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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.6 P.1084~1087

http://doi.org/10.1631/jzus.2006.A1084


Symmetric alteration of four knots of B-spline and NURBS surfaces


Author(s):  LI Ya-juan, WANG Guo-zhao

Affiliation(s):  Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   liyajuan9104@163.com

Key Words:  B-spline surface, NURBS surface, Knot modification, Path


LI Ya-juan, WANG Guo-zhao. Symmetric alteration of four knots of B-spline and NURBS surfaces[J]. Journal of Zhejiang University Science A, 2006, 7(6): 1084~1087.

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author="LI Ya-juan, WANG Guo-zhao",
journal="Journal of Zhejiang University Science A",
volume="7",
number="6",
pages="1084~1087",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1084"
}

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%T Symmetric alteration of four knots of B-spline and NURBS surfaces
%A LI Ya-juan
%A WANG Guo-zhao
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 6
%P 1084~1087
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1084

TY - JOUR
T1 - Symmetric alteration of four knots of B-spline and NURBS surfaces
A1 - LI Ya-juan
A1 - WANG Guo-zhao
J0 - Journal of Zhejiang University Science A
VL - 7
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SP - 1084
EP - 1087
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1084


Abstract: 
Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Hoffmann, M., 2004. Constrained shape modification of cubic B-spline curves by means of knots. Computer-Aided Design, 36(4):437-445.

[2] Hoffmann, M., Juhász, I., 2004. On the knot modification of a B-spline curve. Publicationes Mathematicae Debrecen, 65:193-203.

[3] Hoffmann, M., Juhász, I., 2005. Symmetric alteration of two knots of B-spline curves. Journal for Geometry and Graphics, 9(1):43-49.

[4] Juhász, I., 2001. A shape modification of B-spline curves by symmetric translation of two knots. Acta. Acad. Paed. Agriensis, 28:69-77.

[5] Juhász, I., Hoffmann, M., 2001. The effect of knot modifications on the shape of B-spline curves. Journal for Geometry and Graphics, 5:111-119.

[6] Juhász, I., Hoffmann, M., 2003. Modifying a knot of B-spline curves. Computer Aided Geometric Design, 20(5):243-245.

[7] Li, Y., Wang, G., 2005. On knot modifications of B-spline or NURBS surface. Journal of Computer-Aided Design and Computer Graphics, 17(5):986-989.

[8] Li, Y., Wang, G., 2006. Constrained shape modification of cubic NURBS curve based on knots and weights. Applied MathematicsA Journal of Chinese Universities, 21(1):118-124 (in Chinese).

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