A Technique for Volumetric CSG based on Morphology

  • Andreas Bærentzen
  • Niels Jørgen Christensen
Part of the Eurographics book series (EUROGRAPH)


In this paper, a new technique for volumetric CSG is presented. The technique requires the input volumes to correspond to solids which fulfill a voxelization suitability criterion. Assume the CSG operation is union. The volumetric union of two such volumes is defined in terms of the voxelization of the union of the two original solids.

The theory behind the new technique is discussed, the algorithm and implementation are presented. Finally, we present images and timings.


Close Point Closedness Property Colour Plate Volume Visualization Constructive Solid Geometry 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Christoph M. Hoffmann. Geometric and Solid Modeling. Morgan Kaufmann, 1989.Google Scholar
  2. 2.
    Andreas Bærentzen, Miloš Šrámek, and Niels Jørgen Christensen. A Morphological Approach to the Voxelization of Solids. In Vaclav Skala, editor, Proceedings of WSCG 2000, volume I, February 2000.Google Scholar
  3. 3.
    Miloš Šrámek and Arie Kaufman. Alias-free voxelization of geometric objects. IEEE Transactions on Visualization and Computer Graphics, 5(3), July/September 1999.Google Scholar
  4. 4.
    Sidney Wang and Arie E. Kaufman. Volume-Sampled 3D Modeling. IEEE Computer Graphics El Applications, 1994.Google Scholar
  5. 5.
    Min Chen, John V. Tucker, and Adrian Leu. CROVE - A Rendering System for Constructive Representations of Volumetric Environments. In International Workshop on Volume Graphics, Swansea 1999, 1999.Google Scholar
  6. 6.
    Shiaofen Fang and Rajagopalan Srinivasan. Volumetric-CSG - A Model Based Volume Visualization Approach. In WSCG’98. The Sixth International Conference in Central Europe on Computer Graphics and Visualization’98, 1998.Google Scholar
  7. 7.
    Andreas Bærentzen. Octree-based Volume Sculpting. In Craig M. Wittenbrink and Amitabh Varshney, editors, LBHT Proceedings of IEEE Visualization ‘88, October 1998.Google Scholar
  8. 8.
    Arie Kaufman, Daniel Cohen, and Roni Yagel. Volume Graphics. IEEE Computer, 26 (7), July 1993.Google Scholar
  9. 9.
    David E. Breen. Constructive Cubes. In F.H. Post and W. Barth, editors, Eurographics ‘81, 1991.Google Scholar
  10. 10.
    Bradley A. Payne and Arthur W. Toga. Distance Field Manipulation of Surface Models. IEEE Computer Graphics & Applications, 12 (1), 1992.Google Scholar
  11. 11.
    David E. Breen, Sean Mauch, and Ross T. Whitaker. 3D Scan Conversion of CSG Models into Distance Volumes. In Stephen Spencer, editor, Proceedings of IEEE Symposium on Volume Visualization, October 1998.Google Scholar
  12. 12.
    Sarah F.F. Gibson. Using Distance Maps for Accurate Surface Representation in Sampled Volumes. In Stephen Spencer, editor, Proceedings of IEEE Symposium on Volume Visualization, October 1998.Google Scholar
  13. 13.
    Jean Serra. Image Analysis and Mathematical Morphology,volume 1. Academic Press, 1982.Google Scholar
  14. 14.
    J. Andreas Bœrentzen. Volumetric Manipulations with Applications to Sculpting. PhD thesis, IMM, Technical University of Denmark, 2001.Google Scholar
  15. 15.
    Jon Louis Bentley. Multidimensional Binary Search Trees Used for Associative Searching. Communications of the ACM, 18 (9), 1975.Google Scholar

Copyright information

© Springer-Verlag/Wien 2001

Authors and Affiliations

  • Andreas Bærentzen
    • 1
  • Niels Jørgen Christensen
    • 1
  1. 1.IMM, Technical University of DenmarkDenmark

Personalised recommendations