A hierarchical spatial index for cell complexes

  • Elisabetta Bruzzone
  • Leila De Floriani
  • Monica Pellegrinelli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 692)


A new hierachical spatial index for object representation schemes based on three-dimensional cell complexes is introduced. We consider a domain consisting of general n-dimensional spatial objects described by n-dimensional cell complexes. The new hierarchical spatial index, called a cellular n-tree, generalizes similar structures developed for planar maps, and is defined as a recursive subdivision of a universe containing the cell complex into regular blocks. Terminal blocks may be completely inside a cell or outside the complex, or may contain indices to sets of cells within the complex. We briefly review the properties of n-dimensional cell complexes, that we call cellular decompositions, and introduce a few basic atomic operators for building them in the three-dimensional case. We shortly describe algorithms for building a cellular octree from a 3D cellular decomposition and for updating the cellular octree, when the cellular decomposition is modified by applying the atomic constructive operators introduced. Algorithms for solving point location and proximity queries on a cellular decomposition with a cellular octree superimposed are presented.


Cell Complex Query Point Spatial Index Spatial Query Spatial Entity 
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.


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  1. 1.
    Arvo, J., Kirk, D., “A Survey of Ray Tracing Acceleration Techniques”, in An Introduction to Ray Tracing, A.S. Glassner editor, 201–262, 1989.Google Scholar
  2. 2.
    Ayala, D., Brunet, P., Juan, R., Navazo, I., “Object Representation by Means of non Minimal Division Quadtrees and Octrees”, ACM Transactions on Graphics, 4, 1, 41–59, 1985.Google Scholar
  3. 3.
    Brisson, E., “Representing Geometric Structures in d-dimensions: Topology and Order”, Proceedings 5th ACM Symposium on Computational Geometry, Saarbruchen, 218–227, 1989.Google Scholar
  4. 4.
    Brunet, P., Navazo, I., “Solid Representation and Operation using Extended Octrees”, ACM Transactions on Graphics, 8, 1989.Google Scholar
  5. 5.
    Bruzzone, E., De Floriani, L., “Two Data Structures for Building Tetrahedralizations”, The Visual Computer, 6, 266–283, 1990.Google Scholar
  6. 6.
    Carlbom, I., Chakravarty, I., Vanderschel, D., “A Hierarchical Data Structure for Representing Spatial Decomposition of 3-D Objects”, IEEE Computer Graphics and Applications, 5, 4, 24–31, 1985.Google Scholar
  7. 7.
    De Floriani, L., Pellegrinelli, M., Bruzzone, E., “Building a Hierarchical Representation for Cellular Decompositions”, Technical Report, DISI, University of Genoa, 1992.Google Scholar
  8. 8.
    De Floriani, L., Marzano, P., Puppo, E., “Spatial Queries and the Hybrid Models”, in preparation.Google Scholar
  9. 9.
    Dobkin, D., Laszlo, M., “Primitives for the Manipulation of Three-Dimensional Subdivisions”, Proceeedings 3rd ACM Symposium on Computational Geometry Models, Canada, 86–90, 1987.Google Scholar
  10. 10.
    Edelsbrunner, H., Algorithms in Combinatorial Geometry, Springer Verlag, 1987.Google Scholar
  11. 11.
    Egenhofer, M.J., Frank, A.U., Jackson, J.P., “A topological Model for Spatial Database”, Design and Implementation of Large Spatial Database, SSD 89, Lecture Notes in Computer Science, Springer Verlag, 271–286, 1989.Google Scholar
  12. 12.
    Frank, A., Kuhn, W., “Cell Graphs: A Provable Correct Method for the Storage of Geometry”, Proceedings 2nd International Symposium on Spatial Data Handling, Seattle, Washington, 411–436, 1986.Google Scholar
  13. 13.
    Ferrucci, V., Paoluzzi, A., “Extension and Boundary Evaluation for Multidimensional Polyhedra”, Computer Aided Design, 23, 1, 40–50, 1991.Google Scholar
  14. 14.
    Hoel, E.G., Samet, H., “Efficient Processing of Spatial Queries in Line Segment Database”, Computer Science, 525, Springer Verlag, Berlin, 1991.Google Scholar
  15. 15.
    Lienhart, P., “Topological Models for Boundary Representations: a Comparison with n-dimensional Generalized Maps”, Computer Aided Design, 23, 1, 59–82, 1991.Google Scholar
  16. 16.
    Nelson, R.C., Samet, H., “A Consistent Hierarchical Representation for Vector Data”, Computer Graphics 20, 4, 197–206, 1986.Google Scholar
  17. 17.
    Rossignac, J.R., O'Connor, M.A., “SGC: A Dimensional-Independent Model for Pointsets with Internal Structures and Incomplete Boundaries”, Geometric Modeling for Product Engineering, Wozny, M.J., Turner, J.U., and Preiss, K., editors, Elsevier Science Publishers B.V. (North Holland), 145–180, 1990.Google Scholar
  18. 18.
    Rossignac, J.R., “Through the Cracks of the Solid Modeling Milestone”, Eurographics 91 State of the Art Report on Solid Modeling, 23–109, 1991.Google Scholar
  19. 19.
    Samet, H., The Design and Analysis of Spatial Data Structures, Addison-Wesley, Reading, MA, 1990.Google Scholar
  20. 20.
    Samet, H., Applications of Spatial Data Structures, Addison-Wesley, Reading, MA, 1990.Google Scholar
  21. 21.
    Takala, T., “A Taxonomy on Geometric and Topological Models”, Proceedings Eurographics Workshop on Mathematics and Computer Graphics, S. Margherita, Genova, Italy, October 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Elisabetta Bruzzone
    • 1
  • Leila De Floriani
    • 2
  • Monica Pellegrinelli
    • 2
  1. 1.Elsag Bailey S.p.A. Research and DevelopmentGenovaItaly
  2. 2.Department of Computer and Information SciencesUniversity of GenovaGenovaItaly

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