??sa???? st? ??a?e???s?

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??sa???? st? ??a?e???s?

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Title: Spatial Databases with OGC Specifications Author: Kostas Patroumpas Last modified by: DS Created Date: 5/14/2002 11:37:06 AM Document presentation format – PowerPoint PPT presentation

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Title: ??sa???? st? ??a?e???s?

1

??sa???? st? ??a?e???s?
Ge???????? ?ed?µ????
17 Feß???a???? 2014

????? ? ???t??a ??????? ded?µ????
?a? ??????? ?e?t?????e?

3
Teµat?????a

?????? st???e?a se ß?se?? ded?µ????
???f?? a?apa??stas?? ??t?t?t??
??????? ß?se?? ded?µ????
???t??? ??????? ded?µ????
?as???? t?p?? ded?µ????
S?st?µata ?e???af???? a?af????
??????? ?e?t?????e?
???d?a??af?? OGC
??p???????? s??se??
?pe?e??as?a e??t?µ?t??
?????? e??et???a
?e??d?????a filter refinement

4
G?at? ?e???af??? ded?µ??a

??a?e???s? ?a? a????s? ?e???af???? ded?µ????
e?e???t??? ?a? p?a?t??? ped?? µe?????? s?µas?a?
80 t?? p???t???? ?a? ??????µ???? ap?f?se??
eµp?????? ?µesa ? ?µµesa ?e???af???? p????f???e?.
??????a s?µa?t???? ?a? d?µ?f???? efa?µ????
Google Maps / Google Earth
OpenStreetMap
Wikimapia
S??e??? a??a??µe??? ????? ?e???????? ded?µ????
???st?? ap? s?s?e??? GPS ? sta ????????? d??t?a
S??e??? a??a??µe?? a????? ??a s?st?µata ?a?
µe??d??? p?? ?p?st??????? t? s??????, d?a?e???s?,
epe?e??as?a, a????s?, ?a? ape?????s? ded?µ????
p?? a?af????ta? st? ???? (?a? e?de??µ????
µetaß?????ta? st? ?????)

5
GIS vs. Spatial DBMS

S?st?µata Ge???af???? ?????f???a? (GIS)
???s?µa ??a ape?????s? a????s? ???????
p????f???a?
??a??t?se?? (find location, address, )
?????s? (buffer, overlay, )
?pe?e??as?a a?a???f?? (slope, drainage network,
)
?etaß???? (proximity, change detection, )
?et??se?? (distance, area, perimeter, direction,
)
?p??e? ?a ???s?µ?p??e? ??a DBMS ?? ap????e?t???
????
S?st?µata ??????? ß?se?? ded?µ???? (SDBMS)
S??ep?? t???s? µe????? ????? ded?µ????
???s? ??????? e??et????? ??a d?e??????s?
a?a??t?se??
?e?t?st?p???s? e?t??es?? e??t?µ?t??
????? ?a?t???af??? e??a?e?a (zoom, pan,)

6
?????? ded?µ??a se ?.?.

S?es?a??? ß?se?? ded?µ????
?p?st??????? ap???? t?p??? ded?µ????, p.?.
number, varchar, date
?p?st????? ??????? ded?µ???? µp??e? ?a ???e?
ap?????, p.?. ??a s?µe?? ?? d?? a???µ??
???a ap? s?es?a??? ß?se?? ded?µ????
object oriented (OO) vs. object relational (OR)
DBMS ?p?st??????? abstract data types (ADTs)
p?? ??????ta? ap? t? ???st?, ?p?te e??a? ef??t? ?
p??s???? ??????? t?p?? ded?µ???? (p.?. polygon)

7
??????? ß?se?? ded?µ????

??a SDBMS (Spatial DBMS S?st?µa ??a?e???s??
??se?? ??????? ?ed?µ????) e??a? ????sµ??? p??
s??e????eta? µe ??a ?f?st?µe?? DBMS
?p?st????e? µ??t??a ?a? t?p??? a?apa??stas??
??????? p????f???a? (µ?s? abstract data types -
ADTs) ?a? ???sse? epe??t?se?? (p.?. SQL) p??
µp????? ?a ?a???? a?t??? t??? t?p??? ded?µ????
p??sf??e? ?p?st????? ??a e?e?d??e?µ??a e??et???a,
a??????µ??? epe?e??as?a? ??????? e??t?µ?t??,
p??sa?µ?sµ????? ?a???e? ße?t?st?p???s??
e??t?µ?t??

8
?a??de??µa

?st? µ?a ?????? ??
County boundary (d?a?e??µµ??? ?e??? ??aµµ?)
Census block - name, population, boundary
(s????e? ??aµµ??)
Water bodies (s????a p??????a)
Satellite imagery (?????a pixels)
Ta ep???µ??saµe t?? ap????e?s? se p??a?e?, ?p??
create table census_blocks (
name string,
population number,
boundary polygon )

9
??ast?se?? ?e???af???? ??t?t?t??

???e ??t?t?ta pe?????feta? ap? ??a s?????
?????sµ?t?? (?a?a?t???st???? ? ?d??t?t??), ta
?p??a p??sd???????ta? s?µf??a µe t?? efa?µ???.
p.?. se µ?a efa?µ??? ?t?µat???????, ? ??t?t?ta
?t?sµa ??e? ta ?????sµata d?e????s?, eµßad??,
?µe??µ???a ?atas?e???, ??p.
?a ?????sµata t?? ?e???af???? ??t?t?t??
ta????µ???ta? se t?e?? ?at?????e?
ta?t?t?ta
?????? d??stas?
?eµat??? d??stas?

10
??ast?se?? ?e???af???? ??t?t?t??

?a?t?t?ta
?a???e? ??a µ?s? a?af???? st?? ?e???af????
??t?t?te?.
???a? s?µa?t??? t? s?st?µa a???es?? ta?t?t?t?? ?a
e??a? a???ß??, s??ep?? ?a? ??a?? ?a e?????e? t?
µ??ad???t?ta t?? ta?t?t?t??.
?????? d??stas?
?e???af??? ??s?
?µes? ??s? (a?af??? se ??a ?a?tes?a??, p??ß?????,
?e???af??? s?st?µa)
?µµes? ??s? (d?e????s?, p.?. ?d??, a???µ??,
?.?.,)
s?et??? ??s? (p.?. ß??e?a, e?t??,)
?e?µet??a
p.?. s??µa (µ??f?), pe??µet???, eµßad??, ?????
Teµat??? d??stas?
?e???aµß??e? ??a ta ?eµat??? ? µ?-??????
?????sµata t?? ?e???af???? ??t?t?t?? (p.?. t?p??
?t?sµat??, ???µa d??a??????, ?at?????a ?d??, )

11
??apa??stas? t?? ?????

?p? t?? p?a?µat??? ??sµ? ... se ???te?

??t?t?te? Features
?????sµa Vector
??f?d?t? Raster
Ge?µet??e? Geometries
12
Teµat??? ep?peda

? ????? a?t?µet?p??eta? sa? s????? ?p??????
???e ?p??????...
f????e?e? µ?a ?at?????a ded?µ???? ?a?
d?af???p??e?ta? ap? t??? ?????? µe ß?s? t? ??µa

13
???t??? ??f?d?t?? (Raster)

?at?tµ?s? t?? ????? se ??f?de?
St???e??de??, µ? ep??a??pt?µe?e? pe??????
???e ??f?da (?e??) ?a?a?t????eta? µ???s?µa?ta ap?
??a ?eµat??? ?a?a?t???st??? (p.?. ???s? ???)
??f?de? 2, 3 ? p???ap??? d?ast?se??
S??µa ?a? µ??e??? ??f?d??
?a?????? (?.?. grid) ??a????st?
(p.?. TIN)

14
???????a ?at? Thiessen

???sµ?? ?st? s????? S ap? ? s?µe?a st? ep?ped?.
??te?ta? ? ?at?tµ?s? t?? ????? se ? p??????a.
???e p??????? ?a pe????e?e? ??a s?µe?? t?? S ?a?
??e? t?? ??se?? t?? ????? p?? ß??s???ta? p??
???t? st? s?µe?? a?t? ap? ?p???d?p?te ???? s?µe??
t?? s??????.
?a??de??µa ?a????sµ?? ????? p?? e??p??et??? 10
s???e?a ? ???t?a ??e?a? (???t???? e??p???t?s?? ?
e???t?ta)

15
??a??sµat??? µ??t??? (Vector)

S?????? ap? d?a??sµat???? ??t?t?te?
???e ??t?t?ta a?apa??stata? ap? ?e?µet??a
???a??? s???de?eta? ap? ?eµat???? ?d??t?te?
?e?t??µ??e? ep?d?se?? st?? epe?e??as?a t??
st???e???
???f?? ?e?µet????
S?µe?o (point)
??????aµµ? (polyline)
?p?f??e?a (surface)

16
?????? st???e?a se ß?se?? ded?µ????

??e??e?t?µata
??a?e???s? µe????? ????? ded?µ????
?????? s?s??t?s? µe pe????af??? ded?µ??a
???a??sµ?? asf??e?a? ?a? t???s?? t?? st???e???
?e?t???? ?p?st????? p???ap??? efa?µ????
?µ????e??? t??p?? ap????e?s?? ?a? p??sp??as??
st???e???
?e?t??µ??e? ep?d?se?? st?? epe?e??as?a t??
st???e???
??s????e?
?s?te???? a?apa??stas? ?e?µet??a?
??a?e???s? ???????? e??????? t?? st???e???
Stad?a?? s?ss??e?s? ????? ded?µ???? (Terabytes)

17
?????? st???e?a se ß?se?? ded?µ????

?a?????te? ??a t???s? ??????? st???e??? se ß.d.
???µ???s? ????? ded?µ???? ap? p???ap??? p????
apa?t?se?? s???????? efa?µ???? ??ad??t??
a???p?ste? d?µ?? ?a? µ???d?? p??sp??as??
ded?µ????
asf??e?a, a??e?t???t?ta, s???pe?a s?st?µ?t?? ß.d.
???at?t?te? ???p???s??
S?es?a?? µ??t???
p??a?e? ??a t???s? s??teta?µ???? s?µe???, ??aµµ??
??p.
p??ß??µat??? de??t?d?t?s?, epe?e??as?a e??t?µ?t??
??t??e?µe??st?ef?? µ??t???
af???µ???? t?p?? ded?µ???? (ADT) ??a ???????
??t?t?te?
e???????s? (encapsulation) d?epaf?
(interface)
a????? e??e???? ?p?st?????? ?e?µet?????
a??????µ?? e?d???? d?µ?? e??et????? e?t?? t??
s?st?µat?? ß.d.

18
?????? st???e?a se ß?se?? ded?µ????

?µp????? s?st?µata µe ??????? epe?t?se??
Oracle Spatial
IBM DB2 Spatial Extender Geodetic Management
Feature
IBM Informix Spatial DataBlade Geodetic
DataBlade
Microsoft SQL Server
ESRI ArcSDE middleware ? ArcGIS Server
ap????e?s? st???e??? se Oracle, PostgreSQL, IBM
DB2, Informix, MS-SQL Server, ?.?. ??a ???s? ap?
ESRI ArcGIS
S?st?µata a????t?? ??d??a (e?e??e?? ????sµ???)
PostgreSQL
PostGIS (ep??tas? t?? PostgreSQL)
MySQL

19
Teµat?????a

?????? st???e?a se ß?se?? ded?µ????
???f?? a?apa??stas?? ??t?t?t??
??????? ß?se?? ded?µ????
???t??? ??????? ded?µ????
?as???? t?p?? ded?µ????
S?st?µata ?e???af???? a?af????
??????? ?e?t?????e?
???d?a??af?? OGC
??p???????? s??se??
?pe?e??as?a e??t?µ?t??
?????? e??et???a
?e??d?????a filter refinement

20
??t??e?µe??st?ef?? µ??t??? OGC

Ge?µet????? t?p?? ded?µ????
?e?µet??a GEOMETRY
s?µe?? POINT
?aµp??? CURVE
??aµµ? LINESTRING
ep?f??e?a SURFACE
p??????? POLYGON
s???eta s??µata
p???s?µe?? MULTIPOINT
p?????aµµ? MULTILINESTRING
s???et? ?aµp??? MULTICURVE
s???et? p??????? MULTIPOLYGON
s???et? ep?f??e?a MULTISURFACE
s?????? ?e?µet???? GEOMETRYCOLLECTION
???t?te se s?st?µa a?af???? (SPATIAL REFERENCE
SYSTEM)

21
?e?a???a ?e?µet????? s??µ?t?? OGC

Instantiable
Non instantiable

22
???t??? ded?µ???? Oracle Spatial

???ta?????? ?e?µet????? t?p??

23
???d?a??af?? ?e?µet???? ?at? OGC

???d?a??af?? ap??? s??µ?t??
(OGC Simple Feature Specification
for SQL, 1999)
??a s????? ?e?µet????? t?p?? ded?µ???? ßas?sµ????
st? ?e?µet???? µ??t??? t?? OGC
?e?t?????e? SQL ep? t?t???? t?p?? ded?µ????
(µ???d??, a?a??t???? s??a?t?se??, t?p????????
te?est??)
? ???? s??µa (feature) ?p?d????e? ??a ??????
a?t??e?µe?? st?? p?a?µat??? ??sµ? µ?a d?a???t?
??t?t?ta
Ge?µet???? µ??t??? ded?µ????
?a??pte? a?t??e?µe?a ? 2 d?ast?se??
µeta?? ????f?? e??? s??µat?? ?s??e? ??aµµ???
pa?eµß???

24
???t??? ded?µ????

?e?a????? d?µ? ?e???af???? ded?µ????
ep?ped? (?.?. ?????)
?e?µet??a (?.?. ????S ??????O?)
st???e?? (?.?. ????S)

25
???t??? ded?µ????

St???e?? (Element)
?? s??teta?µ??e? ???e st???e??? ?? ?e??? ltX,Ygt
p??a??? p???ap?? st???e?a st?? ?d?a ?e?µet????
??t?t?ta
?as??? d?µ??? µ???da t?? ?e?µet??a?
s?µe?? ??a ?e???? s??teta?µ????
p?????aµµ? a???????a e??????µµ?? tµ?µ?t??
p??????? ???e a?µ? t?? p???????? ????eta? ap t?
?e???? t?? a?t?st????? ????f??
?? s??teta?µ??e?
?ata??????ta? d?ateta?µ??e?
???? ap? t? p???????
d?af??et??? d??ta??
??a t?? es?te???? ?a?
t?? e??te???? da?t????

26
???t??? ded?µ????

Ge?µet??a (Geometry)
? a?apa??stas? t?? s??µat?? µ?a? ???????
??t?t?ta? se ??a s?st?µa s??teta?µ????
d?ateta?µ??? a???????a ap? p??ta????? st???e?a
??a??a?t???? µ??f?? ?e?µet??a?
??a µ??? st???e??
st??µ??t?p? e??? ap t??? p??ta???????
?e?µet?????? t?p??? ?p?? POINT, LINE, POLYGON
?.?.
?µ????e??? s?????? st???e???
?.?. MULTIPOLYGON ??a s?st?da ??s???
ete???e??? s?????? st???e???
?.?. COLLECTION ??a p??????a ?a? ta ?e?t??e?d?
t???

27
???t??? ded?µ????

Teµat??? ep?ped? (Layer)
ete???e??? s?????? ?e?µet????? ??t?t?t?? µe t?
?d?? s????? ?????sµ?t?? (attributes)
ta ?e?µet???? st???e?a ?a? ta s?et??? ??????
e??et???a ap????e???ta? e?t?? t?? ß.d.
????ap?? ep?peda µp????? ?a a??e?ep?d???? µeta??
t??? ?a? ?a s??µat????? ??a? ???t?
???sµ?? µetaded?µ???? (p.?. s?st?µa ?e?a?af????)
?a??de??µa
??µ??
???µ??
???e??

28
???t??? ded?µ????

????? (Tolerance)
e?t?µ?s? t?? a???ße?a? ? t??
????t?ta? t?? ??????? ded?µ????
?? ? ap?stas? d?? s?µe??? e??a?
µ????te?? ap? t?? t?µ? t?? a?????,
ta s?µe?a ?e??e?ta? ?t? ta?t????ta?
Oracle Spatial ???s? pa?aµ?t??? a?????
se ??????? s??a?t?se?? ?a? te?est?? ?at? t??
d?at?p?s? e??t?µ?t??
sta µetaded?µ??a t?? ??????? ep?p?d?? (a? e??a?
e?a???? ???st?)
??a ?e?da?t??? ded?µ??a e?f???eta? st??
a?t?st???? µ???da µ?t??s?? (p.?. se µ?t?a)

29
S?st?µa Ge?a?af????

Spatial/Coordinate Reference Systems (CRS)
?e????af? ??s?? ?e???af???? ??t?t?t??
??e???? s?s?et?se?? µeta?? ??t?t?t?? (?.?. t?µ?)
??????a s?st?µata a?af????
?a?tes?a??? s??teta?µ??e? st? ep?ped?
Ge?da?t???? (?e???af????) s??teta?µ??e?
?.?. s?st?µa WGS84 (s??teta?µ??e? se lat/lon)
???ß????? s?st?µa a?af????
?.?. ?GS?87 (s??teta?µ??e? se µ?t?a)
??p??? s?st?µa a?af????
p.?. se CAD efa?µ????
??d??? s?st?µa a?af???? ???sµ??? ap? t?? ???st?
???at?t?ta a??a??? ?e?a?af???? ??a ???????a
ep?peda ? µeµ???µ??e? ??t?t?te?

30
S?st?µa Ge?a?af????

S?st?µa s??teta?µ????
???sd?????e? ??se?? ?? p??? t?? a??? t?? a?????
Ge??e?t???? (x,y,z ?? ap?st?se??)
Ge?da?t??? (lat/lon ?? ????e?)
?a?tes?a?? (??a µ?????, s?ed?? ep?pede?
ep?f??e?e?)
???e???e?d??
???se????e? t? ???t??
?a? t? s??µa t?? G??
Datum Ge?a?af???
T?s? e??e???e?d???
?? p??? t? ???t?? t?? G??
?p?t??pe? µ?t??s? ap?st?se??
???ß???
?p? t?? ???t? ep?f??e?a st? ep?ped?

31
S?st?µa Ge?a?af????

??af??et??? a?apa??stas? ?d??? ??t?t?t??
?at?????? EPSG
WGS84 (EPSG4326) ?GS?87 (EPSG2100)

32
Teµat?????a

?????? st???e?a se ß?se?? ded?µ????
???f?? a?apa??stas?? ??t?t?t??
??????? ß?se?? ded?µ????
???t??? ??????? ded?µ????
?as???? t?p?? ded?µ????
S?st?µata ?e???af???? a?af????
??????? ?e?t?????e?
???d?a??af?? OGC
??p???????? s??se??
?pe?e??as?a e??t?µ?t??
?????? e??et???a
?e??d?????a filter refinement

33
SQL µe ?e?µet?????? t?p???

?p?st????? s?st?µ?t?? a?af????
??????ta? se e?d??? p??a?a t?? ß.d.
(SPATIAL_REF_SYS)
???e ?e?µ. s??µa ??e? ?e?a?af??? se ??p???
s?st?µa
?p?st????? ßas???? ?e?µet????? t?p?? OGC
??p??a s?st?µata ß.d. µp??e? ?a ???p?????
?p?s????? t???
????????ste? a?apa?ast?se?? ?e?µet????
Well-Known Binary (WKB) se d?ad??? µ??f?
Well-Known Text (WKT) se µ??f? ?e?µ????
??d???? ?e?t?????e? ??a
d?µ??????a ?e?µet????? s??µ?t?? (?.?.
GeomFromText)
d?e??????s? a?ta??a??? ded?µ???? (?.?. AsText,
AsGml)

34
Ge?µet??e? se µ??f? ?e?µ???? SQL

?p?? s??µata
S?µe??
'POINT(3 7)'
?p?? s?µe?? st? ep?ped?

35
Ge?µet??e? se µ??f? ?e?µ???? SQL

?p?? s??µata
S?µe??
'POINT(3 7)'
????s?µe??
'MULTIPOINT(3 7, 4 2, 8 6)'
S?????? 2-d??stat?? s?µe???

36
Ge?µet??e? se µ??f? ?e?µ???? SQL

?p?? s??µata
S?µe??
'POINT(3 7)'
????s?µe??
'MULTIPOINT(3 7, 4 2, 8 6)'
G?aµµ?
'LINESTRING(1 2, 3 6, 9 4)'
????????a 2-d??stat?? s?µe???

37
Ge?µet??e? se µ??f? ?e?µ???? SQL

?p?? s??µata
S?µe??
'POINT(3 7)'
????s?µe??
'MULTIPOINT(3 7, 4 2, 8 6)'
G?aµµ?
'LINESTRING(1 2, 3 6, 9 4)'
??????aµµ?
'MULTILINESTRING((1 8, 4 4),(4 9, 8 5, 6 2, 1
4))'
????eta? ap? p???ap??? a?t?te?e?? ??aµµ??
e?de??µ???? de? ?p???e? s???fe?a µeta?? ep?µ?????
??aµµ??

38
Ge?µet??e? se µ??f? ?e?µ???? SQL

?p?? s??µata
S?µe??
'POINT(3 7)'
????s?µe??
'MULTIPOINT(3 7, 4 2, 8 6)'
G?aµµ?
'LINESTRING(1 2, 3 6, 9 4)'
??????aµµ?
'MULTILINESTRING((1 8, 4 4),(4 9, 8 5, 6 2, 1
4))'
????????
'POLYGON((1 2, 6 1, 9 3, 8 5, 3 6, 1 2))'
????eta? ap? ??a? ??e?st? e??te???? da?t????
e?de??µ???? pe???aµß??e? es?te?????? da?t??????
(?p??)

39
Ge?µet??e? se µ??f? ?e?µ???? SQL

S???ete? ?e?µet??e?
???????? µe ?p??
'POLYGON(
(1 2, 6 1, 9 3, 8 5, 3 6, 1 2),
(3 3, 5 5, 6 2, 3 3))'
???S??? st?? f??? t?? a???????a? s??teta?µ????
a?????????a?? (counter-clockwise) ??a t??
e??te???? da?t????
???????a?? (clockwise) ??a es?te?????? da?t??????
?? es?te???? t?? p???????? ß??s?eta? p??t?te
a??ste?? ???e da?t????? (es?te????? ? e??te?????)

40
Ge?µet??e? se µ??f? ?e?µ???? SQL

S???ete? ?e?µet??e?
S???et? p???????
'MULTIPOLYGON(
((1 2, 6 1, 9 3, 3 6, 1 2)),
((4 9, 7 6, 9 8, 4 9)))'
S?????? ap? µ? s??e??µe?e? p?????????? ep?f??e?e?
?e? ep?t??p??ta? t?µ?? µeta?? ep?µ????? p????????
?µ?? ta p??????a µp??e? ?a ef?pt??ta?
???????? µp??e? ?a ???ste? e?t?? ?p?? ?????
p????????

41
Ge?µet??e? se µ??f? ?e?µ???? SQL

S???ete? ?e?µet??e?
S?????? ete???e??? s??µ?t??
??a t???s? p??????? st???e???
s?µe?a
??aµµ??
p??????a ?.?.
... ?? e??a?a ??t?t?ta
µe t?? ?d?a ?e?a?af???
?a??de??µa
'GEOMETRYCOLLECTION(
POINT(4 5), POINT(7 4), POINT(6 2),
LINESTRING(4 5, 6 7, 7 4, 6 2),
POLYGON((1 2, 6 1, 9 3, 8 5, 3 6, 1 2)))'

42
?as???? µ???d??

???sd???????? ?d??t?te? µ?a? ?e?µet??a?
Dimension(g) gt d?ast?se?? (ßa?µ??) s??µat??
(0 s?µe?a, 1
??aµµ??, 2 ep?f??e?e?)
GeometryType(g) gt t?p?? ?e?µet??a? (?.?.
LINESTRING)
SRID(g) gt s?st?µa ?e?a?af????
Envelope(g) gt e????st? pe??ß????? ?????????
(MBR)
AsText(g) gt ?e?µet??a se µ??f? ?e?µ????
AsBinary(g) gt ?e?µet??a se d?ad???
a?apa??stas?
IsEmpty(g) gt ??e???? ??a ?e?? ?e?µet??a
Boundary(g) gt pe????aµµa ?e?µet??a?

43
?e?t?????e? ??????? a????s??

?p?????sµ?? ß?se? ?e?µet????
Distance(a,b) gt µ????te?? ap?stas? µeta??
s??µ?t??
Length(g) gt µ???? ??aµµ?? / pe??µet???
da?t?????
Area(g) gt eµßad?? ep?f??e?a?
Intersection(a,b) gt t?µ? ?e?µet???? (a AND b)
Union(a,b) gt ???s? ?e?µet???? (a OR b)
Difference(a,b) gt d?af??? ?e?µet???? (a AND
(NOT b))
SymDifference(a,b) gt s?µµet???? d?af??? (a XOR
b)
Centroid(g) gt ?e?t??e?d?? ?e?µet??a?
Buffer(g,d) gt ???? ep?????? p????? d
ConvexHull(g) gt ???t? pe??ß??µa
?e?µet??a?
?? pe??ss?te?e? ep?st??f??? ??a ?e?µet????
s??µata
...e?t?? ap t?? s??a?t?se?? Distance, Length,
Area
???sµ??e? efa?µ????ta? se ?e??? ?e?µet?????
s??µ?t??

44
??????? s?s?et?se??

???????? s?s?et?se?? µeta?? ??t?t?t??
ß?se? t?? ??se?? t??? st?? ????
??p?? s?s?et?se??
??p????????
Ge?t??as?
?p???????
??µ? ...
??a?????te? se µetas??µat?sµ??? (?.?. st??f?)
?ate????t????
???e?a, a?at?????, ... ap? ...
????, p?s?, de???, ... ap? ...
?et??t????
???t? se...
?a???? ap? ...

45
??p???????? te?est??

???t??? Egenhofer
EQUAL DISJOINT
COVERED BY COVER
MEET OVERLAP
INSIDE CONTAIN

46
??p???????? te?est?? OGC

??e???? ??????? s??se?? µeta?? s??µ?t?? -gt
TRUE/FALSE
EQUALS ?????? ?s?t?ta
DISJOINT ?e?µet??e? ???e? µeta?? t???
INTERSECTS t?µ?e?
TOUCHES ef?pteta?
CROSSES d?asta????e?
WITHIN ?e?ta? e?t??
CONTAINS pe????e?e?
OVERLAPS ep??a??pte?
RELATE s?et??eta?
?a?at???ste t?? ?s?d??aµ?e?
DISJOINT(a,b) ? NOT INTERSECTS(a,b)
WITHIN(a,b) ? CONTAINS(b,a)
? te?est?? RELATE s???de?eta? ap? µ?t?ß? t??
s?s??t?s??
p.?. OVERLAPS s?µf??a µe t? 9-intersection model

47
?p??p???µ??? µ??t??? 9-t?µ??

???a?a? 3?3 ??a t?p??????? ??e???
pe????aµµa (boundary, ?A)
es?te???? (interior , Ao )
e??te???? (exterior, A )
?a?ade??µata t?t???? ?p???af?? (1TRUE /
0FALSE)
TOUCHES WITHIN
OVERLAPS
A B A B
A B

48
?????µ??? µ??t??? 9-t?µ?? (DE-9IM)

???a?a? 3?3 µe d??f??e? t?µ??
d?ast?se?? t?µ?? 0, 1, 2
?pa??? t?µ?? T 0,1,2, F
ad??f???
Yp???af?? p???????? a?a????? t?? ?e?µet????
CONTAINS CROSSES
OVERLAPS
A B A B
A B

49
Teµat?????a

?????? st???e?a se ß?se?? ded?µ????
???f?? a?apa??stas?? ??t?t?t??
??????? ß?se?? ded?µ????
???t??? ??????? ded?µ????
?as???? t?p?? ded?µ????
S?st?µata ?e???af???? a?af????
??????? ?e?t?????e?
???d?a??af?? OGC
??p???????? s??se??
?pe?e??as?a e??t?µ?t??
?????? e??et???a
?e??d?????a filter refinement

50
?a?ade??µata ??????? ???t?µ?t??

???t?µa ??e? ???µa, p????sµ? ?a? eµßad?? ???e
???a? t?? p??a?a Country.
SELECT C.Name, C.Pop, Area(C.Shape)
FROM Country C

51
?a?ade??µata ??????? ???t?µ?t??

???t?µa ??e? ta ???µata ???? t?? ????? p?? e??a?
?e?t??e? t?? ???.
SELECT C1.Name
FROM Country C1, Country
C2 WHERE
Touch(C1.Shape, C2.Shape) 1 AND C2.Name
USA

52
?a?ade??µata ??????? ???t?µ?t??

???t?µa G?a ??a ta p?t?µ?a st?? p??a?a River,
ß?e? t?? ???e? ap? t?? ?p??e? pe????e.
SELECT R.Name, C.Name
FROM River R, Country C
WHERE Cross(R.Shape,
C.Shape) 1

53
?a?ade??µata ??????? ???t?µ?t??

???t?µa ?? p?t?µ? St. Lawrence µp??e? ?a
p??µ??e?e? µe ?e?? p??e?? se ap?stas? 300 ??µ.
??e?te t?? p??e?? a?t??.
SELECT C.Name
FROM City C, River R
WHERE
Overlap(C.Shape, Buffer(R.Shape, 300)) 1 AND
R.Name St.Lawrence

54
?a?ade??µata ??????? ???t?µ?t??

???t?µa ??af??ate t?? ???e?, ta????µ?µ??e? a??
p????? ?e?t?????? ?????
SELECT C.Name, Count(?.Name)
FROM Country C, Country ?
WHERE Touch(C.Shape, ?.Shape)
GROUP BY C.Name
ORDER BY
Count(?.Name)

55
?e??t?d?t?s? ??????? ded?µ????

??????? de??te? ? e??et???a (spatial indices)
µ??a??sµ?? ??a e??tt?s? t?? a?a??t?se??
ßas?sµ???? se ?????? ???t???a
p.?. p????t?ta, ep??????? ?.?. ?e?µet?????
??t?t?t??
???s?µ?t?ta se e??t?µata
pa?a????? (range) ?????? s??des? (spatial
join)

56
?e??t?d?t?s? ??????? ded?µ????

R-d??d?a
????a d?µ? de??t?d?t?s??
?e?a????? ?p?d?a??es?
t?? ded?µ????
se ???t???? s?st?de?
?et?ad??? d??d?a (quadtrees)
e?a??a?t??? d?µ? e??et?????
?e?a????? ?p?d?a??es?
t?? ????? se teta?t?µ???a
??a?es?µ?t?ta d?µ??
? ep????? e??et????? e?a?t?ta? ap? t? e?d?? t??
epe?e??as?a?

57
?e??t?d?t?s? ??????? ded?µ????

?a?a?t???st??? R-d??d???
p??s????s? t?? ?e?µet??a? a?t??e?µ????
p???ap??? d?ast?se??
µe e????sta pe??ß?????ta pa?a???????aµµa (MBR)
ta??te?? e?t??es? p????µ???? e??t?µ?t??
e???te??? ?e?t??a (te?est?? SDO_NN) ?a?
e?t?? ap?st?se?? (te?est?? SDO_WITHIN_DISTANCE)
d?s???e?a a?ap??sa?µ???? ?ta? s?µßa????? s?????
e??µe??se?? (updates) st?? ?e?µet??a t?? st???e???

58
?e??t?d?t?s? ??????? ded?µ????

?a?a?t???st??? tet?ad???? d??d??? (quadtrees)
efa?µ????ta? ?????? ??a a?t??e?µe?a 2 d?ast?se??
?ept?µe??? p??s????s? t?? ?e?µet??a?
µe ?at?????? ???µ?s? pa?aµ?t???
(tiling level, number of tiles)
a??? e?t??es? e??t?µ?t??
e???te??? ?e?t??a (SDO_NN)
ep??e????ta? e????sta ap? s?????
a??a??? st?? ?e?µet??a (updates)

59
?e??t?d?t?s? ded?µ????

??µ??????a ??????? ?a???ß?? (spatial grid)
...ß?se? t?? MBR µ?a? ?e?µet????? ??t?t?ta?
?µ????e??? ?at?tµ?s? t?? ?????
se ?????? tet?????a (?e???)
sta?e??? µe??????
?? e??et???? ap????e?e?
t?? t?µ?? t?? ?e???? µe ta MBR
t?? ??d??? t?? ??t?t?ta?
?e?a????? ???p???s? ?a???ß??
????? 3 ep?peda µe ???? µe????? st???e??d???
?e????
??t??e?µe?a d?af??et???? µe??????
de??t?d?t???ta? se d?af??et??? ep?peda
???p???t?s? e??t?µ?t?? ??a p??????? µe??????
ded?µ??a

60
?pe?e??as?a e??t?µ?t??

??? ßa?µ?de? epe?e??as?a? (two-tier query model)
???te??? f??t?? (filter) ß?se? t?? e??et?????
??????? ep????? ?pe?s?????? µe ?p???f?e?
apa?t?se??
µ??? a?t? ta st???e?a ?a e?e?????? µe t?
de?te?e??? f??t??
?e?te?e??? f??t?? (refinement)
a???ße?? ?e?µet????? ?p?????sµ?? µe ????????
te?est??
efa?µ??eta? µ??? ??a t?? ?e?µet????? ??t?t?te?
p?? ?aµß????ta? ap? t? p??te??? f??t??
? s??d?asµ?? t?? d?? ßa?µ?d?? te???? ep?st??fe?
a???ße?? apa?t?se??

refinement
filtering
?p???f?e? apa?t?se??
??????? ??t?t?te?
????ße?? apa?t?se??
61
?pe?e??as?a e??t?µ?t??

?a??de??µa a?a??t?s?? µe tet?ad??? d??d??

filtering
refinement
62

????? ? ???ß??µata e??es?? ß??t?st?? d?ad??µ??
se ?d??? d??t?a

63
Teµat?????a

??as???? a??????µ?? e??es?? s??t?µ?te???
d?ad??µ??
DIJKSTRA
Bi-Directional DIJKSTRA
A
????????µ???? p??a?e? ap?st?se??
?????µ??e? ?e??????
Contraction Hierarchies
Transit-Node Routing
A Landmarks
Edge Labels
S?????se??
?pe?t?se??

64
??????s? se ?d??? d??t?a
65
???es? s??t?µ?te??? d?ad??µ??

?? ?d??? d??t?? a?apa??stata? ap? ??a?
?ate?????µe?? ???f?
G (V,E)
??µß?? a?apa??st??? sta???d??µ?a
??µ?? a?apa??st??? ?d??? tµ?µata
???? st?? a?µ?? a?apa??st??? t? ????? (?
?e????te?a ??st??) p?? ??e???eta? ??a ?a
d?a??s??µe t? ?d??? tµ?µa
???es? s??t?µ?te??? ?d???? d?ad??µ??
a?a??t?s? t?? s??t?µ?te???
µ???pat??? st? ???f?

66
???es? s??t?µ?te??? d?ad??µ??
67
???????µ??

???s? ??as???? µe??d?? a?a??t?s?? se ???f?
Dijkstra
?µf?d??µ?? Dijsktra
?
????????µ???? p??a?e? ap?st?se??

68
???????µ?? DIJKSTRA

??????
? e?a??t????? ??µß?? e??a? e?e????, µe ap?stas? 0
? ap?stas? ??a t??? ?p????p??? ??µß??? e??a? 8
Se ???e epa??????
?p?????se t?? ap?st?se?? t?? ?e?t?????? ??µß??
t?? e?e???? ??µß??
??p???t?se t?? e?e??? ??µß? st? s????? t?? ??µß??
p?? ????µe ep?s?ef?e?
?e?µ?t?se a? ????µe ep?s?ef?e? t?? te?µat???
??µß?
??e???? ??µß?? ???eta? ? ??µß?? p?? de? ????µe
ep?s?ef?e? ?a? ??e? t? µ????te?? ap?stas?

69
?µf?d??µ?? a??????µ?? DIJKSTRA

??? ta?t?????e? a?a??t?se??
???e?a a?a??t?s? ap? t?? e?a??t???? ??µß?
??t?st??f? a?a??t?s? ap? t?? te?µat??? ??µß?
?e?µat??e? ?ta? ?? d?? a?a??t?se?? s??a?t?????
???s?µ?p??e?ta? ap? p??????µ??e? te??????

70
???????µ?? A

?? s??t?µ?te?e? d?ad??µ?? s?????? ?d????? p???
t?? ?ate????s? t?? st????
? a??????µ?? ?
???p?p??e? t? ß???? ???e a?µ?? w(u,v)
w(u, v) - p(u) p(v)
p(v) e??a? ??a ??t?tat? ???? t?? ap?stas??
a??µesa st?? ??µß? v ?a? t?? te?µat??? ??µß?
?a ???a ??a t?? ap?st?se?? µp????? ?a
?p?????st??? µe ß?s? e????de?e? ap?st?se??

71
????? a?a??t?s??

DIJSKTRA
Bidirectional DIJSKTRA
A

72
????????µ???? p??a?a? ap?st?se??

???-?p?????sµ?? e????st?? d?ad??µ?? ??a ???e
?e???? ??µß?? st? d??t??
?p????e?s? t?µ?? se p??a?a
?a e??t?µata e??es?? e????st?? d?ad??µ??
apa?t??ta? µe µ?a a?a??t?s? st?? p??a?a
?p?t?ept??? µ??e??? ?d???? d??t???
??e???eta? ?a ep??????µe ta s?µa?t??? ?e???

73
??a?t??? p??ß??µata

???e??? ?d???? d??t???
???t?? ??t???? ????p??
18.000.000 ??µß??
??as???? µ???d?? a?a??t?s?? de? µp????? ?a
???s?µ?p??????? p?a?t???
??µet???e?s? st???e??? t?? p??ß??µat??
??µ? t?? ?d???? d??t???
?e?a?????
S?ed?? ep?ped? (planar)
???-epe?e??as?a ded?µ????
St????
?a?e?a ap????s? se e??t?µata
?aµ???? ????? ap????e?µ???? ded?µ????

74
Teµat?????a

??as???? a??????µ?? e??es?? s??t?µ?te???
d?ad??µ??
DIJKSTRA
Bi-Directional DIJKSTRA
A
????????µ???? p??a?e? ap?st?se??
?????µ??e? ?e??????
Contraction Hierarchies
Transit-Node Routing
A Landmarks
Edge Labels
S?????se??
?pe?t?se??

75
Contraction Hierarchies

???-epe?e??as?a ?
?a????µ?s? t?? ??µß?? t?? d??t???
µe ß?s? t? sp??da??t?t? t???
???t???a sp??da??t?ta?
??se? a?µ?? ?a p??pe? ?a p??ste???? st???
?p????p??? ??µß??? ??a ?a d?at??????? ??
e????ste? ap?st?se?? st? ???f?
??s?? ??µß?? ????? ?d? afa??e?e? ap? t?
s???e???µ??? pe????? t?? ??af?µat??
S??d?asµ?? ???t?????

76
Contraction Hierarchies

???-epe?e??as?a ??
?? ??µß?? afa?????ta? ap? t? ???f? a????????ta?
t?? ta????µ?s?
?ta? ??a? ??µß?? afa??e?ta?
??at???s? s??t?µ?te??? d?ad??µ?? a??µesa se
?e?t??????? ??µß???
???s???? ?at??????? a?µ??
??t?? ???µ????ta? s??t?µe?se??

77
Contraction Hierarchies
5
3
7
3
4
S?µas?a
78
Contraction Hierarchies

??a??t?s?
?µf?d??µ?? a??????µ?? Dijkstra st??
?????? ???f?
?e t?? p??s???? t?? s??t?µe?se??
? a?a??t?s? p??????e? ap???e?st??? se ??µß???
a????sa? s?µas?a?
?e?µat?sµ?? ?ta? s??a?t????? st?? p??
s?µa?t??? ??µß? st? µ???p?t?

79
Transit Nodes

?a ß??t?sta µa????? µ???p?t?a s?????? pe?????
ap? ??a? pe?????sµ??? a???µ? ??µß??

80
Transit Nodes

???-epe?e??as?a
??e??es? transit nodes
G?a ???e ??µß? st? ???f?µa
???-?p?????sµ?? ap?stas?? ??a ???e ??a?
???t??? transit node
???-?p?????sµ?? ap?stas?? a??µesa se ???e ?e????
ap? transit nodes

81
Transit Nodes

???t?µata
G?a ??µß??? u,v
?e set ap? ???t????? transit nodes
Tu ?a? Tv a?t?st???a
??e? t? ?e???? tu ap? t? Tu ?a? tv ap? t? Tv
p?? e?a??st?p??e? t?? ap?stas?
d(u, tu) d(tu,tv) d(tv,v)

82
Transit Nodes

??e? ?? ap?st?se?? p?? ??e?????ta? ?????
p??-?p?????ste?
?? ???t???? transit nodes de? e??a? p?????
?e??aµat??? pe??p?? 10 ??a US Network
???? ??????e? ap????se?? se e??t?µata (µs)
?e????? ?????? p??-epe?e??as?a? ?a? ?????
ap????e?µ???? ded?µ????
???t??? e??t?µata
?e?a???a ap? transit nodes

83
A Landmarks

????e?d?e? s??teta?µ??e? st?? a??????µ? ? de?
e??a? ? ß??t?st? ep?????
???s? ??µß?? t?? d??t??? ?? Landmarks
???-?p?????sµ?? ap?st?se?? ??a ???e ?e???? ??µß??
?a? Landmark
???s? t?? t????????? a??s?t?ta? ??a ?p?????sµ?
????? t?? ap?stas?? a??µesa se ??µß???
S?????? ep??????ta? pe??p?? 20 Landmarks
?p????? Landmarks ?ata?eµ?µ???? st? ?d??? d??t??

84
A Landmarks

???s? t????????? a??s?t?ta?
dist(u, v) dist(u, w) dist(w, v)
??a ???e ??µß? u, v, w
????st??? t?µ?
h(u)max(dist(u,l)dist(t,l),dist(l,t)dist(l,u))
h(u) dist(u,t)
?p????? Landmark l p?? µe??st?p??e? t? h(u)

85
A Landmarks
Vertices visited by Dijkstras algorithm (left),
A search with Manhattan lower bounds (middle),
and ALT algorithm (right)
86
Edge Labels

???epe?e??as?a
G?a ???e a?µ? e p??-?p??????eta? t? s????? M(e)
t?? ??µß?? p?? ß??s???ta? se ??a s??t?µ?te??
µ???p?t? p?? ?e????e? µe t?? a?µ? e
??a??t?s?
?????????µe µ?a a?µ? e µ??? a? ? te?µat????
??µß?? pe????eta? st? M(e)

87
Edge Labels

?p?t????s? t?? p??-epe?e??as?a?, µe??s? ?????
ap????e?s??
?????eta? t? d??t?? se k pe??????
?? pe?????? a?t?? ????? a?t?st???a µe???? ?a?
µ???? a???µ? ??µß?? sta s????? t???
?? M(e) a?apa??st?ta? sa? k-vector ap? edge flags
G?a t?? ?p?????sµ? ??e???eta? µ??? ??a e??t?µa
ap? ????? t??? ??µß??? p?? ß??s???ta? sta s????a
t?? pe??????

88
Edge Labels
89
S??d?asµ?? te??????

?????? ap? t?? µe??d??? p?? a?af??aµe µp????? ?a
s??d?ast???
? aµf?d??µ? e?d??? t?? Dijkstra ???s?µ?p??e?ta?
ap? a??et?? p????µ??e? te??????
? µ???d?? Edge Flags ??e? s??d?aste? µe
?e?a?????? µe??d??? ?p?? Contraction Hierarchies
H µ???d?? Edge Flags se s??d?asµ? µe Transit Node
Routing ep?t?????e? ta ?a??te?a ap?te??sµata
µ???? st??µ??

90
Teµat?????a

??as???? a??????µ?? e??es?? s??t?µ?te???
d?ad??µ??
DIJKSTRA
Bi-Directional DIJKSTRA
A
????????µ???? p??a?e? ap?st?se??
?????µ??e? ?e??????
Contraction Hierarchies
Transit-Node Routing
A Landmarks
Edge Labels
S?????se??
?pe?t?se??

91
?pe?t?se??

?? p??ß??µa e??es?? ß??t?st?? d?ad??µ?? µp??e? ?a
?e???e??e?
St? ßas??? t?? µ??f?, t? p??ß??µa de? e??a?
?ea??st??? ??a ??a e???? p?a?µat???? p??ß??µ?t??
?p????? ß??t?st?? a??????µ?? ??a ???e p??ß??µa
???p?p???s? a??????µ?? ??a t?? ?a??te?? ep???s?
?ea??st???? p??ß??µ?t??

92
F???t?? s?s?e???

????t? t???f??a ?a? s?s?e??? GPS
?????? ????? ap????e?s??
?????? ap????s?? e??te????? µ?s??
????d?? p?? ????? ???s?µ?p????e?
? µe Landmarks
Contraction Hierarchies

93
???te??p???s? st??f??

?? st??f?? ??st????? ??????? se µ?a d?ad??µ?
???µ?????s? µe ß?s? t?? a?µ??
?a ?d??? tµ?µata a?apa??st??ta? ap? ??µß???
??µ?? e?????? ?e??? s??e??µe??? ?d???? tµ?µ?t??
?pe?ß????? µe???? d??t??
S??d?asµ?? d??µ?????s?? µe ß?s? t?? a?µ?? ?a? µe
ß?s? t??? ??µß??? se d?? ep?peda
???s? Contraction Hierarchies

94
????ap?? ???t???a ße?t?st?p???s??

? s????t?s? ?p?????sµ?? t?? ß??t?st?? d?ad??µ??
s?et??eta? p?a?t??? µe p???ap???? pa?????te?
??d?? ???µat??, ta??t?te? p?? a?apt?sse?,
pe?????sµ??
?p?????? t?? ?d????, ??st??/asf??e?a/e?d?af????
d?ad??µ??, ta??t?ta
?e? e??a? ef??t?? ? p??-?p?????sµ?? ???? t??
d??at?? s??d?asµ??
Contraction Hierarchies
? ta????µ?s? t?? ??µß?? ???eta? µ?a f???
?p?????sµ?? s??t?µe?se?? µe ß?s? t? s???e???µ???
s????t?s?

95
???aµ???t?ta

???aµ??? ?d??? d??t?a, ?p?? ?????f???a??
s?µf???s?
???-epe?e??as?a µp??e? ?a e??a? a?at??????
?p??e?t??? a?a???s? t?? ded?µ????
Landmark A ?a? Contraction Hierarchies

96
????ap?? ???t?a

???µ?????s? µe ß?s? p???ap?? d??t?a
?d??? d??t?a
??sa µa????? µetaf????
????ap?? ???t???a
?? a?t?????t? µp??e? ?a e??a? d?a??s?µ? µ??? st??
a??? t?? d?ad??µ??
???t?µ?s? se ????te?e? a??a??? µ?s??
???te??p???s? ???t????? µe t? ???s? labels se
???e a?µ?
?d?a?te?a d?s???? p??ß??µa

97
??????? pe??????a

? ?????? d?ad??µ??, se p????? pe??pt?se??,
s?et??eta? ?µesa µe t?? ??a a?a????s??
???s? µ?s?? µa????? µetaf????,
??af??et???? ta??t?te? sta ?d??? tµ?µata a?????a
µe t?? ??a
?? p??a??? s??d?asµ?? a??????? s?µa?t??? t?
µ??e??? t?? d??t???
??s????a ???s?? aµf?d??µ?? te??????
??s????a e??t?µ?t?? ??a ß??t?st? ??a a?a????s??

98
?a?ap?µp??