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Generating Topological Structures for Surface Models
November 1995 (vol. 15 no. 6)
pp. 35-41
Rapid prototyping processes rigorously require that a CAD model to be manufactured must represent a closed volume and the boundary of the model be continuous and closed. This requirement is difficult to be met by surface models consisting of a collection of separate trimmed and untrimmed surfaces. In practice, however, sophisticated models are mostly constructed by surface modelers. This paper presents a robust algorithm solving this dilemma. The algorithm first converts surface models into the B-rep solid representation and then performs the triangulation satisfying the so-called vertex-to-vertex condition set by the STL file format, the de facto RP industry standard. The essence of the algorithm is a topology analyzer which generates the topological structure for a surface model. The topology analyzer finds the matching surfaces for each surface in the model and subsequently merges the matching boundaries according to the manifold criteria. The robustness of the algorithm has been demonstrated by numerous practical examples.

1. J. Arline, “A User Survey of Problems with Rapid Prototyping Systems,” Prototyping Report, Vol. 1, No. 6, Nov. 1991, pp. 7-8.
2. A.A.G. Requicha and H.B. Voelcker, “Boolean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms,” Proc. IEEE, Vol. 3, No. 7, 1983, pp. 30-44.
3. T. Woo, “Feature Extraction by Volume Decomposition,” Proc. Conf. on CAD/CAM Technology in Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1982, pp. 76-94.
4. T.L. Kunii, T. Satoh, and K. Yamaguchi, “Generation of Topological Boundary Information from Octree Encoding,” IEEE CG&A, Vol. 5, No. 3, Mar. 1985, pp. 29-38.
5. P. Evensen and T. Dokken, “Experiences Using Adjacency Analysis for Building Topology Structures,” in Theory and Practice of Geometric Modeling, W. Strasser and P. Seidel, eds., Springer Verlag, Berlin, 1989, pp. 419-432.
6. J.H. Bøhn and M.J. Wozny, "A Topology-Based Approach for Shell-Closure," Geometric Modeling for Product Realization, P.R. Wilson et al., eds., pp. 297-319. North-Holland, 1993.
7. G. Farin,Curves and Surfaces for Computer Aided Geometric Design, 3rd ed. New York: Academic Press, 1992.
8. J. Hoschek and D. Lasser, Grundlagen der Geometrischen Datenverarbeitung, B.G. Teubner, Stuttgart, Germany, 1992.
9. Initial Graphics Exchange Specification—Version 4.0, IGES Organization, 1988.
10. German Automotive Association (VDA), VDA Surface Interface Specification—Version 3.0, Druckerei Henrich, Frankfurt, Germany, 1987.
11. M. Mantyla, An Introduction to Solid Modeling.Rockville, Md., Computer Science Press, 1988.
12. D. Filip, R. Magedson, and R. Markot, “Surface Algorithm Using Bounds on Derivatives,” Computer Aided Geometric Design, Vol. 3, No. 4, 1986, pp. 295-311.
13. X. Sheng and B.E. Hirsch, “Triangulation of Trimmed Surfaces in Parametric Space,” Computer Aided Design, Vol. 24, No. 8, Aug. 1992, pp. 437-444.

Index Terms:
representation conversion, manifold solids, topology, trimmed surfaces, rapid prototyping.
Xuejun Sheng, Ingo R. Meier, "Generating Topological Structures for Surface Models," IEEE Computer Graphics and Applications, vol. 15, no. 6, pp. 35-41, Nov. 1995, doi:10.1109/38.469517
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