The Visual Computer

, Volume 11, Issue 1, pp 52–62 | Cite as

On generating topologically consistent isosurfaces from uniform samples

  • B. K. Natarajan


A set of sample points of a function of three variables may be visualized by defining an interpolating functionf of the samples and examining isosurfaces of the formf(x, y, z)=t for various values oft. To display the isosurfaces on a graphics device, it is desirable to approximate them with piecewise triangular surfaces that (a) are geometrically good approximations, (b) are topologically consistent, and (c) consist of a small number of triangles. By topologically consistent we mean that the topology of the piecewise triangular surface matches that of the surfacef(x, y, z)=t, i.e., the interpolantf determines both the geometry and the topology of the piecewise triangular surface. In this paper we provide an efficient algorithm for the case in whichf is the piecewise trilinear interpolant; for this case existing methods fail to satisfy all three of the above conditions simultaneously.

Key words

Isosurfaces Topologically consistent Saddle points Trilinear interpolation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Artzy E, Frieder G, Herman G (1980) The theory, design, implementation and evaluation of a three dimensional surface generation program. Comput Graph 14:2–9Google Scholar
  2. Christiansen HN, Sederberg TW (1978) Conversion of complex contour lines into polygonal element mosaics. Comput Graph 12:187–192Google Scholar
  3. Cline HE, Lorensen WE, Ludke S, Crawford CR, Teeter BC (1988) Two algorithms for the reconstruction of surfaces from tomograms. Medical Physics 15:320–337Google Scholar
  4. Drebin RA, Carpenter L, Hanrahan P (1988) Volume rendering. Comput Graph 22:65–74Google Scholar
  5. Durst MJ (1988) Letters: additional reference to “marching cubes”. Comput Graph 22:72–73Google Scholar
  6. Fuchs H, Kedem ZM, Uselton SP (1977) Optimal surface reconstruction from planar contours. Commun ACM 10:693–702Google Scholar
  7. Kaufman A (1991) 1991 Volume Visualization, IEEE Computer Society Press, Los AlamitosGoogle Scholar
  8. Levoy M (1988) Display of surfaces from volume data. IEEE Comput Graph Appl 8:29–37Google Scholar
  9. Levoy M (1991) Viewing algorithms. In: Volume Visualization, IEEE Computer Society Press, Los Alamitos, Calif. pp 89–92Google Scholar
  10. Malzbender T (1993) Fourier volume rendering ACM Trans Graph 12(3):233–250Google Scholar
  11. Natarajan BK (1991) On generating topologically correct isosurfaces from uniform samples. Hewlett Packard Laboratories, Technical Report HPL-91-76Google Scholar
  12. Nielsen GM, Hamann B (1991) The asymptotic decider: resolving the ambiguity in marching cubes. Proc IEEE Visualization'911 pp 83–91Google Scholar
  13. Ning P, Hesselink L (1992) Octree pruning for variable resolution isosurfaces. Proc Computer Graphics International, pp 349–363Google Scholar
  14. Wilhelms J, Van Gelder A (1990a) Topological considerations in isosurface generation. Comput Graph 24:79–86Google Scholar
  15. Wilhelms J, Van Gelder A (1990b) Octrees for faster isosurface generation. Comput Graph, 24:57–62Google Scholar
  16. Wu, K, Hessellink L (1988) Computer display of reconstructed 3-D scalar data. Appl Optics 27:395–404Google Scholar
  17. Wyvill G, McPheeters C, Wyvill B (1986) Data structures for soft objects. Visual Comput 2:227–234Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • B. K. Natarajan
    • 1
  1. 1.Hewlett-Packard LaboratoriesPalo AltoUSA

Personalised recommendations