The Visual Computer

, Volume 22, Issue 6, pp 372–386 | Cite as

Single-strips for fast interactive rendering

  • Pablo Diaz-Gutierrez
  • Anusheel Bhushan
  • M. Gopi
  • Renato Pajarola
Special Issue Paper


Representing a triangulated two manifold using a single triangle strip is an NP-complete problem. By introducing a few Steiner vertices, recent works find such a single-strip, and hence a linear ordering of edge-connected triangles of the entire triangulation. In this paper, we extend previous results [10] that exploit this linear ordering in efficient triangle-strip management for high-performance rendering. We present new algorithms to generate single-strip representations that follow different user defined constraints or preferences in the form of edge weights. These functional constraints are application dependent. For example, normal-based constraints can be used for efficient rendering after visibility culling, or spatial constraints for highly coherent vertex-caching. We highlight the flexibility of this approach by generating single-strips with preferences as arbitrary as the orientation of the edges. We also present a hierarchical single-strip management strategy for high-performance interactive 3D rendering.


Single-strip Weighted perfect matching Hamiltonian cycle Vertex cache Visibility culling 


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  1. 1.
    Akeley, K., Haeberli, P., Burns, D.: The tomesh.c program. Tech. Rep. SGI Developer’s Toolbox CD, Silicon Graphics (1990)Google Scholar
  2. 2.
    Arkin, E.M., Held, M., Mitchell, J.S.B., Skiena, S.: Hamiltonian triangulations for fast rendering. Visual Comput. 12(9), 429–444 (1996)Google Scholar
  3. 3.
    Bar-Yehuda, R., Gotsman, C.: Time/space tradeoffs for polygon mesh rendering. ACM Trans. on Graph. 15(2), 141–152 (1996)CrossRefGoogle Scholar
  4. 4.
    Belmonte, O., Remolar, I., Ribelles, J., Chover, M., Rebollo, C., Fernandez, M.: Multiresolution triangle strips. In: IASTED International Conference on Visualization, Imaging and Image Processing (VIIP 2001), pp. 182–187 (2001)Google Scholar
  5. 5.
    Bogomjakov, A., Gotsman, C.: Universal rendering sequences for transparent vertex caching of progressive meshes. In: Watson, B., Buchanan, J.W. (eds.) Proceedings of Graphics Interface 2001, pp. 81–90. Canadian Formation Processing Society (2001). URL Scholar
  6. 6.
    Chow, M.M.: Optimized geometry compression for real-time rendering. In: VIS ’97: Proceedings of the 8th conference on Visualization ’97, pp. 347–ff. IEEE Computer Society Press, Los Alamitos, CA (1997)Google Scholar
  7. 7.
    Cohen-Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. ACM Trans. on Graph. 23(3), 905–914 (2004)CrossRefGoogle Scholar
  8. 8.
    Cook, W., Rohe, A.: Computing minimum-weight perfect matchings. INFORMS J. Comput. 11, 138–148 (1999)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Deering, M.: Geometry compression. URL Scholar
  10. 10.
    Diaz-Gutierrez, P., Bhushan, A., Gopi, M., Pajarola, R.: Constrained strip generation and management for efficient interactive 3D rendering. In: Proceedings Computer Graphics International Conference, pp. 115–121. IEEE Computer Society (2005)Google Scholar
  11. 11.
    Diaz-Gutierrez, P., Gopi, M.: Quadrilateral and tetrahedral mesh stripification using 2-factor partitioning of the dual graph. Visual Comput. 21(8–10), 689–697 (2005)Google Scholar
  12. 12.
    Diaz-Gutierrez, P., Gopi, M., Pajarola, R.: Hierarchyless simplification, stripification and compression of triangulated two-manifolds. Comput. Graph. Forum 24(3), 457–467 (2005)CrossRefGoogle Scholar
  13. 13.
    Dillencourt, M.: Finding Hamiltonian cycles in delaunay triangulations is NP-complete. In: Canadian Conference on Computational Geometry (CCCG), pp. 223–228 (1992)Google Scholar
  14. 14.
    El-Sana, J.A., Azanli, E., Varshney, A.: Skip strips: Maintaining triangle strips for view-dependent rendering. In: Ebert, D., Gross, M., Hamann, B. (eds.) IEEE Visualization ’99, pp. 131–138. San Francisco (1999). URL Scholar
  15. 15.
    Evans, F., Skiena, S., Varshney, A.: Completing sequential triangulations is hard. Tech. Rep., Department of Computer Science, State University of New York at Stony Brook (1996)Google Scholar
  16. 16.
    Evans, F., Skiena, S.S., Varshney, A.: Optimizing triangle strips for fast rendering. In: Yagel, R., Nielson G.M. (eds.) IEEE Visualization, pp. 319–326 (1996)Google Scholar
  17. 17.
    Garland, M., Willmott, A., Heckbert, P.S.: Hierarchical face clustering on polygonal surfaces. In: SI3D ’01: Proceedings of the 2001 Symposium on Interactive 3D graphics, pp. 49–58. ACM Press, New York (2001). DOI Scholar
  18. 18.
    Gopi, M.: Controllable single-strip generation for triangulated surfaces. In: Pacific Conference on Computer Graphics and Applications, pp. 61–69. IEEE Computer Society (2004)Google Scholar
  19. 19.
    Gopi, M., Eppstein, D.: Single-strip triangulation of manifolds with arbitrary topology. Comput. Graph. Forum 23(3), 371–379 (2004)CrossRefGoogle Scholar
  20. 20.
    Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. In: European Symposium on Algorithms, pp. 179–193. Springer (1996)Google Scholar
  21. 21.
    Hoppe, H.: Optimization of mesh locality for transparent vertex caching. In: A. Rockwood (ed.) Siggraph 1999, Computer Graphics Proceedings, pp. 269–276. Addison Wesley Longman, Los Angeles, CA (1999). URL Scholar
  22. 22.
    Lu, H.I., Ravi, R.: Approximating maximum leaf spanning trees in almost linear time. J. Algorithms 29(1), 132–141 (1998)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Kornmann, D.: Fast and simple triangle strip generation. In: Varian Medical Systems Finland, Espoo (1999)Google Scholar
  24. 24.
    Low, K.L., Tan, T.S.: Model simplification using vertex-clustering. In: SI3D ’97: Proceedings of the 1997 Symposium on Interactive 3D Graphics, pp. 75–ff. ACM Press, New York (1997). DOI Scholar
  25. 25.
    Luebke, D., Erikson, C.: View-dependent simplification of arbitrary polygonal environments. In: SIGGRAPH ’97: Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, pp. 199–208. ACM Press/Addison-Wesley Publishing Co., New York (1997). DOI Scholar
  26. 26.
    Luebke, D., Erikson, C.: View-dependent simplification of arbitrary polygonal environments. Comput. Graph. 31(Annual Conference Series), pp. 199–208 (1997)Google Scholar
  27. 27.
    Luebke, D., Reddy, M., Cohen, J.D., Varshney, A., Watson, B., Huebner, R.: Level of Detail for 3D Graphics. Morgan Kaufmann Publishers, San Francisco, CA (2003)Google Scholar
  28. 28.
    Mitani, J., Suzuki, H.: Making papercraft toys from meshes using strip-based approximate unfolding. ACM Trans. Graph. 23(3), 259–263 (2004)CrossRefGoogle Scholar
  29. 29.
    Neider, J., Davis, T., Woo, M.: OpenGL Programming Guide. Addison Wesley, Reading, MA (1993)Google Scholar
  30. 30.
    Pajarola, R., Antonijuan, M., Lario, R.: Quadtin: Quadtree based triangulated irregular networks. URL Scholar
  31. 31.
    Pugh, W.: Skip lists: a probabilistic alternative to balanced trees. Commun. ACM 33(6), 668–676 (1990)CrossRefMathSciNetGoogle Scholar
  32. 32.
    Shafae, M., Pajarola, R.: Dstrips: Dynamic triangle strips for real-time mesh simplification and rendering. In: Jon Rokne, W.W., Klein, R. (eds.) Proceedings Pacific Graphics 2003, pp. 271–280. IEEE (2003)Google Scholar
  33. 33.
    Stewart, A.J.: Tunneling for triangle strips in continuous level-of-detail meshes. In: Graphics Interface 2001, pp. 91–100. Canadian Formation Processing Society (2001)Google Scholar
  34. 34.
    Yoon, S.E., Lindstrom, P., Pascucci, V., Manocha, D.: Cache-oblivious mesh layouts. ACM Trans. Graph. 24(3), 886–893 (2005)CrossRefGoogle Scholar
  35. 35.
    Vanecek, P., Kolingerová, I.: Multi-path algorithm for triangle strips. In: Computer Graphics International, pp. 2–9 (2004)Google Scholar
  36. 36.
    Velho, L., de Figueiredo, L.H., Gomes, J.: Hierarchical generalized triangle strips. Visual Comput. 15(1), 21–35 (1999)CrossRefGoogle Scholar
  37. 37.
    Xiang, Held, Mitchell: Fast and effective stripification of polygonal surface models (short). In: SODA: ACM-SIAM Symposium on Discrete Algorithms ( A Conference on Theoretical and Experimental Analysis of Discrete Algorithms) (1999). URL Scholar
  38. 38.
    Peterson, J.P.C.: Die theorie der regulären graphen. Acta Mathematica 15, 193–220 (1891)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Pablo Diaz-Gutierrez
    • 1
  • Anusheel Bhushan
    • 1
  • M. Gopi
    • 2
  • Renato Pajarola
    • 3
  1. 1.444, Computer Science BuildingUniversity of California, IrvineIrvineUSA
  2. 2.430, Computer Science BuildingUniversity of California, IrvineIrvineUSA
  3. 3.Department of InformaticsUniversity of ZurichZürichSwitzerland

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