“Gap Processing for Adaptive Maximal Poisson-Disk Sampling” by Yan and Wonka

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    Gap Processing for Adaptive Maximal Poisson-Disk Sampling

Session/Category Title:   Sampling

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Abstract:


    In this article, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or when their radii are changed. We build on the concepts of regular triangulations and the power diagram. Third, we show how our analysis contributes to the state-of-the-art in surface remeshing.

References:


    1. Alliez, P., Ucelli, G., Gotsman, C., and Attene, M. 2008. Recent advances in remeshing of surfaces. In Shape Analysis and Structuring. Springer, 53–82.
    2. Amenta, N. and Bern, M. 1999. Surface reconstruction by voronoi filtering. Discr. Comput. Geom. 22, 481–504.
    3. Amenta, N., Bern, M., and Kamvysselis, M. 1998. A new voronoi-based surface reconstruction algorithm. In Proceedings of the ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques. 415–421.
    4. Ash, P. F. and Bolker, E. D. 1986. Generalized dirichlet tessellations. Geometrae Dedicata 20, 2, 209–243.
    5. Aurenhammer, F. 1987. Power diagrams: Properties, algorithms and applications. SIAM J. Comput. 16, 78–96.
    6. Aurenhammer, F. 1991. Voronoi diagrams-A survey of a fundamental geometric data structure. ACM Comput. Surv. 23, 3, 345–405.
    7. Balzer, M., Schlomer, T., and Deussen, O. 2009. Capacity constrained point distributions: A variant of lloyds method. ACM Trans. Graph. 28, 6, 86:1–86:8.
    8. Barber, C. B., Dobkin, D., and Huhdanpaa, H. 1996. The quickhull algorithm for convex hulls. ACM Trans. Math. Softw. 22, 4, 469–483.
    9. Bowers, J., Wang, R., Wei, L.-Y., and Maletz, D. 2010. Parallel poisson disk sampling with spectrum analysis on surfaces. ACM Trans. Graph. 29, 6, 166:1–166:10. Google ScholarDigital Library
    10. Bridson, R. 2007. Fast poisson disk sampling in arbitrary dimensions. In ACM SIGGRAPH Sketches.
    11. Cgai. 2013. Computational geometry algorithms library. http://www. cgal.org
    12. Chen, Z., Yuan, Z., Choi, Y.-K., Liu, L., and Wang, W. 2012. IEEE Trans. Vis. Comput. Graph. 18, 10, 1784–1796.
    13. Cheng, S.-W., Dey, T. K., and Levine, J. A. 2007. A practical delaunay meshing algorithm for a large class of domains. In Proceedings of the 16th International Meshing Roundtable. 477–494.
    14. Chew, L. P. 1989. Guaranteed-quality triangular meshes. Tech. rep. 89–983, Department of Computer Science, Cornell University.
    15. Cline, D., Jeschke, S., Razdan, A., White, K., and Wonka, P. 2009. Dart throwing on surfaces. Comput. Graph. Forum 28, 4, 1217–1226.
    16. Cook, R. L. 1986. Stochastic sampling in computer graphics. ACM Trans. Graph. 5, 1, 69–78.
    17. Corsini, M., Cignoni, P., and Scopigno, R. 2012. Efficient and flexible sampling with blue noise properties of triangular meshes. IEEE Trans. Vis. Comput. Graph. 18, 6, 914–924.
    18. de Goes, F., Breeden, K., Ostromoukhov, V., and Desbrun, M. 2012. Blue noise through optimal transport. ACM Trans. Graph. 31, 171:1–171:12.
    19. Devillers, O. and Teillaud, M. 2006. Pertubations and vertex removal in delaunay and regular 3d triangulations. Rapport de recherché, INRIA.
    20. Dippe, M. A. Z. and Wold, E. H. 1985. Antialiasing through stochastic sampling. In Proceedings of the ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques. 69–78.
    21. Dunbar, D. and Humphreys, G. 2006. A spatial data structure for fast poisson-disk sample generation. ACM Trans. Graph. 25, 3, 503–508.
    22. Ebeida, M. S., Mitchell, S. A., Davidson, A. A., Patney, A., Knupp, P. M., and Owens, J. D. 2011a. Efficient and good delaunay meshes from random points. Comput.-Aid. Des. 43, 11, 1506–1515.
    23. Ebeida, M. S., Mitchell, S. A., Patney, A., Davidson, A. A., and Owens, J. D. 2012. A simple algorithm for maximal poisson-disk sampling in high dimensions. Comput. Graph. Forum 31, 2, 785–794.
    24. Ebeida, M. S., Patney, A., Mitchell, S. A., Davidson, A. A., Knupp, P. M., and Owens, J. D. 2011b. Efficient maximal poisson-disk sampling. ACM Trans. Graph. 30, 4, 49:1–49:12.
    25. Edelsbrunner, H. and Shah, N. R. 1996. Incremental topological flipping works for regular triangulations. Algorithmica 15, 3, 223–241.
    26. Edelsbrunner, H. and Shah, N. R. 1997. Triangulating topological spaces. Int. J. Comput. Geom. Appl. 7, 4, 365–378.
    27. Fattal, R. 2011. Blue-noise point sampling using kernel density model. ACM Trans. Graph. 28, 3, 48:1–48:10.
    28. Frey, P. and Borouchaki, H. 1997. Surface mesh evaluation. In Proceedings of the 6th International Meshing Roundtable. 363–374.
    29. Fu, Y. and Zhou, B. 2008. Direct sampling on surfaces for high quality remeshing. In Proceedings of the ACM Symposium on Solid and Physical Modeling (SPM’08). 115–124.
    30. Gamito, M. N. and Maddock, S. C. 2009. Accurate multi-dimension poisson-disk sampling. ACM Trans. Graph. 29, 1, 8:–8:19.
    31. Jones, T. R. 2006. Efficient generation of poisson disk sampling patterns. J. Graph. Tools 11, 2, 27–36.
    32. Kalantari, N. K. and Sen, P. 2011. Efficient computation of blue noise point sets through importance sampling. Comput. Graph. Forum 30, 4, 1215–1221.
    33. Kopf, J., Cohen-Or, D., Deussen, O., and Lischinski, D. 2006. Recursive wang titles for real time blue noise. ACM Trans. Graph. 11, 2, 509–518.
    34. Lagae, A. and Dutre, P. 2008. A comparison of methods for generating poisson disk distributions. Comput. Graph. Forum 27, 1, 114–129.
    35. Lloyd, S. 1982. Least square quantization in pcm. IEEE Trans. Inf. Theory 28, 2, 129–137.
    36. McCool, M. and Fiume, E. 1992. Hierarchical poisson disk sampling distributions. In Proceedings of the Conference on Graphics Interface. 94–105.
    37. Mitchell, D. P. 1987. Generating antialiased images at low sampling densities. In Proceedings of the ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques. 65–72.
    38. Mitchell, D. P. 1991. Spectrally optimal sampling for distribution ray tracing. Proceedings of the ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques. 157–164.
    39. Mitchell, S. A., Rand, A., Ebieda, M. S., and Bajaj, C. L. 2012. Variable radii poisson disk sampling. In Proceedings of the 24th Canadian Conference on Computational Geometry (CCCG’12). 185–190.
    40. Nivoliers, V., Yan, D.-M., and Levy, B. 2012. Fitting polynomial surfaces to triangular meshes with voronoi squared distance minimization. In Proceedings of the 20th International Meshing Roundtable. 601–618.
    41. Ostrommoukhov, V., Donohue, C., and Jodoin, P.-M. 2004. Fast hierarchical importance sampling with blue noise properties. ACM Trans. Graph. 23, 3, 488–495.
    42. Schechter, H. and Bridson, R. 2012. Ghost sph for animating water. ACM Trans. Graph. 31, 4, 61:1–61:8.
    43. Schlomer, T. and Deussen, O. 2011. Accurate spectral analysis of two-dimensional point sets. J. Graph. GPU Game Tools 15, 3, 152–160.
    44. Schlomer, T., Heck, D., and Deussen, O. 2011. Farthest-point optimized point sets with maximized minimum distance. In Proceedings of the Conference on High Performance Graphics. 135–142.
    45. Shewchuk, J. R. 2002. What is a good linear element? Interpolation, conditioning, and quality measures. In Proceedings of the 11th International Meshing Roundtable. 115–126.
    46. Surazhsky, V., Alliez, P., and Gotsman, C. 2003. Isotropic remeshing of surfaces: A local parameterization approach. In Proceedings of the 12th International Meshing Roundtable. 204–231.
    47. Turk, G. 1993. Generating random points in triangles. In Graphics Gems. Academic Press, 24–28.
    48. Valette, S., Chassery, J.-M., and Prost, R. 2008. Generic remeshing of 3d triangular meshes with metric-dependent discrete voronoi diagrams. IEEE Trans. Vis. Comput. Graph. 14, 2, 369–381.
    49. Vigo, M., Pla, N., and Cotrina, J. 2002. Regular triangulations of dynamic sets of points. Comput. Aid. Geom. Des. 19, 2, 127–149.
    50. Wei, L.-Y. 2008. Parallel poisson disk sampling. ACM Trans. Graph. 27, 3, 20:1–20:9.
    51. Wei, L.-Y. 2010. Multi-class blue noise sampling. ACM Trans. Graph. 29, 4, 79:1–79:8.
    52. Wei, L.-Y. and Wang. R. 2011. Differential domain analysis for non-uniform sampling. ACM Trans. Graph. 30, 4, 50:1–50:8.
    53. White, K. B., Cline, D., and Egbert, P. K. 2007. Poisson disk point sets by hierarchical dart throwing. In Proceedings of the IEEE Symposium on Interactive Ray Tracing. 129–132.
    54. Xu, Y., Hu, R., Gotsman, C., and Liu, L. 2012. Blue noise sampling of surfaces. Comput. Graph. 36, 4, 232–240.
    55. Yan, D.-M., Levy, B., Liu, Y., Sun, F., and Wang, W. 2009. Isotropic remeshing with fast and exact computation of restricted voronoi diagram. Comput. Graph. Forum 28, 5, 1445–1454.
    56. Yan, D.-M., Wang, W., Levy, B., and Liu, Y. 2013. Efficient computation of clipped voronoi diagram for mesh generation. Comput.-Aid. Des. 45, 4, 843–852.

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