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Generalized Unstructured Decimation
November 1996 (vol. 16 no. 6)
pp. 24-32
This article presents a general algorithm for decimating unstructured discretized data sets. The discretized space may be a planar triangulation, a general 3D surface triangulation, or a 3D tetrahedrization. Local dynamic vertex removal is performed without history information, while preserving the initial topology and boundary geometry. The decimation algorithm generates a candidate tessellation and topologically identifies the set of valid n-simplices that tessellate the convex/nonconvex hole. The algorithm uses only existing vertices and assumes manifold geometry. The research focuses on how to remove a vertex from an existing unstructured n-dimensional tessellation, not on the formulation of application specific decimation criteria.

1. T. Funkhouser and C. Sequin, “Adaptive Display Algorithm for Interactive Frame Rates During Visualization of Complex Virtual Environments,” Proc. SIGGRAPH '93, pp. 247-254, 1993.
2. P. Cignoni, L. De Floriani, C. Montoni, E. Puppo, and R. Scopigno, "Multiresolution Modeling and Visualization of Volume Data Based on Simplicial Complexes," Proc. 1994 Symp. Volume Visualization, pp. 19-26, 1994.
3. W.J. Schroeder, J.A. Zarge, and W.E. Lorensen, “Decimation of Triangle Meshes,” Proc. SIGGRAPH '92, pp. 65-70, 1992.
4. G. Turk, "Retiling Polygonal Surfaces," Computer Graphics(Proc. Siggraph 92), vol. 26, no. 2, 1992, pp. 55-64.
5. B. Hamann, "A Data Reduction Scheme for Triangulated Surfaces," Computer Aided Geometric Design, vol. 11, no. 2, pp. 197-214 1994.
6. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Mesh Optimization,” Proc. SIGGRAPH '93, pp. 19-26, 1993.
7. J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F.P. Brooks Jr., and W.V. Wright, "Simplification Envelopes," Computer Graphics Proc. Ann. Conf. Series (Proc. Siggraph '96), pp. 119-128, 1996.
8. M. Bern and D. Eppstein, Mesh Generation and Optimal Triangulation, Xerox PARC Technical Report CSL-92-1, Xerox Palo Alto Research Center, Palo Alto, Calif., 1992.
9. T.J. Barth, "On Unstructured Grids and Solvers," NASA Ames Research Center, Moffett Field, Calif., 1990.
10. M. Margaliot and C. Gotsman, "Approximation of Smooth Surfaces and Adaptive Sampling by Piecewise-Linear Interpolants," Computer Graphics: Developments in Virtual Environments (Proc. Computer Graphics Int'l), R. Earnshaw and J. Vince, eds., Academic Press, San Diego, Calif., 1995, pp. 17-28.
11. D.F. Watson, "Computing the n-dimensional Delaunay Tessellation with Application to Voronoi Polytopes," Computer J., Vol. 24, No. 2, 1981, pp. 167-172.
12. F.P. Preparata and M.I. Shamos, Computational Geometry. Springer-Verlag, 1985.
13. B. Chazelle and L. Palios, "Triangulating a Nonconvex Polytope," Proc. 5th Ann. ACM Symp. on Computational Geometry, 1989, pp. 393-400.
14. J. Ruppert and R. Seidel, "On the Difficulty of Tetrahedralizing 3-Dimensional Non-Convex Polyhedra," Proc. Fifth ACM Symp. Computational Geometry, pp. 380-392, 1989.
15. K.J. Renze, Unstructured Surface and Volume Decimation of Tessellated Domains, PhD dissertation, Iowa State University, Ames, Iowa, 1995.

Index Terms:
decimation, Voronoi diagram, tessellation, unstructured mesh, simplification, reduction, adaptation
Citation:
Kevin J. Renze, James H. Oliver, "Generalized Unstructured Decimation," IEEE Computer Graphics and Applications, vol. 16, no. 6, pp. 24-32, Nov. 1996, doi:10.1109/38.544069
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