. 2000. p. 162-171 838248 (Proceedings - Geometric Modeling and Processing 2000: Theory and Applications).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Constrained C1 piecewise bicubic Bézier surface interpolation

AU - Zhang, Caiming

AU - Cheng, Fuhua

AU - Barsky, B. A.

PY - 2000

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N2 - The construction of a C1 piecewise bicubic Bézier surface that interpolates a set of data points and lies on the same side of a given plane as the data points is presented. The main tasks in this construction process are the adjustment of the tangent vectors and the determination of the twist vectors at the data points. The tangent vectors are modified by decreasing their magnitudes. The twist vectors are first set by an energy minimization process and then filtered through a modification process to ensure the constructed surface lies on one side of the given plane. The technique for determining the twist vectors has an interpolation precision of cubic polynomials.

AB - The construction of a C1 piecewise bicubic Bézier surface that interpolates a set of data points and lies on the same side of a given plane as the data points is presented. The main tasks in this construction process are the adjustment of the tangent vectors and the determination of the twist vectors at the data points. The tangent vectors are modified by decreasing their magnitudes. The twist vectors are first set by an energy minimization process and then filtered through a modification process to ensure the constructed surface lies on one side of the given plane. The technique for determining the twist vectors has an interpolation precision of cubic polynomials.

KW - constraint

KW - energy

KW - parametric interpolation

KW - polynomial curve/surface

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BT - Proceedings - Geometric Modeling and Processing 2000

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