Geoapplications development http://rgeo.wikience.org Higher School - PowerPoint PPT Presentation

Geoapplications development http://rgeo.wikience.org Higher School of Economics, Moscow, www.cs.hse.ru

2 Agenda

3 Binary search and DB index Index Data Index Data 1 34 2 3 2 3 3 12 3 12 5 21 4 55 1 34 5 21 4 55 Approach 1 Approach 2 (straightforward) : (optimized) : Sequential scan, O(N) Binary search, O(log N) Drawback : slow Drawback: need to maintain index

4 Intersection problem: approach 1 Approach 1 (straightforward) : for each pair (gi, gj) compute Egenhofer matrix, if it is not empty, gi and gj intersect Drawback : slow, because operation is complex

5 Intersection problem: approach 2 Approach 2 (with MBR): 1. for each geometry gi find MBR_i 2. for each (MBR_i, MBR_j) test whether they intersect ( fast ) 3. if they do, compute Egenhofer matrix, check for intersection pattern ( slower ) Significantly reduce the need to perform step 3

6 Minimum Bounding Rectangle (MBR) http://purl.oclc.org/coordinates/a2.htm 3D case – Minimum Bounding Box (MBB) https://en.wikipedia.org/wiki/Minimum_bounding_box http://www.scriptspot.com/files/u9133/tm_bbox.png https://en.wikipedia.org/wiki/Minimum_bounding_rectangle

7 Java Topology Suite: Envelope/MBR Checks package com.vividsolutions.jts.geom; public boolean crosses(Geometry g) { // short-circuit test if (! getEnvelopeInternal().intersects(g.getEnvelopeInternal())) return false ; return relate(g).isCrosses(getDimension(), g.getDimension()); } public boolean intersects(Envelope other) { if (isNull() || other.isNull()) { return false ; } return !(other. minx > maxx || other. maxx < minx || other. miny > maxy || other. maxy < miny ); }

8 PostGIS Envelope geometry ST_Envelope (geometry g1 ); Implements : • OpenGIS Simple Features Implementation Specification for SQL 1.1. • SQL/MM specification. SQL-MM 3: 5.1.15 geometry ST_MakeEnvelope (double precision xmin , double precision ymin , double precision xmax , double precision ymax , integer srid=unknown ); Example: SELECT ST_AsText(ST_Envelope('LINESTRING(0 0, 1 3)'::geometry)); POLYGON((0 0,0 3,1 3,1 0,0 0)) http://postgis.net/docs/manual-2.2/ST_Envelope.html

9 Subset problem Approach 1 (straightforward) : Compute intersection of points/geometries with rectangle Approach 2:

10 Geohash https://en.wikipedia.org/wiki/Geohash

11 Geohash: decode example, step 1 Only 5 bits are valid (2^31 = 11111) u = 26 (decimal) = 11010 (binary) c = 11 = ‭ 01011 ‭ f = 14 = ‭ 01110 ‭ t = 25 = ‭ 11001 ‭ and so on . . . the resulting sequence of bits 11010 01011 01110 11001 . . . https://en.wikipedia.org/wiki/Geohash

12 Geohash: decode example, step 2 11010 01011 01110 11001 . . . Odd bits for lat, even bits for lon (left to right): lat = 1001101010 . . . lon = 1100111101 . . . https://en.wikipedia.org/wiki/Geohash

13 Geohash: decode example, step 3 lat = 1001101010 …, lon = 1100111101 … • • 1001101010 …

14 Geohash properties: precision source

15 Geohash properties: neighborhood

16 Geohash limitations Source

17 Geohash algorithms: filter by rectangle • • source

18 Geohash algorithms: Ngram Tree Traveral 1. Determine a “good” grid cell size with minimal overlap of grid to query shape 2. Get list of overlapping grid cells <g1, g2 , …, gN> 3. For each grid cell gi: • Seek all points with geohashes with having prefix of gi gird cell • For each point decode its geohash and intersect with query shape source

19 Geohash algorithms: filter – fixed grid depth 1. Index each point at every grid level : D, DR, DRT, DRT2, DRT2Y 2. Recursive loop across top grid cells: • If cell is within query shape, simply add all assigned documents to result • If cell intersects query shape, recursive(cell.subcells) This requires careful implementation source

20 Geohash uses GeoHash Java implementations: https://github.com/kungfoo/geohash-java https://github.com/astrapi69/jgeohash https://github.com/davidmoten/geo

21 R-Tree • Query not intersecting MBR • of a given node, cannot • intersect any of the • contained geometries •

22 R-Tree: challenges • •

23 R-Tree: one more example https://en.wikipedia.org/wiki/R-tree

24 R-Tree operations: insert • • • • •

25 R*-Tree, R+Tree https://en.wikipedia.org/wiki/R%2B_tree https://en.wikipedia.org/wiki/R*_tree

26 JTS and R-Tree • •

27 PostGIS and R-Tree http://postgis.net/docs/manual-2.2/using_postgis_dbmanagement.html#gist_indexes

28 Problem: efficient read of 2D slice from disk

29 Hilbert Curve https://en.wikipedia.org/wiki/Hilbert_curve

30 Readings • https://en.wikipedia.org/wiki/Geohash • • •

31 Practical task