# 2009. April. 01 Yongsu Song PNU STEM Lab

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2009. April. 01 Yongsu Song PNU STEM Lab
The Quadtree and Related Hierarchical Data Structures HANAN SAMET Computer Science Department, University of Maryland, College Park, Maryland 20742 2009. April. 01 Yongsu Song PNU STEM Lab

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

Similar to divide and conquer Geographic Information System, Image processing and so on..

Cont. N H M I O G F B L Q J 37 38 39 40 57 58 59 B F G H I J L M N O Q
1 N H M I O G F B L Q J 37 38 39 40 57 58 59 60 A B C D E F G H I J K L M 37 38 39 40 N O P Q 57 58 60 59

2. Basic Operation Start, Merge, Split, Group

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

Rope and Net Fast! But.. N H M I O G F B L Q J
37 38 39 40 57 58 59 60 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. A B C D E F G H I J K L M 37 38 39 40 N O P Q 57 58 60 59 Fast! But..

Fewer leaf nodes : 4 sons -> 2 sons Good at higher dimensional data!

2^k branching factor for k dimension k-d tree

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

Octree Structure to store the volume element Is it possible?

Cont. Stair case 3 7 2 5 1 5 2 7 5

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

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

Cont. Intersecting two strip trees. Curve approximation. Null Clear.
Possible

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

Cont. Any questions?