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Received: 2007-07-02

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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.4 P.470-480

http://doi.org/10.1631/jzus.A071357


Trimming self-intersections in swept volume solid modeling


Author(s):  Zhi-qi XU, Xiu-zi YE, Zhi-yang CHEN, Yin ZHANG, San-yuan ZHANG

Affiliation(s):  State Key Laboratory of CAD & CG, School of Computer Science and Technology, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   learlynn@zju.edu.cn, syzhang@cs.zju.edu.cn

Key Words:  Self-intersection, Swept volume (SV), Solid modeling


Zhi-qi XU, Xiu-zi YE, Zhi-yang CHEN, Yin ZHANG, San-yuan ZHANG. Trimming self-intersections in swept volume solid modeling[J]. Journal of Zhejiang University Science A, 2008, 9(4): 470-480.

@article{title="Trimming self-intersections in swept volume solid modeling",
author="Zhi-qi XU, Xiu-zi YE, Zhi-yang CHEN, Yin ZHANG, San-yuan ZHANG",
journal="Journal of Zhejiang University Science A",
volume="9",
number="4",
pages="470-480",
year="2008",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A071357"
}

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%T Trimming self-intersections in swept volume solid modeling
%A Zhi-qi XU
%A Xiu-zi YE
%A Zhi-yang CHEN
%A Yin ZHANG
%A San-yuan ZHANG
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 4
%P 470-480
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A071357

TY - JOUR
T1 - Trimming self-intersections in swept volume solid modeling
A1 - Zhi-qi XU
A1 - Xiu-zi YE
A1 - Zhi-yang CHEN
A1 - Yin ZHANG
A1 - San-yuan ZHANG
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 4
SP - 470
EP - 480
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A071357


Abstract: 
Swept volume solid modeling has been applied to many areas such as NC machining simulation and verification, robot workspace analysis, collision detection, and CAD. But self-intersections continue to be a challenging problem in the boundary representation of swept volume solids. A novel algorithm is presented in this paper to trim self-intersection regions in swept volume solids modeling. This trimming algorithm consists of two major steps: (1) roughly detecting self-intersection regions by checking intersections or overlapping of the envelop profiles; (2) splitting the whole envelop surfaces of the swept volume solid into separate non-self-intersecting patches to trim global self-intersections, and to trim local self-intersections, dividing local self-intersecting regions into patches and replacing self-intersecting patches with non-self-intersecting ones. Examples show that our algorithm is efficient and robust.

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

Reference

[1] Abdel-Malek, K., Yeh, H.J., 1997. Geometric representation of the swept volume using Jacobian rank-deficiency conditions. Computer-Aided Design, 29(6):457-468.

[2] Abdel-Malek, K., Yang, J., Blackmore, D., Ken, J., 2006. Swept volumes: foundations, perspectives and applications. Int. J. Shape Modeling, 12(1):87-127.

[3] Andersson, L.E., Peters, T.J., Stewart, N.F., 1998. Self-intersection of composite curves and surfaces. Computer Aided Geometric Design, 15(5):507-527.

[4] Blackmore, D., Leu, M.C., 1992. Analysis of swept volume via Lie group and differential equations. Int. J. Rob. Res., 11(6):516-537.

[5] Blackmore, D., Leu, M.C., Wang, L.P., 1997a. The sweep-envelop differential equation algorithm and its application to NC machining verification. Computer-Aided Design, 29(9):629-637.

[6] Blackmore, D., Leu, M.C., Wang, L.P., Jiang, H., 1997b. Swept volumes: a retrospective and prospective view. Neural, Parallel and Scientific Computations, 5:81-102.

[7] Blackmore, D., Samulyak, R., Leu, M.C., 1999. Trimming swept volumes. Computer-Aided Design, 31(3):215-223.

[8] Cohen, E., Ho, C.C., 2000. Surface Self-intersection. In: Lyche, T., Schumaker, L.L. (Eds.), Mathematical Methods for Curves and Surfaces, p.183-194.

[9] Kim, Y.J., Varadhan, G., Leu, M.C., Dinesh, M., 2004. Fast swept volume approximation of complex polyhedral models. Computer-Aided Design, 36:1013-1027.

[10] Mann, S., Bedi, S., 2002. Generalization of the imprint method to general surfaces of revolution for NC machining. Computer-Aided Design, 34(5):373-378.

[11] Martin, R.R., Stephenson, P.C., 1990. Sweeping of three-dimensional objects. Computer-Aided Design, 22(4):223-234.

[12] Peternell, M., Pottmann, H., Steiner, T., Zhao, H., 2005. Swept volumes. Computer Aided Design and Applications, 2:95-104.

[13] Piegl, L., Tiller, W., 1997. The NURBS Book. Springer Verlag, Berlin.

[14] Pottmann, H., Peternell, M., 2000. Envelops—Computational Theory and Applications. Proc. Spring Conf. on Computer Graphics and its Applications, p.3-23.

[15] Requicha, A.A.G., Voelcker, H.B., 1982. Solid modeling: a historical summary and contemporary assessment. IEEE Computer Graph. Appl., 2(2):9-24.

[16] Rossignac, J., Kim, J.J., Song, S.C., Suh, K.C., Joung, C.B., 2007. Boundary of the volume swept by a free-form solid in screw motion. Computer-Aided Design, 39(9):745-755.

[17] Wang, W.P., Wang, K.K., 1986. Geometric modeling for swept volume of moving solids. IEEE Computer Graph. Appl., 6(12):8-17.

[18] Weinert, K., Du, S.J., Damm, P., Stautner, M., 2004. Swept volume generation for the simulation of machining process. Int. J. Machine Tools Manufacture, 44(6):617-628.

[19] Weld, J., Leu, M., 1990. Geometric representation of swept volume with application to polyhedral objects. Int. J. Rob. Res., 9(5):105-117.

[20] Xu, Z.Q., Chen, Z.Y., Ye, X.Z., Zhang, S.Y., 2007. Approximate the Swept Volume of Revolutions along Curved Trajectories. Proc. ACM Symp. on Solid and Physical Modeling, p.309-314.

[21] Yu, H.B., Wang, Y.X., 2003. Swept volume and its application to mechanical design. J. Eng. Graph., 24(1):63-70 (in Chinese).

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