Geoapplications development

http://rgeo.wikience.org

Higher School of Economics, Moscow, www.cs.hse.ru

Agenda2

Binary search and DB index3

Approach 1 (straightforward): Sequential scan, O(N)Drawback: slow

Index Data

1 34

2 3

3 12

4 55

5 21

Index Data

2 3

3 12

5 21

1 34

4 55

Approach 2 (optimized): Binary search, O(log N)Drawback: need to maintain index

Intersection problem: approach 14

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

Intersection problem: approach 25

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

Minimum Bounding Rectangle (MBR)6

http://purl.oclc.org/coordinates/a2.htm

3D case – Minimum Bounding Box (MBB)

https://en.wikipedia.org/wiki/Minimum_bounding_boxhttps://en.wikipedia.org/wiki/Minimum_bounding_rectangle

http://www.scriptspot.com/files/u9133/tm_bbox.png

Java Topology Suite: Envelope/MBR Checks7

public boolean crosses(Geometry g) {// short-circuit testif (! 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);

}

package com.vividsolutions.jts.geom;

PostGIS Envelope8

http://postgis.net/docs/manual-2.2/ST_Envelope.html

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))

Subset problem9

Approach 1 (straightforward):

Compute intersection of points/geometries with the rectangle

Approach 2:

Geohash10

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

Geohash: decode example, step 111

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

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 is

11010 01011 01110 11001 . . .

Geohash: decode example, step 212

01234 56789

11010 01011 01110 11001 . . .

Odd bits for lat, even bits for lon. Q: why?

left to right:

lat = 1100111101 . . .

lon = 1001101010 . . .

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

Geohash: decode example, step 313

lat = 1100111101…, lon = 1001101010…

1100111101…

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Geohash: step 214

01234 56789

11010 01011 01110 11001 . . .

Odd bits for lat, even bits for lon. Q: why?

ANSWER:

Lon range = 2 x lon range (twice larger)

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

Geohash properties: precision15

source

Geohash properties: neighborhood16

Geohash limitations17

Source

Geohash algorithms: filter by rectangle18

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source

Geohash algorithms: Ngram Tree Traveral19

source

1. Determine a “good” grid cell size with reasonable overlap of grid to query shape

2. Get the list of overlapping grid cells <g1, g2, …, gN>3. For each grid cell gi:

• Seek all points with geohashes having prefix of gi gird cell

• For each point decode its geohash and intersect with query shape

Geohash algorithms: filter – fixed grid depth20

source

1. Index each point at every grid level :D, DR, DRT, DRT2, DRT2Y

2. Recursive loop across top grid cells:• If a cell is within the query shape, simply

add all assigned entities to the result• If a cell intersects the query shape,

recursive(cell.subcells)

This requires careful implementation

Geohash uses21

GeoHash Java implementations:https://github.com/kungfoo/geohash-javahttps://github.com/astrapi69/jgeohashhttps://github.com/davidmoten/geo

R-Tree22

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Query not intersecting MBR of a given node, cannot intersect any of the contained geometries

R-Tree: challenges23

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R-Tree: one more example24

https://en.wikipedia.org/wiki/R-tree

R-Tree operations: insert25

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R*-Tree, R+Tree26

https://en.wikipedia.org/wiki/R%2B_treehttps://en.wikipedia.org/wiki/R*_tree

JTS and R-Tree27

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PostGIS and R-Tree28

http://postgis.net/docs/manual-2.2/using_postgis_dbmanagement.html#gist_indexes

Problem: efficient read of a 2D slice from disk29

Hilbert Curve30

https://en.wikipedia.org/wiki/Hilbert_curve

Readings31

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

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Practical task32