Full Text:   <1439>

CLC number: TP391.72

On-line Access: 

Received: 2006-03-20

Revision Accepted: 2006-05-23

Crosschecked: 0000-00-00

Cited: 0

Clicked: 3275

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.12 P.2050~2056

http://doi.org/10.1631/jzus.2006.A2050


A new algorithm for designing developable Bézier surfaces


Author(s):  ZHANG Xing-wang, WANG Guo-jin

Affiliation(s):  Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   wanggj@zju.edu.cn

Key Words:  Bé, zier surfaces, Developable surfaces, Bernstein basis, Linear independence, Characteristic equations


ZHANG Xing-wang, WANG Guo-jin. A new algorithm for designing developable Bézier surfaces[J]. Journal of Zhejiang University Science A, 2006, 7(12): 2050~2056.

@article{title="A new algorithm for designing developable Bézier surfaces",
author="ZHANG Xing-wang, WANG Guo-jin",
journal="Journal of Zhejiang University Science A",
volume="7",
number="12",
pages="2050~2056",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A2050"
}

%0 Journal Article
%T A new algorithm for designing developable Bézier surfaces
%A ZHANG Xing-wang
%A WANG Guo-jin
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 12
%P 2050~2056
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A2050

TY - JOUR
T1 - A new algorithm for designing developable Bézier surfaces
A1 - ZHANG Xing-wang
A1 - WANG Guo-jin
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 12
SP - 2050
EP - 2056
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A2050


Abstract: 
A new algorithm is presented that generates developable ;zier surfaces through a ;zier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.

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

Reference

[1] Aumann, G., 1991. Interpolation with developable Bézier patches. Computer Aided Geometric Design, 8(5):409-420.

[2] Aumann, G., 2003. A simple algorithm for designing developable Bézier surfaces. Computer Aided Geometric Design, 20(8-9):601-619.

[3] Bodduluri, R.M.C., Ravani, B., 1993. Design of developable surfaces using duality between plane and point geometries. Computer-Aided Design, 25(10):621-632.

[4] Chalfant, J.S., Maekawa, T., 1998. Design for manufacturing using B-spline developable surfaces. Journal of Ship Research, 42(3):206-214.

[5] Chen, F., Zheng, J., Sederberg, T., 2001. The µ-basis of a rational ruled surface. Computer Aided Geometric Design, 18(1):61-72.

[6] Chu, C.H., Séquin, C.H., 2002. Developable Bézier patches properties and design. Computer-Aided Design, 34(7):511-527.

[7] Frey, W.H., Bindschadler, D., 1993. Computer Aided Design of a Class of Developable Bézier Surfaces. GM Research Publications, R&D-8057.

[8] Lang, J., Röschel, O., 1992. Developable (1, n)-Bézier surfaces. Computer Aided Geometric Design, 9(4):291-298.

[9] Ma, W., Kruth, J., 1998. NURBS curve and surface fitting for reverse engineering. International Journal of Advanced Manufacturing Technology, 14(12):918-927.

[10] Maekawa, T., 1998. Design and tessellation of B-spline developable surfaces. ASME Trans. Journal of Mechanical Design, 120(3):453-461.

[11] Mancewicz, M.J., Frey, W.H., 1992. Developable Surfaces Properties, Representations and Methods of Design. GM Research Publications, GMR-7637.

[12] Piegl, L., Tiller, W., 1997. The NRUBS Book (2nd Ed.), Springer-Verlag New York, Inc., New York.

[13] Pottmann, H., Farin, G., 1995. Developable rational Bézier and B-spline surfaces. Computer Aided Geometric Design, 12(5):513-531.

[14] Pottmann, H., Wallner, J., 2001. Computational Line Geometry. Springer, Berlin.

[15] Spivak, M., 1975. Differential Geometry. Publish or Perish Inc., Boston.

[16] Tang, K., Wang, M., Chen, L., Chou, S., Woo, T., Janardan, R., 1997. Computing planar swept polygons under translation. Computer-Aided Design, 29(12):825-836.

[17] Zheng, J., Sederberg, T., 2001. A direct approach to computing the µ-basis of planar rational curves. Journal of Symbolic Computation, 31(5):619-629.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE