Complementary Space for Enhanced Uncertainty and Dynamics Visualization

  • Chandrajit Bajaj
  • Andrew Gillette
  • Samrat Goswami
  • Bong June Kwon
  • Jose Rivera
Part of the Mathematics and Visualization book series (MATHVISUAL)


Many computational modeling pipelines for geometry processing and visualization focus on topologically and geometrically accurate shape reconstruction of “primal” space, meaning the surface of interest and the volume it contains. Certain features of a surface such as pockets, tunnels, and voids (small, closed components) often represent important properties of the model and yet are difficult to detect or visualize in a model of primal space alone. It is natural, then, to consider what information can be gained from a model and visualization of complementary space, i.e. the space exterior to but still “near” the surface in question. In this paper, we show how complementary space can be used as a tool for both uncertainty and dynamics visualizations and analysis.


Unstable Manifold Medial Axis Mouth Area Normal Mode Analysis Thin Region 
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.



We would like to thank previous members of the CCV lab who worked on these projects, including Katherine Claridge, Vinay Siddavanahalli, and Bong-Soo Sohn. This research was supported in part by NSF grants DMS-0636643, CNS-0540033 and NIH contracts R01-EB00487, R01-GM074258, R01-GM07308.


  1. 1.
    C. Bajaj, A. Gillette, and S. Goswami. Topology based selection and curation of level sets. In H.-C. Hege, K. Polthier, and G. Scheuermann, editors, Topology-Based Methods in Visualization II, pages 45–58. Springer-Verlag, 2009.Google Scholar
  2. 2.
    C. Bajaj and S. Goswami. Automatic fold and structural motif elucidation from 3d EM maps of macromolecules. In ICVGIP 2006, pages 264–275, 2006.Google Scholar
  3. 3.
    N. Basdevant, D. Borgis, and T. Ha-Duong. A coarse-grained protein-protein potential derived from an all-atom force field. Journal of Physical Chemistry B, 111(31):9390–9399, 2007.CrossRefGoogle Scholar
  4. 4.
    F. Cazals, F. Chazal, and T. Lewiner. Molecular shape analysis based upon the morse-smale complex and the connolly function. In 19th Ann. ACM Sympos. Comp. Geom., pages 351–360, 2003.Google Scholar
  5. 5.
    R. Chaine. A geometric convection approach of 3D reconstruction. In Proc. Eurographics Sympos. on Geometry Processing, pages 218–229, 2003.Google Scholar
  6. 6.
    F. Chazal and A. Lieutier. Stability and homotopy of a subset of the medial axis. In Proc. 9th ACM Sympos. Solid Modeling and Applications, pages 243–248, 2004.Google Scholar
  7. 7.
  8. 8.
    T. K. Dey, J. Giesen, and S. Goswami. Shape segmentation and matching with flow discretization. In F. Dehne, J.-R. Sack, and M. Smid, editors, Proc. Workshop Algorithms Data Strucutres (WADS 03), LNCS 2748, pages 25–36, Berlin, Germany, 2003.Google Scholar
  9. 9.
    H. Edelsbrunner. Surface reconstruction by wrapping finite point sets in space. In B. Aronov, S. Basu, J. Pach, and M. Sharir, editors, Ricky Pollack and Eli Goodman Festschrift, pages 379–404. Springer-Verlag, 2002.Google Scholar
  10. 10.
    H. Edelsbrunner, M. Facello, and J. Liang. On the definition and the construction of pockets in macromolecules. Discrete Applied Mathematics, 88:83–102, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
  12. 12.
    J. Giesen and M. John. The flow complex: a data structure for geometric modeling. In Proc. 14th ACM-SIAM Sympos. Discrete Algorithms, pages 285–294, 2003.Google Scholar
  13. 13.
    S. Goswami, T. K. Dey, and C. L. Bajaj. Identifying flat and tubular regions of a shape by unstable manifolds. In Proc. 11th ACM Sympos. Solid and Phys. Modeling, pages 27–37, 2006.Google Scholar
  14. 14.
    S. Goswami, A. Gillette, and C. Bajaj. Efficient Delaunay mesh generation from sampled scalar functions. In Proceedings of the 16th International Meshing Roundtable, pages 495–511. Springer-Verlag, October 2007.Google Scholar
  15. 15.
    M. Levitt, C. Sander, and P. S. Stern. Protein normal-mode dynamics: Trypsin inhibitor, crambin, ribonuclease and lysozyme. Journal of Molecular Biology, 181:423 – 447, 1985.CrossRefGoogle Scholar
  16. 16.
    J. Liang, H. Edelsbrunner, and C. Woodward. Anatomy of protein pockets and cavities: measurement of binding site geometry and implications for ligand design. Protein Sci, 7(9):1884–97, 1998.CrossRefGoogle Scholar
  17. 17.
    V. Natarajan and V. Pascucci. Volumetric data analysis using morse-smale complexes. In SMI ’05: Proceedings of the International Conference on Shape Modeling and Applications 2005, pages 322–327, Washington, DC, USA, 2005.Google Scholar
  18. 18.
    S. Osher and J. A. Sethian. Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations. J. Comput. Phys., 79(1):12–49, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    J. A. Sethian. A fast marching level set method for monotonically advancing fronts. In Proc. Nat. Acad. Sci, pages 1591–1595, 1996.Google Scholar
  20. 20.
    F. Tama. Normal mode analysis with simplified models to investigate the global dynamics of biological systems. Protein and Peptide Letters, 10(2):119 – 132, 2003.CrossRefGoogle Scholar
  21. 21.
    Z. Yu and C. Bajaj. Detecting circular and rectangular particles based on geometric feature detection in electron micrographs. Journal of Structural Biology, 145:168–180, 2004.CrossRefGoogle Scholar
  22. 22.
    X. Zhang and C. Bajaj. Extraction, visualization and quantification of protein pockets. In Comp. Syst. Bioinf. CSM2007, volume 6, pages 275–286, 2007.Google Scholar

Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  • Chandrajit Bajaj
    • 1
  • Andrew Gillette
    • 1
  • Samrat Goswami
    • 1
  • Bong June Kwon
    • 1
  • Jose Rivera
    • 1
  1. 1.Center for Computational VisualizationUniversity of Texas at AustinAustinUSA

Personalised recommendations