Survey of Curve and Surface Reconstruction Algorithms from a Set of Unorganized Points

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 258)

Abstract

Reconstruction of curves and surfaces from a set of unorganized points is a problem with a lot of practical relevance and thus has been an active area of research. In the review various curve and surface reconstruction algorithms which take an unorganized set of points have been discussed. Also it highlights the major advantages and disadvantages of these algorithms. Delaunay triangulations are most important structures used in surface reconstruction algorithms as they work without the geometric properties of the points. Most of the curve and surface reconstruction algorithms combine different approaches with Delaunay Triangulations in order to make reconstruction more systematic and robust. All such types of major issues pertaining to surface reconstruction have been reviewed and mentioned.

Keywords

Surface reconstruction Delaunay triangulations Robust 

References

  1. 1.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Mesh optimization. In: Proceedings of SIGGRAPH, ACM, pp. 19–26 (1993)Google Scholar
  2. 2.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proceedings of SIGGRAPH, ACM, pp. 71–78 (1992)Google Scholar
  3. 3.
    William, E.L., Harvey, E.C.: Marching cubes: a high resolution 3D surface reconstruction algorithm. In: Proceedings of SIGGRAPH, ACM, pp. 163–169, Jul 1987Google Scholar
  4. 4.
    de Berg, M., Cheong, O., Van Kreveld, M., Overmars, M.: Computational Geometry. Springer, Heidelberg (2008)Google Scholar
  5. 5.
    Dyer, R., Zhang, H., Moller, T.: A survey of Delaunay structures for surface representation. In: Technical Report, School of Computing Science, Simon Fraser University, Canada, Jan 16 2009Google Scholar
  6. 6.
    Amenta, N., Bern, M., Epppstein, D.: The crust and the beta skeleton: combinatorial curve reconstruction. Graph. Models Image Process. 60, 125–135 (1998)Google Scholar
  7. 7.
    Dey, T.K., Mehlhorn, K., Ramos, E.A: Curve reconstruction: connecting dots with good reason. Comput. Geom. Theor. Appl. 15, 229–244 (1999)Google Scholar
  8. 8.
    Dey, T.K., Kumar, P.: A simple provable algorithm for curve reconstruction. In: Proceedings of 10th ACMSIAM Symposium. Discrete Algorithms, pp 893–894, Jan 1999Google Scholar
  9. 9.
    Dey, T.K., Wenger, R.: Reconstructing curves with sharp corners. Comput. Geom. Theor. Appl. 19, 89–99 (2001)Google Scholar
  10. 10.
    Zeng, Y., Nguyen, T.A., Yan, B., Li, S.: A distance-based parameter free algorithm for curve reconstruction. Comput. Aided Des. 40, 210–222 (2008)Google Scholar
  11. 11.
    Guo, F.: Reconstructing curves from point clouds. In: 2nd International Conference on Materials, Mechatronics and Automation, Lecture Notes in Information Technology, pp 186–191 (2012)Google Scholar
  12. 12.
    Amenta, N., Bern, M.: Surface reconstruction by Voronoi filtering. Discrete Comput. Geom. 22, 481–504 (1998)Google Scholar
  13. 13.
    Amenta, N., Bern, M., Kamvysselis, M.: A new Voronoi—based surface reconstruction algorithm. In: Proceedings of SIGGRAPH, ACM, pp. 415–421 (1998)Google Scholar
  14. 14.
    Amenta, N., Choi, S., Dey, T.K, Leekha, N.: A simple algorithm for homeomorphic surface reconstruction. In: Proceedings of the sixteenth annual symposium on Computational geometry, pp. 213–222 (2000)Google Scholar
  15. 15.
    Amenta, N., Choi, S., Kolluri, R.K.: The power crust, union of balls, and the medial axis transform. Comput. Geom. 19, 127–153 (2001)Google Scholar
  16. 16.
    Dey, T.K., Goswami, S.: Tight Cocone: a water-tight surface reconstructor. J. Comput. Inf. Sci. Eng. 3, 302–307 (2003)Google Scholar
  17. 17.
    Kuo, C.C., Yau, H.-T.: A Delaunay-based region-growing approach to surface reconstruction from unorganized points. Comput. Aided Des. 37, 825–835 (2005)Google Scholar
  18. 18.
    Dey, T.K., Goswami, S.: Provable surface reconstruction from noisy samples. Computational Geometry, 35, 124–141 (2006)Google Scholar
  19. 19.
    Dey, T.K., Edgar, K.L., Ramos, A., Wenger1, R.: Isotopic reconstruction of surfaces with boundaries. In: Eurographics Symposium on Geometry Processing, pp. 1371–1382 (2009)Google Scholar
  20. 20.
    Hiyoshi, H.: Optimization-based approach for curve and surface reconstruction. Comput. Aided Des. 41, 366–374 (2009)Google Scholar
  21. 21.
    Gopi, M., Krishnan, S.: A fast and efficient projection based approach for surface reconstruction. In: Proceedings of High Performance Computer Graphics, Multimedia and Visualisation, pp. 179–186 (2002)Google Scholar
  22. 22.
    Kil, Y.J., Amenta, N.: GPU—assisted surface reconstruction on locally—uniform smples. In: Proceedings of International Meshing Roundtable, pp 369–385 (2008)Google Scholar
  23. 23.
    Zhou, K., Gong, M., Huang, X., Guo, B.: Data-parallel octrees for surface reconstruction. IEEE Trans. Vis. Comput. Graph. 17, 669–681 (2011)Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.USICT, Guru Gobind Singh Indraprastha UniversityDelhiIndia

Personalised recommendations