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 2 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 <#OUT37.1> * the previous unit defined the basic idea of a quadtree * this unit examines how quadtrees are used in several simple processes, including: o measurement of area o overlay o finding adjacent leafs o measuring the area of contiguous patches * in addition, this unit will look at how quadtrees can be used to provide indexes for faster access to vector-coded objects * finally, alternative forms of spatial indexing will be reviewed Definition <#OUT37.1.1> * to traverse a quadtree: o begin by moving down the leftmost branch to the first leaf o after processing each leaf in this branch, move back up to the previous branching point, and turn right o this will either lead down to another leaf, or back to a previous branching point diagram overhead - First map o several of the following examples use this simple raster and its associated quadtree B. AREA ALGORITHM <#OUT37.2> Procedure <#OUT37.2.1> * to measure the area of A on the map: o traverse the tree and add those leafs coded A, weighted by the area at the level of the leaf Example <#OUT37.2.2>
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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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