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Snehal Thakkar Spatial Data Structures Hanan Samet Computer Science Department University of Maryland. Spatial Data Structures. Introduction Spatial Indexing Region Data Point Data Rectangle Data Line Data Conclusion. Introduction. Spatial Objects
Spatial Data Structures
Computer Science Department
University of Maryland
Points, Lines, Regions, Rectangles …..
Unlike conventional data sort has to be on space occupied by data
Based on recursive decomposition, similar to divide and conquer method
- Same, Higher or Lower Dimension
- Good storage purposes, queries like intersect
- Problems with queries like nearest
- Grid file, BANG file, LSD trees, Buddy trees….
- Buckets based on not the representative point, but based on actual space.
- Ideal for uniformly distributed data
- More data-independence then R+-trees
- Space decomposed on blocks on uniform size
- Higher overhead
- Space is decomposed based on data points
- Sensitive to positioning of the object
- Width of the blocks is restricted to power of two
- Good for Set-theory type operations, like composition of data.
- Break array into 1*m blocks, row representation
- Union of Maximal Square blocks
- Blocks may overlap
- Block are specified by center and radius
- Is Metal Axis Transformation
- Whose blocks are required to be disjoint
- To have standard sizes(squares whose sides are power of two)
- To be at standard locations
- Based on successive subdivision of image array into four equal size quadrants.
- Quadtree with rectangular quadrants
- Adoption of Binary Search Tree to two dimensions or more
- Useful for location based queries like where is nearest theatre from the location.
- Descending the tree till you find the node for location based queries.
- For nearest neighbor, search is continued in the neighborhood of the node containing object.
- Feature based queries tough because index is based on spatial occupancy not on features.
- Exponentially tapering stack of arrays, each one quarter size of previous
- Useful for feature based queries like where does wheat grow in California.
- Nodes that are not at maximum level of resolution contain summary information
- Three dimensional analog of quadtree
- Recursively subdivide into eight octants
- Treats image as a collection of leaf nodes, each encoded by pair of numbers
- First is base 4 number, sequence of directional codes that locates leaf from the root
- Second depth at which node is found or size
- Represents the image in form of traversal of nodes of its quadtree
- Very Compact storage, each node type can be encoded with two bits.
- Not easy to use when random access to nodes is required.
- Number of nodes in quadtree representation is O(p+q) for 2q*2q image with perimeter p measured in pixel width.
- It also holds for more dimensions.
- Regular decomposition of space into quadrants
- Organized same way as the region quadtree
- Leaf nodes are either empty or contain data point and its co-ordinates
- A quadrant contains at most one data point
- Shape of the tree is independent of the order in which points are inserted
- If points are close together then decomposition can be deep
- Can use quadrants with capacity c
- Good for search within specified distance of given record
- Each rectangle reduced to a point in higher dimension
- Made up of Cartesian product of two one dimensional intervals
- Each interval is represented by center and extent
- Set of intervals is represented by Grid File
- Grid File uses two dimensional array of grid blocks called Grid Directory
- Grid Directory has address of the bucket
- Set of linear scales is kept in the core to access grid block in the grid directory
- Guarantees access to record in two operations
- First operation to access the grid block
- Second operation to access the grid bucket
- Based on Quadtree
- Decomposition of space into rectangles
- Each rectangle is associated with a quadtree node corresponding to the smallest block which contains it in its entirety
- Subdivision stops when nodes block contains no rectangles or at predetermined size
- Rectangles can be associated with terminal and non-terminal nodes
- Based on regular decomposition of space
- Partitioning occurs as long as a block contains more than one line segment unless the line segments are incident at a vertex in the block
- Vertex-based implementation
- Useful because space requirements for polyhedral objects are smaller then conventional octree
- Edge-based variant of PM quatree
- Uses probabilistic splitting rule
- Block contains variable number of line segments
- Each line segment is inserted into all blocks that it intersects or occupies
- If block has more line segments than permitted, it is divided into four blocks once and only once
- During deletion line segment is removed from all blocks and blocks are checked for merging