Merging Faces: A New Orthogonal Simplification of Solid Models

  • Irving Cruz-Matías
  • Dolors Ayala
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)


A new approach to simplify orthogonal pseudo-polyhedra (OPP) and binary volumes is presented. The method is incremental and produces a level-of-detail (LOD) sequence of OPP. Any object of this sequence contains the previous objects and, therefore, it is a bounding orthogonal approximation of them. The sequence finishes with the minimum axis-aligned bounding box (AABB). OPP are represented by the Extreme Vertices Model, a complete model that stores a subset of their vertices and performs fast Boolean operations. Simplification is achieved using a new approach called merging faces, which relies on the application of 2D Boolean operations. We also present a technique, based on the model continuity, for a better shape preservation. The method has been tested with several datasets and compared with two similar methods.


Simplification LOD Bounding Volumes Orthogonal Polyhedra Binary volumes 


  1. 1.
    Aguilera, A., Ayala, D.: Orthogonal Polyhedra as Geometric Bounds in CSG. In: IVth Symp. on Solid Modeling and Appl., pp. 56–67. ACM (1997)Google Scholar
  2. 2.
    Biedl, T., Genç, B.: Reconstructing orthogonal polyhedra from putative vertex sets. Computational Geometry 44(8), 409–417 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Biswas, A., et al.: A linear-time combinatorial algorithm to find the orthogonal hull of an object on the digital plane. Information Sciences 216, 176–195 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cignoni, P., et al.: Simplification of tetrahedral meshes with accurate error evaluation. In: Proceedings of the IEEE Visualization Conference, pp. 85–92 (2000)Google Scholar
  5. 5.
    Cignoni, P., Montani, C., Scopigno, R.: A comparison of mesh simplification algorithms. Computers and Graphics 22(1), 37–54 (1998)CrossRefGoogle Scholar
  6. 6.
    Coming, D.S., Staadt, O.G.: Velocity-aligned discrete oriented polytopes for dynamic collision detection. IEEE Trans. Vis. and Computer Graphics 14, 1–12 (2008)CrossRefGoogle Scholar
  7. 7.
    Cruz-Matías, I., Ayala, D.: CUDB: An improved decomposition model for orthogonal pseudo-polyhedra. Tech. Rep. LSI-11-2-T, UPC (2011)Google Scholar
  8. 8.
    Esperança, C., Samet, H.: Orthogonal Polygons as Bounding Structures in Filter-Refine Query Processing Strategies. In: Scholl, M.O., Voisard, A. (eds.) SSD 1997. LNCS, vol. 1262, pp. 197–220. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  9. 9.
    Fuchs, R., Welker, V., Hornegger, J.: Non-convex polyhedral volume of interest selection. J. of Computerized Medical Imaging and Graphics 34(2), 105–113 (2010)CrossRefGoogle Scholar
  10. 10.
    Gagvani, N., Silver, D.: Shape-based volumetric collision detection. In: VVS 2000: Proceedings of the 2000 IEEE Symp. on Volume Visualization, pp. 57–61. ACM Press (2000)Google Scholar
  11. 11.
    Greß, A., Klein, R.: Efficient representation and extraction of 2-manifold isosurfaces using kd-trees. Graphical Models 66, 370–397 (2004)CrossRefGoogle Scholar
  12. 12.
    Hagbi, N., El-Sana, J.: Carving for topology simplification of polygonal meshes. Comput. Aided Des. 42, 67–75 (2010)CrossRefGoogle Scholar
  13. 13.
    Huang, P., Wang, C.: Volume and complexity bounded simplification of solid model represented by binary space partition. In: Proc. SPM 2010, pp. 177–182 (2010)Google Scholar
  14. 14.
    Jiménez, P., Thomas, F., Torras, C.: 3D collision detection: A survey. Computers and Graphics 25(2), 269–285 (2000)Google Scholar
  15. 15.
    Klosowski, J.T., et al.: Efficient collision detection using bounding volume hierarchies of k-dops. IEEE Trans. Vis. and Computer Graphics 4(1), 21–36 (1998)CrossRefGoogle Scholar
  16. 16.
    Ripolles, O., Chover, M., Gumbau, J., Ramos, F., Puig, A.: Rendering continuous level-of-detail meshes by masking strips. Graphical Models 71(5), 184–195 (2009)CrossRefGoogle Scholar
  17. 17.
    Rodríguez, J., Ayala, D., Aguilera, A.: EVM: A Complete Solid Model for Surface Rendering. In: Geometric Modeling for Scientific Vis., pp. 259–274. Springer (2004)Google Scholar
  18. 18.
    Samet, H., Kochut, A.: Octree approximation and compression methods. In: Proceedings of the 1st Int. Symp. 3DPVT, pp. 460–469. IEEE Computer Society (2002)Google Scholar
  19. 19.
    Sun, R., Gao, S., Zhao, W.: An approach to b-rep model simplification based on region suppression. Computers & Graphics 34(5), 556–564 (2010)CrossRefGoogle Scholar
  20. 20.
    Suri, S., Hubbard, P.M., Hughes, J.F.: Analyzing bounding boxes for object intersection. ACM Trans. Graph. 18, 257–277 (1999)CrossRefGoogle Scholar
  21. 21.
    Tarini, M., Pietroni, N., Cignoni, P., Panozzo, D., Puppo, E.: Practical quad mesh simplification. Computer Graphics Forum 29(2), 407–418 (2010)CrossRefGoogle Scholar
  22. 22.
    Tilove, R., Requicha, A.: Closure of boolean operations on geometric entities. Computer-Aided Design 12(5), 219–220 (1980)CrossRefGoogle Scholar
  23. 23.
    Vanderhyde, J., Szymczak, A.: Topological simplification of isosurfaces in volume data using octrees. Graphical Models 70, 16–31 (2008)CrossRefGoogle Scholar
  24. 24.
    Vigo, M., Pla, N., Ayala, D., Martínez, J.: Efficient algorithms for boundary extraction of 2D and 3D orthogonal pseudomanifolds. Grap. Models 74, 61–74 (2012)CrossRefGoogle Scholar
  25. 25.
    Wald, I., Boulos, S., Shirley, P.: Ray tracing deformable scenes using dynamic bounding volume hierarchies. ACM Trans. Graph. 26 (January 2007)Google Scholar
  26. 26.
    Williams, J., Rossignac, J.: Tightening: Morphological simplification. International Journal of Computational Geometry & Applications 17(5), 487–503 (2007)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Irving Cruz-Matías
    • 1
  • Dolors Ayala
    • 1
  1. 1.Department de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations