Advertisement

Spatial Data Indexing and Point Location

  • Jakob Andreas Bærentzen
  • Jens Gravesen
  • François Anton
  • Henrik Aanæs

Abstract

This chapter is concerned with spatial databases. Anyone designing algorithms for geometry processing will invariably need to store data in spatial databases. The chapter begins with an introduction to spatial databases and moves on to discuss particular data structures.

The kD tree for instance is a simple and very popular data structure for storing points in space. Essentially, a kD tree is a binary tree that recursively divides space into smaller regions. The same is true of a binary space partitioning tree, but the planes that divide space can be arbitrarily oriented, and a BSP tree is often used for triangles. Quadtrees and octrees divide space into four and eight sub-regions at each node and thus have a higher branching factor.

The chapter closes with a discussion of object-driven spatial access methods. The distinguishing characteristic of these is that objects are grouped as opposed to space being divided.

Keywords

Spatial Data Voronoi Diagram Random Access Memory Spatial Database Minimum Bound Rectangle 
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.

References

  1. 1.
    Elmasri, R., Navathe, S.B.: Fundamentals of Database Systems. Benjamin-Cummings, Redwood City (1989) MATHGoogle Scholar
  2. 2.
    Shekhar, S., Chawla, S.: Spatial Databases: A Tour. Prentice Hall, New York (2002). http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&path=ASIN/0130174807 Google Scholar
  3. 3.
    Shekhar, S., Chawla, S., Ravada, S., Fetterer, A., Liu, X., Lu, C.-t.: Spatial databases-accomplishments and research needs. IEEE Trans. Knowl. Data Eng. 11(1), 45–55 (1999). doi: 10.1109/69.755614 CrossRefGoogle Scholar
  4. 4.
    Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975). doi: 10.1145/361002.361007 MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
  6. 6.
    Fuchs, H., Kedem, Z.M., Naylor, B.F.: On visible surface generation by a priori tree structures. In: SIGGRAPH ’80: Proceedings of the 7th Annual Conference on Computer Graphics and Interactive Techniques, pp. 124–133. ACM, New York (1980). doi: 10.1145/800250.807481 Google Scholar
  7. 7.
    Finkel, R.A., Bentley, J.L.: Quad trees: a data structure for retrieval on composite keys. Acta Inform. 4, 1–9 (1974) MATHCrossRefGoogle Scholar
  8. 8.
    Meagher, D.: Octree encoding: a new technique for the representation, manipulation and display of arbitrary three dimensional objects by computer. Technical report IPL,TR-80-111, Rensselaer Polytechnic Institute, Troy, NY, USA (1980) Google Scholar
  9. 9.
  10. 10.
    Guttman, A.: R-trees: a dynamic index structure for spatial searching. In: SIGMOD ’84: Proceedings of the 1984 ACM SIGMOD International Conference on Management of Data, pp. 47–57. ACM, New York (1984). doi: 10.1145/602259.602266 CrossRefGoogle Scholar
  11. 11.
  12. 12.
    Sellis, T.K., Roussopoulos, N., Faloutsos, C.: The R+-tree: a dynamic index for multi-dimensional objects. In: VLDB ’87: Proceedings of the 13th International Conference on Very Large Data Bases, pp. 507–518. Morgan Kaufmann, San Francisco (1987) Google Scholar
  13. 13.
    Beckmann, N., Kriegel, H.-P., Schneider, R., Seeger, B.: The R*-tree: an efficient and robust access method for points and rectangles. In: SIGMOD ’90: Proceedings of the 1990 ACM SIGMOD International Conference on Management of Data, pp. 322–331. ACM, New York (1990). doi: 10.1145/93597.98741 CrossRefGoogle Scholar
  14. 14.
    Arge, L., de Berg, M., Haverkort, H.J., Yi, K.: The priority r-tree: a practically efficient and worst-case optimal r-tree. In: SIGMOD ’04: Proceedings of the 2004 ACM SIGMOD International Conference on Management of Data, pp. 347–358. ACM, New York (2004). doi: 10.1145/1007568.1007608 CrossRefGoogle Scholar
  15. 15.
    Mount, D.M., Arya, S.: ANN: a library for approximate nearest neighbor searching. http://www.cs.umd.edu/~mount/ANN/ (2010)

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Jakob Andreas Bærentzen
    • 1
  • Jens Gravesen
    • 2
  • François Anton
    • 1
  • Henrik Aanæs
    • 1
  1. 1.Department of Informatics and Mathematical ModellingTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark

Personalised recommendations