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1 The Quadtree and Related Hierarchical Data Structures HANAN SAMET Computer Science Department, University of Maryland, College Park, Maryland 20742 2009.

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Presentation on theme: "1 The Quadtree and Related Hierarchical Data Structures HANAN SAMET Computer Science Department, University of Maryland, College Park, Maryland 20742 2009."— Presentation transcript:

1 1 The Quadtree and Related Hierarchical Data Structures HANAN SAMET Computer Science Department, University of Maryland, College Park, Maryland April. 01 Yongsu Song PNU STEM Lab

2 STEMPNU 2 Plan Part 1 : Overview of Quadtree Part 2 : Basic Operation  Start, Merge, Split, Group  Example of tiling  Rope and Net Part 3 : Alternates of Quadtree  Octree  K-d tree  Approximation Methods Part 4 : Conclusion

3 STEMPNU Overview of Quadtree 3 Similar to divide and conquerGeographic Information System, Image processing and so on.. Recursive decomposition.

4 STEMPNU Cont A B CDE FGHIJ K LM NO P Q N H M I O GF B LQ J

5 STEMPNU 2. Basic Operation Start, Merge, Split, Group 5

6 STEMPNU Example of tiling 6 1.Uniform orientation 2.Easy to implement Yamaguchi et al. [1984] Triangular quadtree to generate an isometric view from octree. (3D)

7 STEMPNU Fast! But.. Rope and Net 7 A B CDE FGHIJ K LM NO P Q N H M I O GF B LQ J Rope : Link between two adjacent nodes of equal size where at least one of them is a leaf node. Net : Linked list whose elements are all the nodes that are adjacent along a given side of a node.

8 STEMPNU Alternates of Quadtree k-d tree 8 Quadtree K-d tree Fewer leaf nodes : 4 sons -> 2 sons Good at higher dimensional data!

9 STEMPNU Point quadtree vs k-d tree 9 Quadtree 2^k branching factor for k dimension k-d tree

10 STEMPNU Approximation Methods Image approximation.  Shape approximation. 10 Good : High resolution levels to low resolution. Bad : Comparing similar shapes.

11 STEMPNU Octree Structure to store the volume element 11 Is it possible?

12 STEMPNU Stair case Cont

13 STEMPNU Curvilinear Data Boundaries of regions? Strip tree 13 Point to left child node? Point to right child node? X1? Y1? X2? Y2? WL? WR? More complex?

14 STEMPNU Cont. Special case  Closed curve by strip tree.  Extends past its endpoints. 14 So what?

15 STEMPNU Intersecting two strip trees.  Curve approximation. Cont. 15 NullClear.Possible

16 STEMPNU Conclusion The main idea  Recursive decomposition Efficient For Region and Point  Divide and conquer  Reduce size range of target data Important of data structure  Apply Approximation skills 16

17 STEMPNU Cont. Any questions? 17


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