Convert non-convex meshes to convex meshes for depth sorting in volume rendering

  • Yong Zhou
  • Zesheng Tang
Session CG1c — Rendering
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1024)


Irregular mesh depth sorting plays an important role for volume rendering in scientific visualization. In recent years, some algorithms have been proposed for the depth sorting of irregular convex meshes, but less attention has been devoted to the depth sorting of non-convex meshes. In this paper, two different approaches for converting non-convex meshes into convex meshes are proposed. The first one is to fill original meshes with a set of tetrahedra on the exterior boundaries of meshes. The second one is to take the plane of exterior faces of meshes to divide the space until each subspace includes only one acyclic convex submesh. The subdivision process is represented by a binary tree, Binary Mesh Partitioning tree (BMP tree). Theoretical analysis and experimental results are shown.


Filling Process Original Mesh Exterior Boundary Scientific Visualization Irregular Mesh 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    A. M. Day, “The Implementation or An Algorithm to Find the Convex Hull of a Set of 3D Points”, ACM Trans. on Graphics, Vol. 9, No. 1, Jan. 1990, pp. 105–132.Google Scholar
  2. 2).
    T. Fruhauf. “ Raycasting of Nonregularly Structured Volume Data”, Computer Graphics Forum (Eurographics'94), Vol. 13, No. 3, 1994.Google Scholar
  3. 3).
    C. Giertsen, “Volume Visualization of Sparse Irregular Meshes,” IEEE CG&A, Vol. 12, No. 2, March 1992, pp. 40–48.Google Scholar
  4. 4).
    M. Garrity, “ Raytracing Irregular Volume Data”, Computer Graphics, Vol. 24, No. 5, 1990.Google Scholar
  5. 5).
    N. Max, P. Hanrahan, and R. Crawfis, “Area and Volume Coherence for Efficient Visualization of 3D Scalar Functions,” Computer Graphics, Vol. 24, No.5, Nov. 1990, pp. 27–33.Google Scholar
  6. 6).
    M. S. Paterson and F. F. Yao, “Binary Partitions with Application to Hidden-Surface Removal and Solid Modeling”, In Proc. 5th Annual Symposium on Computational Geometry, June 1989, pp.23–32.Google Scholar
  7. 7).
    P. Speray and S. Kennon, “Volume Probe: Interactive Data Exploration on Arbitrary Grids”, Computer Graphics, Vol. 24, No. 5, 1990, pp. 5–12.Google Scholar
  8. 8).
    W. C. Thibault and B. F. Naylor, “Set Operations on Polyhedra Using Binary Space Partitioning Trees”, Computer Graphics. Vol. 21, No.4 July 1987. pp. 153–162.Google Scholar
  9. 9).
    B. Tabatabai, E. A. Sessarego, and H. F. Mayer, “Volume Rendering on Nonregular Grids”, Computer Graphics Forum (Eurographics'94), Vol. 13, No. 3, 1994.Google Scholar
  10. 10).
    J. Wilhelms and A.V. Gelder, “A Coherent Projection Approach to Direct Volume Rendering”, Computer Graphics, Vol. 25, No.4, July 1991, pp. 275–284.Google Scholar
  11. 11).
    P. L. Williams, “Visibility Ordering Meshed Polyhedra”, ACM Transaction on Graphics, Vol. 11, No. 2, April 1992, pp. 103–126.Google Scholar
  12. 12).
    Yong Zhou and Zesheng Tang, “Constructing Isosurfaccs in 3D Data Sets Taking Account of Polyhedra Depth Sorting”, Journal of Computer Science and Technology, Vol.9, No. 2, April 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Yong Zhou
    • 1
  • Zesheng Tang
    • 1
  1. 1.Department of Computer Science and TechnologyTsinghua UniversityBeijingP. R. China

Personalised recommendations