UNIT 37 - QUADTREE ALGORITHMS AND SPATIAL INDEXES

UNIT 37 - QUADTREE ALGORITHMS AND SPATIAL INDEXES

  • A. INTRODUCTION
  • B. AREA ALGORITHM
  • C. OVERLAY ALGORITHM
  • D. ADJACENCY ALGORITHM
  • E. AREA OF A CONTIGUOUS PATCH ALGORITHM
  • F. QUADTREE INDEXES
  • G. R-TREE INDEXES
  • REFERENCES
  • DISCUSSION AND EXAM QUESTIONS
  • NOTES

    This unit is very long and deals with more advanced algorithms. Depending on the abilities and interests of your students, you may want to omit the third and fourth algorithms included or consider providing this as extra handouts. Advanced students may be pleased to have the opportunity to examine the more subtle, complex nature of these advanced algorithms. The later section on indexes does not depend on material covered in the earlier sections.

    UNIT 37 - QUADTREE ALGORITHMS AND SPATIAL INDEXES

    A. INTRODUCTION

    Definition

    B. AREA ALGORITHM

    Procedure

    Example

    C. OVERLAY ALGORITHM

    Procedure

    Result

    D. ADJACENCY ALGORITHM

    Problem

    Definition

    Two cases

    Tesseral Arithmetic

    Determining Adjacency

    Length of common boundary

    E. AREA OF A CONTIGUOUS PATCH ALGORITHM

    Problem

    Method

    Algorithm

    Results

    F. QUADTREE INDEXES

    Indexing using quadtrees

    Setting up the index

    Using the index

    Generalizations

    G. R-TREE INDEXES

    Method

    Problem

    REFERENCES

    Buchmann, A., O. Gunther, T.R. Smith and Y.-F. Wang. Design and Implementation of Large Spatial Databases, Unit Notes in Computer Science 409, Springer Verlag, Berlin. Contains a collection of papers on spatial data indexing.

    Guttman, A, 1984. "R-trees: A dynamic index structure for spatial searching," ACM SIGMOD, pp. 47-57.

    Mark, D.M., and J.P. Lauzon, 1984. "Linear quadtrees for Geographic Information Systems," Proceedings, International Symposium on Spatial Data Handling, Zurich, 2:412-430.

    Noronha, V., 1988. "A survey of Hierarchical Partitioning Methods for Vector Images," Proceedings, Third International Symposium on Spatial Data Handling, Sydney, Australia, pp. 185-199.

    Oosterom, P. van, 1990. "A modified binary space partitioning tree for geographic information systems," International Journal of Geographical Information Systems 4(2):133-46.

    The two Samet books listed as references for Unit 36 contain useful discussions of quadtree algorithms.

    DISCUSSION AND EXAM QUESTIONS

    1. Compare the formal methods of indexing (quadtree, R-tree, 1-D sort) with informal methods in common use (e.g. continents, nation-states, major civil divisions, ZIP codes, etc.).

    2. How would you design a study to compare the effectiveness of different indexing schemes? What data would you use? What measures would you compare?

    3. Current vector-based systems use a wide variety of indexing schemes. Why is there no consensus as to the best? What methods are best for what purposes and area of application?

    4. Devise a means of measuring the Manhattan distance between two quadtree blocks (assume the codes have the same length).


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