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Issue No.06 - November/December (1991 vol.11)
pp: 44-51
ABSTRACT
<p>The Reeb graph represents the topological skeleton of a 3-D object and shows between which contours the surface patches should be generated. To construct the graph automatically, a weight function is defined for a pair of contours with each contour lying on the adjacent cross sections. First, the algorithm automatically generates the major parts of the edges of the Reeb graph where the number of contours does not change. Then the rest of the graph is determined by using the weight function and prior knowledge of the number of holes the object has. Specifically, the graph is completed by adding edges that do not contradict the known number of holes in descending order of the weight.</p>
CITATION
Yoshihisa Shinagawa, Tosiyasu L. Kunii, "Constructing a Reeb graph automatically from cross sections", IEEE Computer Graphics and Applications, vol.11, no. 6, pp. 44-51, November/December 1991, doi:10.1109/38.103393
REFERENCES
1. Y. Shinagawa and T.L. Kunii, "The Homotopy Model: A Generalized Model for Smooth Surface Generation from Cros Sectional Data,"The Visual Computer, Vol. 7, No. 2, Apr. 1991, pp. 72-86.
2. H. Fuchs. Z. M. Kedem, and S. P. Uselton, "Optimal surface reconstruction from planar contours,"Commun. ACM, vol. 20, Oct. 1977.
3. H.N. Christiansen and T.W. Sederberg, "Conversion of Complex Contour Line Definitions into Polygonal Element Mosaics,"Computer Graphics(Proc. SIGGRAPH), Vol. 12, No. 3, Aug. 1978, pp. 187-192.
4. Y. Shinagawa, Y.L. Kergosien, and T.L. Kunii, "Surface Coding Based on Morse Theory,"IEEE CG&A, Vol. 11, No. 5, Sept. 1991, pp. 66-78.
5. Y. Shinagawa et al., "Automating View Function Generation for Walk-through Animation," inProc. of Computer Animation 90, N. Magnenat-Thalmann and D. Thalmann, eds., Springer, New York, 1990, pp. 227-237.
6. T.L. Kunii and Y. Shinagawa, "Visualization: New Concepts and Techniques to Integrate Diverse Application Areas," inScientific Visualization of Physical Phenomena, N.M. Patrikalakis, ed., Springer, New York, 1991, pp. 3-25.
7. G. Reeb, "Sur les Points Singuliers d'une Forme de Pfaff Completement Integrable ou d'un Fonction Numerique [On the Singular Points of a Completely Integrable Pfaff Formor of a Numerical Function],"Comptes Rendus Acad. Sciences Paris, Vol. 222, 1946, pp. 847-849.
8. C. Giersten, A. Halvorsen, and P.R. Flood, "Graph-Directed Modeling from Serial Sections,"Visual Computer, Vol. 6, No. 5, September 1991, pp. 284-290.
9. M.A. Armstrong,Basic Topology, Springer, New York, 1983.
10. Y. Nomura et al., "Walking through a Human Ear,"Acta Otolaryngologica, Vol. 107, No. 5-6, May-June 1989, pp. 366-370.
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