Abstract
We propose a robust, feature preserving and user-steerable mesh sampling algorithm, based on the one-to-many mapping of a regular sampling of the Gaussian sphere onto a given manifold surface. Most of the operations are local, and no global information is maintained. For this reason, our algorithm is amenable to a parallel or streaming implementation and is most suitable in situations when it is not possible to hold all the input data in memory at the same time. Using ε-nets, we analyze the sampling method and propose solutions to avoid shortcomings inherent to all localized sampling methods. Further, as a byproduct of our sampling algorithm, a shape approximation is produced. Finally, we demonstrate a streaming implementation that handles large meshes with a small memory footprint.
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References
Bernardini, F., Mittleman, J., Rushmeier, H., Silva, C., Taubin, G.: The ball-pivoting algorithm for surface reconstruction. IEEE Trans. Vis. Comput. Graph. 5(4), 349–359 (1999)
Clarkson, K.L.: Building triangulations using ε-nets. In: SIGACT Symposium. ACM, New York (2006)
Cohen-Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. ACM Trans. Graph. 23(3), 905–914 (2004). http://doi.acm.org/10.1145/1015706.1015817
Dey, T.K.: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge (2006).
Dong, W., Li, J., Kuo, J.: Fast mesh simplification for progressive transmission. In: Proceedings International Conference on Multimedia and Expo ICME 2000. IEEE Press, New York (2000)
Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: Proceedings ACM SIGGRAPH, pp. 209–216. ACM, New York (1997)
Gopi, M., Krishnan, S., Silva, C.: Surface reconstruction using lower dimensional localized delaunay triangulation. Eurographics 19(3), 467–478 (2000)
Gruber, P.M.: Optimum quantization and its applications. Adv. Math. 186, 456–497 (2004)
Heckbert, P.S., Garland, M.: Survey of polygonal surface simplification algorithms. Tech. Rep., Computer Science Department, Carnegie Mellon University (1997)
Hoppe, H.: Progressive meshes. In: SIGGRAPH, pp. 99–108. ACM, New York (1996)
Isenburg, M., Lindstrom, P.: Streaming meshes. In: Proceedings IEEE Visualization, pp. 231–238 (2005)
Luebke, D.P.: A developer’s survey of polygonal simplification algorithms. IEEE Comput. Graph. Appl. 21(3), 24–35 (2001)
Nadler, E.: Piecewise-linear best l 2 approximation on triangulations. In: Chui, C.K., Schumaker, L.L., Ward, J.D. (eds.) Approximation Theory, pp. 499–502. Academic Press, San Diego (1986)
O’Neill, B.: Elementary Differential Geometry, 2nd edn. Academic Press, San Diego (1997). www.apnet.com
Pajarola, R.: Stream-processing points. In: Proceedings IEEE Visualization, pp. 239–246 (2005)
Pottmann, H., Krasauskas, R., Hamann, B., Joy, K., Seibold, W.: On piecewise linear approximation of quadratic functions. J. Geom. Graph. 4(1), 31–53 (2000)
Sheffer, A.: Model simplification for meshing using face clustering. Comput. Aided Des. 33, 925–934 (2001)
Vetterli, M., Marziliano, P., Blu, T.: Sampling signals with finite rate of innovation. IEEE Trans. Signal Proc. 50(6), 1417–1428 (2002). doi:10.1109/TSP.2002.1003065
Weiler, K.: Edge-based data structures for solid modeling in curved-surface environments. IEEE Comput. Graph. Appl. 5(1), 21–40 (1985)
Yamauchi, H., Gumhold, S., Zayer, R., Seidel, H.P.: Mesh segmentation driven by Gaussian curvature. Vis. Comput. 21(8–10), 649–658 (2005)
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Diaz-Gutierrez, P., Bösch, J., Pajarola, R. et al. Streaming surface sampling using Gaussian ε-nets. Vis Comput 25, 411–421 (2009). https://doi.org/10.1007/s00371-009-0351-3
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DOI: https://doi.org/10.1007/s00371-009-0351-3