Piecewise Tri-linear Contouring for Multi-material Volumes

  • Powei Feng
  • Tao Ju
  • Joe Warren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6130)


The ability to model objects composed of multiple materials has become increasingly more demanded in scientific applications. The visualization of a discrete multi-material volume often suffers from voxelization of the boundary between materials. We propose a contouring method that can be efficiently implemented on the GPU to reduce the artifacts and jaggedness along the material boundaries. Our method extends naturally from the standard tri-linear contouring in a signed volume, and further provides sub-voxel accuracy for representing three or more materials.


Grid Point Interactive Technique Graphic Hardware Signed Scalar Multiple Material 
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.
    Bloomenthal, J.: Implicit surfaces. Computer Aided Geometric Design 5, 341–355 (1997)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Cullip, T.J., Neumann, U.: Accelerating volume reconstruction with 3d texture hardware. Tech. rep. Chapel Hill, NC (1994)Google Scholar
  3. 3.
    Engel, K., Kraus, M., Ertl, T.: High-quality pre-integrated volume rendering using hardware-accelerated pixel shading. In: HWWS 2001: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware, pp. 9–16. ACM, New York (2001)CrossRefGoogle Scholar
  4. 4.
    Feng, P.: Segmentation and Visualization of Volume Maps. Master’s thesis, Rice University, Texas, United States (2010)Google Scholar
  5. 5.
    Frisken, S.F., Perry, R.N., Rockwood, A.P., Jones, T.R.: Adaptively sampled distance fields: a general representation of shape for computer graphics. In: SIGGRAPH 2000: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pp. 249–254. ACM Press/Addison-Wesley Publishing Co., New York (2000)CrossRefGoogle Scholar
  6. 6.
    Fujimori, T., Suzuki, H.: Surface extraction from multi-material ct data. In: Ninth International Conference on Computer Aided Design and Computer Graphics, pp. 319–324 (December 2005)Google Scholar
  7. 7.
    Gibson, S.F.F.: Using distance maps for accurate surface representation in sampled volumes. In: IEEE Symposium on Volume Visualization and Graphics, vol. 0, pp. 23–30 (1998)Google Scholar
  8. 8.
    Hadwiger, M., Berger, C., Hauser, H.: High-quality two-level volume rendering of segmented data sets on consumer graphics hardware. In: VIS 2003: Proceedings of the 14th IEEE Visualization 2003 (VIS 2003), p. 40. IEEE Computer Society Press, Washington (2003)Google Scholar
  9. 9.
    Ju, T., Losasso, F., Schaefer, S., Warren, J.: Dual contouring of hermite data. In: SIGGRAPH 2002: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, pp. 339–346. ACM, New York (2002)CrossRefGoogle Scholar
  10. 10.
    Kobbelt, L.P., Botsch, M., Schwanecke, U., Seidel, H.P.: Feature sensitive surface extraction from volume data. In: SIGGRAPH 2001: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp. 57–66. ACM, New York (2001)CrossRefGoogle Scholar
  11. 11.
    Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3d surface construction algorithm. In: SIGGRAPH 1987: Proceedings of the 14th annual conference on Computer graphics and interactive techniques, pp. 163–169. ACM, New York (1987)CrossRefGoogle Scholar
  12. 12.
    Rezk-Salama, C., Engel, K., Bauer, M., Greiner, G., Ertl, T.: Interactive volume on standard pc graphics hardware using multi-textures and multi-stage rasterization. In: HWWS 2000: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware, pp. 109–118. ACM, New York (2000)CrossRefGoogle Scholar
  13. 13.
    Ricci, A.: A Constructive Geometry for Computer Graphics. The Computer Journal 16(2), 157–160 (1973)zbMATHCrossRefGoogle Scholar
  14. 14.
    Schaefer, S., Warren, J.: Dual contouring: ”the secret sauce”, rice University, Department of Computer Science Technical Report (2003)Google Scholar
  15. 15.
    Shammaa, M.H., Suzuki, H., Ohtake, Y.: Extraction of isosurfaces from multi-material ct volumetric data of mechanical parts. In: SPM 2008: Proceedings of the 2008 ACM symposium on Solid and physical modeling, pp. 213–220. ACM, New York (2008)CrossRefGoogle Scholar
  16. 16.
    Stalling, D., Zckler, M., Hege, H.C.: Interactive segmentation of 3d medical images with subvoxel accuracy. In: Proc. CAR 1998 Computer Assisted Radiology and Surgery, pp. 137–142 (1998)Google Scholar
  17. 17.
    Tiede, U., Schiemann, T., Höhne, K.H.: High quality rendering of attributed volume data. In: VIS 1998: Proceedings of the conference on Visualization 1998, pp. 255–262. IEEE Computer Society Press, Los Alamitos (1998)Google Scholar
  18. 18.
    Wilson, O., VanGelder, A., Wilhelms, J.: Direct volume rendering via 3d textures. Tech. rep., Santa Cruz, CA, USA (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Powei Feng
    • 1
  • Tao Ju
    • 2
  • Joe Warren
    • 1
  1. 1.Rice University 
  2. 2.Washington University in St. Louis 

Personalised recommendations