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Received: 2003-03-18

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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.3 P.259-268


Intersections of two offset parametric surfaces based on topology analysis

Author(s):  OUYANG Ying-xiu, TANG Min, LIN Jun-cheng, DONG Jin-xiang

Affiliation(s):  State Key Laboratory of CAD & CG, AI Institute, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   oyyx_zju@sohu.com

Key Words:  Offset parametric surface, Topology transition point, Surface intersection

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OUYANG Ying-xiu, TANG Min, LIN Jun-cheng, DONG Jin-xiang. Intersections of two offset parametric surfaces based on topology analysis[J]. Journal of Zhejiang University Science A, 2004, 5(3): 259-268.

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T1 - Intersections of two offset parametric surfaces based on topology analysis
A1 - OUYANG Ying-xiu
A1 - TANG Min
A1 - LIN Jun-cheng
A1 - DONG Jin-xiang
J0 - Journal of Zhejiang University Science A
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DOI - 10.1631/jzus.2004.0259

Conventional methods for solving intersections between two offset parametric surfaces often include iteratively using computationally expensive SSI (surface/surface intersections) algorithm. In addition, these methods ignore the relations between the intersection curves of parametric surfaces with different offset distances. The algorithm presented in this paper, makes full use of the topological relations between different intersection loops and calculates intersection loops with the help of previously calculated intersection loops. It first pre-processes two parametric surfaces to obtain the characteristic points, called topology transition points (TTPs), which can help in the subsequent finding of the topologies of the intersection curves. Then these points are categorized into several distinct groups, and we can determine the calculation strategy for searching initial points by analyzing the properties of these TTPs on the surfaces. Hence, all intersection curves can be marched from initial points by the tracing algorithm. The proposed algorithm could calculate intersection curves robustly and effectively and has been tested to be capable of overcoming the degenerate conditions such as loop and singularities leaking that occur frequently in conventional algorithms.

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


[1] Abdel-Malek, K., Yeh, H.J., 1997. On the determination of starting points for parametric surface intersections.Computer Aided Design,29(1):21-35.

[2] Burke, T.M., Sabharwal, C.L., 1996. Data Parallel Implementation of Surface-to-Surface Intersection between Parametric Surfaces.In: Symposium of Applied Computing. Philadelphia, Pennsylvania, p.353-357.

[3] Chang, L.C., Bein, W.W., Angel, E., 1994. Surface intersection using parallelism.Computer Aided Geometric Design,11(1):39-69.

[4] Hohmeyer, M.E., 1992. Robust and Efficient Intersection for Solid Modeling: [dissertation].In: Computer Science Division, Department of Electrical Engineering and Computer Science, University of California, Berkeley.

[5] Hu, S.M., Sun, J.G., Jin, T.G., Wang, G.Z., 2000. Computing the parameters of points on nurbs curves and surface via moving affine frame method.Journal of Software,11(1):49-53(in Chinese).

[6] Jun, C.S., Kim, D.S.,Lee, H.C.,Hwang, J., 2001. Surface slicing algorithm based on topology transition.Computer Aided Design,33:825-838.

[7] Kulkarni, P., Dutta, D., 1995. Adaptive Slicing of Paramterizable Algebraic Surfaces for Layered Manufacturing.In: Proceedings of the 1995 ASME Design Technical Conference. Boston MA.

[8] Ma, Y., Lee, Y.S., 1998. Detection of loops and singularities of surface intersections.Computer Aided Design,30(14):1059-1067.

[9] Mullenheim, G., 1991. On determining start points for a surface/surface intersection algorithm.Computer Aided Design,8(5):401-408.

[10] Nackman, L.R., 1984. Two-dimensional critical point configuration graphs.IEEE Transaction on Pattern Analysis and Machine Intelligence,8(5):401-408

[11] O'Rourke, J., 1993. Computational Geometry in C. Cambridge. Cambridge University Press.

[12] Su, B.Q., Hu, H.S., Shen, C.L., Pan, Y.L., Zhang, G.L., 1979. Differential Geometry. Higher Education Press.

[13] Tait, S.S., Rada, T.F., Mohammad, A.K., Helmut, P., 2002. Optimal slicing of free-form surfaces.Computer Aided Geometric Design,19:43-64.

[14] Tang, M., Dong, J.X., Li, H.L., He, Z.J., 1999. Boolean operation of non-regular precise geometric models.Journal of Software,10(12):1291-1297 (in Chinese).

[15] Tang, M., Dong, J.X., 2000. An accurate intersection method for sculptured solids.The Chinese Journal of Computer,23(4):434-439(in Chinese).

[16] Wu, S.T., Andrade, L.N., 1999. Marching along a regular surface/surface intersection with circular steps.Computer Aided Geometric Design,16:249-268.

[17] Yu, W., 1996. Intersection of offsets parametric surfaces.Computer Aided Geometric Design,13:453-465.

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