[1] Wang Zhiguo, Zhou Laishui, Wang Xiaoping,. Weight-based shape modification of NURBS curvesby constrained optimization [J]. Journal of Southeast University (English Edition), 2004, 20 (4): 458-462. [doi:10.3969/j.issn.1003-7985.2004.04.013]

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Weight-based shape modification of NURBS curvesby constrained optimization()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

20

Issue:

2004 4

Page:

458-462

Research Field:

Computer Science and Engineering

Publishing date:

2004-12-30

Info

Title:

Weight-based shape modification of NURBS curvesby constrained optimization

Author(s):

Wang Zhiguo;  Zhou Laishui;  Wang Xiaoping

Research Center of CAD/CAM Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Keywords:

non-uniform rational B-splines;  shape modification;  constrained optimization;  convex hull

PACS:

TP391

DOI:

10.3969/j.issn.1003-7985.2004.04.013

Abstract:

A new method for shape modification of non-uniform rational B-splines(NURBS)curves is presented, which is based on constrained optimization by means of altering the corresponding weights of their control points. Using this method, the original NURBS curve is modified to satisfy the specified geometric constraints, including single point and multi-point constraints. With the introduction of free parameters, the shapes of modified NURBS curves can be further controlled by users without destroying geometric constraints and seem more naturally. Since explicit formulae are derived to compute new weights of the modified curve, the method is simple and easy to program. Practical examples show that the method is applicable for computer aided design(CAD)system.

References:

[1] Piegl L. Modifying the shape of rational B-spline, part 1: curves [J]. Computer Aided Design, 1989, 21(9): 509-518.
[2] Au C K, Yuen M F. Unified approach to NURBS curve manipulation [J]. Computer Aided Design, 1995, 27(2): 85-93.
[3] Fowler B, Bartels R. Constrained-based curve manipulation [J]. IEEE Computer Graphics and Applications, 1993, 13(5): 43-49.
[4] Sánchez R J. A simple technique for NURBS shape modification [J]. IEEE Computer Graphics and Applications, 1997, 17(1): 52-59.
[5] Hu S M, Li Y F, Ju T, et al. Modifying the shape of NURBS surfaces with geometric constraints [J]. Computer Aided Design, 2001, 33(12): 903-912.
[6] Hu S M, Zhu X, Sun J G. Shape modification of NURBS surfaces via constrained optimization [J]. Journal of Software, 2000, 11(12): 1567-1571.
[7] Terzopoulos D. Elastically deformable models [J]. Computer Graphics, 1987, 21(4): 205-214.
[8] Celniker G, Gossard D. Deformable curve and surface finite-elements for free-form design [J]. Computer Graphics, 1991, 25(4): 327-334.
[9] Welch W, Witkin A. Variational surface modeling [J]. Computer Graphics, 1992, 26(2): 157-166.

Memo

Memo:

Biographies: Wang Zhiguo(1977—), male, graduate; Zhou Laishui(corresponding author), male, doctor, professor, zlsme@nuaa.edu.cn.

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