u37-QUADTREE ALGORITHMS AND SPATIAL INDEXES

# u37-QUADTREE ALGORITHMS AND SPATIAL INDEXES - UNIT 37...

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Sheet1 Page 1 UNIT 37 - QUADTREE ALGORITHMS AND SPATIAL INDEXES <toc.html#UNIT37> UNIT 37 - QUADTREE ALGORITHMS AND SPATIAL INDEXES # A. INTRODUCTION <#SEC37.1> * Definition <#SEC37.1.1> # B. AREA ALGORITHM <#SEC37.2> * Procedure <#SEC37.2.1> * Example <#SEC37.2.2> # C. OVERLAY ALGORITHM <#SEC37.3> * Procedure <#SEC37.3.1> * Result <#SEC37.3.2> # D. ADJACENCY ALGORITHM <#SEC37.4> * Problem <#SEC37.4.1> * Definition <#SEC37.4.2> * Two cases <#SEC37.4.3> * Tesseral Arithmetic <#SEC37.4.4> * Determining Adjacency <#SEC37.4.5> * Length of common boundary <#SEC37.4.6> # E. AREA OF A CONTIGUOUS PATCH ALGORITHM <#SEC37.5> * Problem <#SEC37.5.1> * Method <#SEC37.5.2> * Algorithm <#SEC37.5.3> * Results <#SEC37.5.4> # F. QUADTREE INDEXES <#SEC37.6> * Indexing using quadtrees <#SEC37.6.1> * Setting up the index <#SEC37.6.2> * Using the index <#SEC37.6.3> * Generalizations <#SEC37.6.4> # G. R-TREE INDEXES <#SEC37.7> * Method <#SEC37.7.1> * Problem <#SEC37.7.2> # REFERENCES <#SEC37.8> # DISCUSSION AND EXAM QUESTIONS <#SEC37.9> # NOTES <#SEC37.10>

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Sheet1 Page 3 * in the example quadtree, elements at level 0 have area 16, at level 1 - area 4, at level 2 - area 1 o thus, area of A is: 1 (leaf 00) + 1(leaf 02) + 1 (leaf 03) + 4 (leaf 2) + 1 (leaf 32) = 8 units C. OVERLAY ALGORITHM <#OUT37.3> overhead - Second map o note: this overhead can be physically overlayed on First map Procedure <#OUT37.3.1> * to overlay the two maps: o traverse the trees simultaneously, following all branches which exist in either tree o where one tree lacks branches (has a leaf where the other tree has branches), assign the value of the associated leaf to each of the branches o e.g. node 3 is branched on map 1, not on map 2 + the leafs derived from this node (30, 31, 32 and 33)

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