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A Generic Programming Approach to Multiresolution Spatial Decompositions

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Visualization and Mathematics III

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Summary

We present a generic programming approach to the implementation of multiresolution spatial decompositions. From a set of simple and necessary requirements, we arrive at the Binary Multitriangulation (BMT) concept. We also describe a data structure that models the BMT concept in its full generality. Finally, we discuss applications of the BMT to visualization of volumetric datasets.

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References

  1. J. Alexander. The combinatorial theory of complexes. Ann. Math., 31: 294 – 322, 1930.

    Article  Google Scholar 

  2. G. Berti. Generic software components for Scientific Computing. PhD thesis, BTU Cottbus, 2000.

    MATH  Google Scholar 

  3. Mario Botsch, Stephan Steinberg, Stephan Bischoff, and Leif Kobbelt. Open-mesh - a generic and efficient polygon mesh data structure. In OpenSG PLUS Symposium, 2002.

    Google Scholar 

  4. P. Cignoni, L. De Floriani, P. Magillo, E. Puppo, and R. Scopigno. TAn2 - visualization of large irregular volume datasets. Technical Report DISI-TR-0007, University of Genova (Italy), 2000.

    Google Scholar 

  5. E. Danovaro, L. De Floriani, M. Lee, and H. Samet. Multiresolution tetrahedral meshes: an analysis and a comparison. In Proceedings International Conference on Shape Modeling, 2002.

    Google Scholar 

  6. T. Dey, H. Edelsbrunner, and S. Guha. Computational topology. In B. Chazelle, J. E. Goodman, and R. Pollack, editors, Advances in Discrete and Computational Geometry (Contemporary mathematics 223), pages 109–143. American Mathematical Society, 1999.

    Google Scholar 

  7. D. P. Dobkin and M. J. Laszlo. Primitives for the manipulation of threedimensional subdivisions. Algorithmica, 4: 3 – 32, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  8. Jihad El-Sana and Yi-Jen Chiang. External memory view-dependent simplification. Computer Graphics Forum, 19 (3): 139 – 150, August 2000.

    Article  Google Scholar 

  9. Jihad El-Sana and Amitabh Varshney. Generalized view-dependent simplification. Computer Graphics Forum, 18 (3): 83 – 94, September 1999.

    Article  Google Scholar 

  10. Andreas Fabri, Geert-Jan Giezeman, Lutz Kettner, Stefan Schirra, and Sven Schonherr. On the design of CGAL a computational geometry algorithms library. SP*E, 30 (11): 1167 – 1202, 2000.

    MATH  Google Scholar 

  11. Ricardo Fanas and Claudio T. Silva. Out-of-core rendering of large, unstructured grids. IEEE Computer Graphics * Applications, 21 (4): 42 – 51, July/August 2001.

    Google Scholar 

  12. L. De Floriani, E. Puppo, and P. Magillo. A formal approach to multiresolution modeling. In W. Straßer, R. Klein, and R. Rau, editors, Theory and Practice of Geometric Modeling. SpringerVerlag, 1996.

    Google Scholar 

  13. M. Garland. Multiresolution modeling: Survey & future opportunities. In Eurographics’99, State of the Art Report (STAR), 1999.

    Google Scholar 

  14. L. J. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of voronoi diagrams. ACM Trans. Graph., 4: 74 – 123, 1985.

    Article  MATH  Google Scholar 

  15. Hugues Hoppe. Efficient implementation of progressive meshes. Computers ei Graphics, 22 (1): 27 – 36, February 1998.

    Article  Google Scholar 

  16. M. Lee, L. De Floriani, and H. Samet. Constant time neighbor finding in hierarchical tetrahedral meshes. In Proceedings International Conference on Shape Modeling, pages 286 – 295, 2001.

    Chapter  Google Scholar 

  17. W. B. R. Lickorish. Simplicial moves on complexes and manifolds. In Proceedings of the Kirbyfest, volume 2, pages 299 – 320, 1999.

    Google Scholar 

  18. M. Mäntylä. An Introduction to Solid Modeling. Computer Rockville, Maryland, 1988.

    Google Scholar 

  19. J. Peter May. Simplicial Objects in Algebraic Topology, volume 11. D. Van Nostrand Commpany, Inc., Princeton, 1967.

    Google Scholar 

  20. Greg Nielson. Tools for triangulations and tetrahedrizations and constructing functions defined over them. In Scientific Visualization: Overviews, Methodologies, and Techniques, pages 419–515. IEEE CS Press, 1997.

    Google Scholar 

  21. H. Plantinga and C. R. Dyer. Visibility, occlusion, and the aspect graph. Internat. J. Comput. Vision, 5 (2): 137 – 160, 1990.

    Article  Google Scholar 

  22. E. Puppo. Variable resolution triangulations. Computational Geometry Theory and Applications, 11 (34): 219 – 238, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  23. C. Rocchini and P. Cignoni. Generating random points in a tetrahedron. Journal of Graphics Tools, 5 (4): 9 – 12, 2000.

    Article  MATH  Google Scholar 

  24. T. Roxborough and Gregory M. Nielson. Tetrahedron based, least squares, progressive volume models with application to freehand ultrasound data. In IEEE Visualization 2000, pages 93– 100, October 2000.

    Google Scholar 

  25. P. Shirley and A. A. Tuchuran. Polygonal approximation to direct scalar volume rendering. Computer Graphics, 24 (5): 63 – 70, 1990.

    Article  Google Scholar 

  26. Jeremy G. Siek, Lie-Quan Lee, and Andrew Lumsdaine. Boost Graph Library, The: User Guide and Reference Manual. Addison-Wesley, 2002.

    Google Scholar 

  27. Jeremy G. Siek and Andrew Lumsdaine. The matrix template library: A generic programming approach to high performance numerical linear algebra. In ISCOPE, pages 59 – 70, 1998.

    Google Scholar 

  28. C. T. Silva, J. S. B. Mitchell, and P. Williams. An exact interactive time visibility ordering algorithm for polyhedral cell complexes. In 1998 Volume Visualization Symposium, pages 87 – 94, October 1998.

    Chapter  Google Scholar 

  29. A. A. Stepanov and M. Lee. The Standard Template Library. Technical Report X3J16/94-0095, WG21/N0482, ISO Programming Language C++ Project, 1994.

    Google Scholar 

  30. B. Stroustrup. The C++ Programming Language: Third Edition. Addison-Wesley, 1997.

    Google Scholar 

  31. Luiz Velho and Jonas Gomes. Variable resolution 4-k meshes: Concepts and applications. Computer Graphics forum, 19: 195 – 212, 2000.

    Article  Google Scholar 

  32. Kevin Weiler. Edge-Based Data Structures for Solid Modeling in Surface Environments. IEEE Computer Graphics and Applications, 5 (1): 21 – 40, 1985.

    Article  Google Scholar 

  33. P. Williams. Visibility ordering meshed polyhedra. ACM Transactions on Graphics, 11 (2): 103 – 126, 1992.

    Article  MATH  Google Scholar 

  34. C. Wittenbrink. Cellfast: Interactive unstructured volume rendering. In Proceedings IEEE Visualization’99, Late Breaking Hot Topics, pages 21–24, 1999. Also available as Technical Report, HPL-1999-81R1, Hewlett-Packard Laboratories.

    Google Scholar 

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Author information

Authors and Affiliations

  1. IMPA — Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil

    Vinícius Mello & Luiz Velho

  2. Federal University of Rio de Janeiro — UFRJ, Brazil

    Paulo Roma Cavalcanti

  3. AT&T Labs, 180 Park Ave., Florham Park, NJ, 07932, USA

    Cláudio T. Silva

Authors
  1. Vinícius Mello
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  2. Luiz Velho
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  3. Paulo Roma Cavalcanti
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  4. Cláudio T. Silva
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Editor information

Editors and Affiliations

  1. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustraße 7, 14195, Berlin, Germany

    Hans-Christian Hege

  2. Institut für Mathematik, MA 8–3, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Konrad Polthier

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© 2003 Springer-Verlag Berlin Heidelberg

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Mello, V., Velho, L., Cavalcanti, P.R., Silva, C.T. (2003). A Generic Programming Approach to Multiresolution Spatial Decompositions. In: Hege, HC., Polthier, K. (eds) Visualization and Mathematics III. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05105-4_18

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  • DOI: https://doi.org/10.1007/978-3-662-05105-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05682-6

  • Online ISBN: 978-3-662-05105-4

  • eBook Packages: Springer Book Archive

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