Programming and Computer Software

, Volume 34, Issue 5, pp 245–256 | Cite as

Adaptive terrain triangulation using the representation of quad trees by vertex textures and wavelet estimation of vertex significance

  • E. A. Yusov
  • V. E. Turlapov


A method of adaptive terrain triangulation is proposed that can be implemented in hardware. The method is based on an estimate of the static error of a quad tree nodes using wavelet transforms and on the representation of the resulting quad tree by a vertex texture. The proposed method has the following characteristic features: the adjacent nodes of the generated adapted mesh can differ in any number of hierarchical levels; the triangulation process is not limited by the size of the decomposition segments, which solves the problem of joining segments without inserting additional nodes; the multiscale terrain representation used in the method makes it possible to store the levels of detail in the graphics processor memory as a multilevel vertex texture; thus, the costliest part of the algorithm can be efficiently implemented using a vertex shader.

When constructing the triangulation, the algorithm takes into account both local features of the terrain and the camera location; also, it has a natural support of geomorphing.


Recursive Algorithm Current Node Daubechies Wavelet Camera Location Triangulate Irregular Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Vanĕek, J. and Ježek, B., Real Time Terrain Visualization on PC, Proc. of the 12th Int. Conf. in Central Europe on Computer Graphics, Visualization, and Computer Vision (WSCG’2004), 2004.Google Scholar
  2. 2.
    Lindstrom, P. Koller, D. Ribarsky, W., Hodges, L.F., Faust, N., and Turner, G.A., Real-Time Continuous Level of Detail Rendering of Height Fields, Proc. of SIGGRAPH’96, ACM SIGGRAPH, 1996, pp. 109–118.Google Scholar
  3. 3.
    Elykov, N.A., Belago, I.V., Kuzikovskii, S.A., and Nekrasov, Yu.Yu., Method for Continuous Terrain Refining, Proc. of the Conf. on Computer Graphics and Visualization (GraphiCon’2002), Nizhnii Novgorod, 2002.Google Scholar
  4. 4.
    Heckbert, P. and Garland, M., Survey of Polygonal Surface Simplification Algorithms, SIGGRAPH’97 Course Notes, 1997, vol. 25.Google Scholar
  5. 5.
    Luebke, D., A Developer’s Survey of Polynomial Simplification Algorithms, IEEE Comput. Graph. Appl., 2001, vol. 21, no. 3, pp. 24–35.CrossRefGoogle Scholar
  6. 6.
    Larsen, B.D. and Christences, N.J., Real-Time Terrain Rendering Using Smooth Hardware Optimized Level of Detail, J. WSCG, 2003, vol. 11, no. 1.Google Scholar
  7. 7.
    Garland, M. and Heckbert, P.S., Fast Polygonal Approximation of Terrains and Height Fields, Technical Report of Carnegie Mellon Univ., School of Computer Science, Pittsburgh, 1995, no. CMU-CS-95-181.Google Scholar
  8. 8.
    Hoppe, H., Progressive Meshes, Proc. of SIGGRAPH’ 96, ACM SIGGRAPH, 1996, pp. 99–108.Google Scholar
  9. 9.
    Pajarola, R., Large Scale Terrain Visualization Using the Restricted Quadtree Triangulation, Proc. of Visualization’ 98, IEEE Computer Society, 1998.Google Scholar
  10. 10.
    Balmelli, L., Kovačevic, J., and Vetteri, M., Quadtrees for Embedded Surface Visualization, Constraints, and Efficient Data Structures, Proc. of the IEEE Int. Conf. on Image Processing (ICIP), 1999, vol. 2, pp. 487–491.Google Scholar
  11. 11.
    Pajarola, R., QuadTIN: Quadtree Based Triangulated Irregular Networks, Proc. of the IEEE Visualization 2002, IEEE Computer Society Press, 2002, pp. 395–402.Google Scholar
  12. 12.
    Duchaineau, M., Wolinsky, M., Sigeti, D.E., Miller, M.C., Aldrich, C., and Mineev-Weinstein, M.B., Roaming Terrain: Real-Time Optimally Adapting Meshes, Proc. of the IEEE Visualization, Los Alamitos, Calif., 1997, IEEE Computer Society Press, 1997, pp. 81–88.Google Scholar
  13. 13.
    Evans, W., Kirkpatrick, D., and Townsend, G., Right-Triangulated Irregular Networks, Algorithmica, 2001, vol. 30, no. 2, pp. 264–286.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Pajarola, R., Overview of Quadtree-Based Terrain Triangulation and Visualization, Technical Report of Department of Information & Computer Science, University of California, I&C Science, Irvine, 2002, no. UCI-ICS-02-01.Google Scholar
  15. 15.
    Gross, M.H., Gatti, R., and Staadt, O.G., Fast Multiresolution Surface Meshing, Proc. of the 14th Int. Conf. on Data Engineering, ICDE’98, IEEE, 1998, pp. 550–557.Google Scholar
  16. 16.
    Gross, M.H., Staadt, O.G., and Gatti, R., Efficient Triangular Surface Approximations Using Wavelets and Quadtree Data Structures, IEEE Trans. Visualization Comput. Graph., 1996, vol. 2, no. 2, pp. 130–143.CrossRefGoogle Scholar
  17. 17.
    Asirvatham, A. and Hoppe, H., Terrain Rendring Ising GPU-Based Geometry Clipmaps, in GPU Gems 2, Pharr, M. and Fernando, R., Eds., Addison-Wesley, 2005.Google Scholar
  18. 18.
    Clasen, M. and Hege, H.-C., Terrain Rendering Using Spherical Clipmaps, Proc. of Eurographics, IEEE-VGTC Symposium on Visualization, 2006.Google Scholar
  19. 19.
    Pereberin, A.V., Multiscale Methods for Image Generation and Analysis, Cand. Sci. (Phys.-Math.) Dissertation, Moscow: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 2002.Google Scholar
  20. 20.
    Suglobov, V.I., Appearance-Preserving Terrain Simplification, Proc. of the Conf. on Computer Graphics and Visualization, GraphiCon’2000, Moscow, 2000.Google Scholar
  21. 21.
    Shapiro, J.M., Embedded Image Coding Using Zerotrees of Wavelet Coefficients, IEEE Trans. Signal. Process., 1993, vol. 12, pp. 345–362.Google Scholar
  22. 22.
    Yusov, E.A. and Turlapov, V.E., Dynamic Terrain Optimization Using the Haar Transform and the Vertex Quadtree, Proc. of the Conf. on Computer Graphics and Visualization, GraphiCon’2006, Novosibirsk, 2006.Google Scholar
  23. 23.
    Losasso, F. and Hoppe, H., Geometry Clipmaps: Terrain Rendering Using Nested Regular Grids, Proc. of SIGGRAPH’ 2004, ACM SIGGRAPH, 2004, pp. 769–776.Google Scholar

Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Nizhni Novgorod State UniversityNizhni NovgorodRussia

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