Spatial Data Structures for GIS Visualization. Ed Grundy

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1 Spatial Data Structures for GIS Visualization Ed Grundy

2 GIS Data Elevation maps Satellite imagery (as texture data) Other data we may wish to visualise, such as temperature, population, etc In GIS terms data sets are draped over a base (usually the elevation or satellite image)

3 Elevation data Typically from NASA SRTM shuttle mission 1201x1201 tiles ~1.5m vertices + normals Have been tiled to larger dimensions Typical methods use distance based triangulation to effect continuous level of detail

4 Texture data Large images ~8000x~9000 Multi-channel (usually we are only interested in RGB) Difficult to register onto elevation maps

5 Direct Rendering OpenGL cannot handle textures this size Requires resizing the image, causing loss of data

6 Quadtrees Data structure of choice for 2D subdivision Literature usually discusses Black and White quadtrees where the tree encodes a binary image (internal nodes are called Grey nodes) Leaf data can be approximated in internal nodes to produce discrete level of detail Nodes can be pruned if all siblings have the same data

7 Quadtrees Nodes can be rendered as fans, strips or quads Allows fine level of detail control Geometry is not tied to the tree, i.e. nodes can contain indices into a vertex array

Quadtrees Storage requirements can be large for deep trees Constant value of 4 pointers + growth rate of the tree For a 1024x1024 image with 64x64 sized nodes 43k is needed just for pointers (this is

8 Quadtrees Storage requirements can be large for deep trees Constant value of 4 pointers + growth rate of the tree For a 1024x1024 image with 64x64 sized nodes 43k is needed just for pointers (this is a small tree!) Dynamic allocation strategies often cause heap fragmentation, encouraging page faults leafcount treedepth log l log (256) 4 nodecount d 4 i 0 4 i size 4n* sizeof ( ptr) 4*337*32 ~ 43k 4

9 Linear Quadtrees Using expressions from the previous slide we can calculate the size of the tree and allocate a contiguous block of memory Two problems: How should the nodes be ordered? How do we locate a node?

10 Linear Quadtrees Depth-first ordering Nodes are stored in depth first search order Useful for recursive searching Breadth-first ordering Useful for adjacent searching (GIS problem) Nodes can be located with Location codes (similar to Huffman encoding) as described in Octrees for faster isosurface generation, Wilhelms and Van Gelder, 1992

11 Location Codes Code describes the path from the root to a leaf by storing the branch factor at each level; i.e. the code is a sequence of branch factors Quadtrees use base 4 values, octrees use base 8. Rule of thumb: base = 2^data dimensionality or 2^child count. i.e. binary trees use base 2 in Huffman encoding Location codes have many useful properties Encodes the path to all ancestors Slight modification allows us to locate siblings Further modification allows locating general neighbours Also encodes the array index when the tree is stored in a breadth first manner (

12 Location Codes Ancestor = removing least significant digit A ( q i n ) q n i Siblings = change least significant digit S { 0,1,2,3} ( qn) q i n 1 i Neighbours = performing a carry operation on the code and modifying up to a point Array index given by transforming from base 4 to base 10 Must be careful to note 0s are significant: i 0 i I( q n ) 4 q n i 1

13 Location Codes Faster than traditional tree browsing methods Complexity is linear to the length of the code, i.e. depth of the tree Codes can be constructed by dividing the unit square, removing all need for the tree representation Image co-ordinates can be retrieved from the code

Location Codes Codes are valid for different trees (as long as underlying data is aligned and subdivision methods are equal) Solves a problem of

14 Location Codes Codes are valid for different trees (as long as underlying data is aligned and subdivision methods are equal) Solves a problem of finding related data in GIS drapes i.e. find a location in the elevation data, and the code will present texture, normals, population, temperature, etc

15 Summary Linear quadtree and location codes are a fast and efficient indexing method Can be extended to higher dimensions, (usually by changing 4 to 2^n where n is the dimensionality of the data)

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CSE 554 Lecture 5: Contouring (faster)

CSE 554 Lecture 5: Contouring (faster) Fall 2016 CSE554 Contouring II Slide 1 Review Iso-contours Points where a function evaluates to be a given value (iso-value) Smooth thresholded boundaries Contouring