Journal of Computer Science and Technology

, Volume 33, Issue 6, pp 1192–1203 | Cite as

Back-to-Front Ordering of Triangles in Digital Terrain Models over Regular Grids

  • Jesús Alonso
  • Robert Joan-ArinyoEmail author
Regular Paper


Visiting triangles that conform a digital terrain model is a core operation in a number of fields like animation and video games or generating profiles, cross-sections, and contours in civil engineering. Performing the visit in an efficient manner is an issue specially when the output of the traversal depends in some way on additional parameters or information changing over time, for example, a moving point of view. In this work we report a set of rules that, given a digital terrain model defined over a regular grid and an arbitrary point of view outside the terrain, define a total back-to-front order in the set of digital terrain model triangles with respect to the point. The set of rules is minimal, complete and correct. To assess how the rules perform, we have implemented a CPU-based algorithm for realistically rendering height fields defined over regular grids. The algorithm does not make use of the z-buffer or shaders featured by our graphics card. We show how our algorithm is implemented and show visual results obtained from synthetic and real data. We further discuss the algorithm performance with respect to two algorithms: a naive algorithm that visits triangles according to grid indices and does not solve the hidden line problem, and the z-buffer provided by the graphics card featured by our computer. Our algorithm allows real-time interaction when the point of view arbitrarily moves in 3D space and we show that its performance is as good as that of the z-buffer graphics card.


back-to-front ordering digital terrain model elevation terrain model triangle strip visibility 


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Supplementary material

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  1. [1]
    Fan M, Tang M, Dong J. A review of real time terrain rendering techniques. In Proc. the 8th International Conference on Computer Supported Cooperative Work in Design, May 2004, pp.685-691.Google Scholar
  2. [2]
    Pajarola R, Gobetti E. Survey of semiregular multiresolution models for interactive terrain rendering. The Visual Computer, 2007, 23(8): 583-605.Google Scholar
  3. [3]
    Losasso F, Hoppe H. Geometry clipmaps: Terrain rendering using nested regular grids. ACM Transactions on Graphics, 2004, 23(3): 779-776.Google Scholar
  4. [4]
    Engel W. ShaderX2: Shader Programming Tips & Tricks with DirectX 9. Wordware Publishing Inc., 2004.Google Scholar
  5. [5]
    Frieder G, Gordon D, Reynolds R A. Back-to-front display of voxel-based objects. IEEE Computer Graphics and Applications, 1985, 5(1): 52-60.Google Scholar
  6. [6]
    Wang S L C, Staudhammer J. Visibility determination on projected grid surfaces. IEEE Computer Graphics & Applications, 1990, 10(4): 36-43.Google Scholar
  7. [7]
    Anderson D P. Hidden line elimination in projected grid surfaces. ACM Transactions on Graphics, 1982, 1(4): 274-288.Google Scholar
  8. [8]
    Swan II J E. Object-ordered rendering of discrete objects [Ph.D. Thesis]. Department of Computers and Information Science, The Ohio State University, 1998.Google Scholar
  9. [9]
    Yoon H S, Jung M J, Han J H. Alternation of level-of-detail construction and occlusion culling for terrain rendering. In Proc. the 1st International Symposium on Computational and Information Science, December 2004, pp.1161-1167.Google Scholar
  10. [10]
    Bhattacharjee S, Narayanan P J. Real-time painterly rendering of terrains. In Proc. the 6th IEEE Indian Conference on Computer Vision, Graphics and Image Processing, December 2008, pp.568-575.Google Scholar
  11. [11]
    Chen G, Sander P V, Nehab D, Yang L, Hu L. Depthpresorted triangle lists. ACM Transactions on Graphics, 2012, 31(6): Article No. 160.Google Scholar
  12. [12]
    Deb S, Bhattacharjee S, Patidar S, Narayanan P J. Realtime streaming and rendering terrains. In Proc. the 5th IEEE Indian Conference on Computer Vision, Graphics and Image Processing, December 2006, pp.276-288.Google Scholar
  13. [13]
    Samet H. The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.Google Scholar
  14. [14]
    Agrawal A, Radhakrishna M, Joshi R C. Geometry-based mapping and rendering of vector data over LOD phototextured 3D terrain models. In Proc. the 14th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, January 2006, pp.1-8.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Informatics in Engineering GroupTechnical University of CataloniaBarcelonaSpain
  2. 2.Center for Biomedical Engineering ResearchSant Joan de Déu Research InstituteBarcelonaSpain
  3. 3.Visualization, Interaction and Virtual Reality GroupTechnical University of CataloniaBarcelonaSpain

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