GIS: data processing Example of spatial queries. 3.1 Spatial queries. Chapter III. Geographic Information Systems: Data Processing

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1 GIS: data processng Chapter III Geographc Informaton Systems: Data Processng 3.1 Spatal queres 3.2 Introducton to Spatal Analyss 3.3 Spatal ndexng 3.4 Updatng 3.5 Conclusons 3.1 Spatal queres 1. Example of spatal queres 2. Elementary spatal queres 3. Queres of spatal analyss 4. Topologcal queres 5. Concluson Example of spatal queres What do we have n ths pont? What do we have n ths zone? What s the best path from Lsbon to Warsaw What are the countres at the border of Austra? What are the states crossed by the Msssspp rver? Where s the more polluted zone? Chapter III: GIS: Data Processng 1

2 Example of spatal query Elementary spatal queres zone #1 457 zone #4 709 zone #2 784 zone #3 539 #zone Number of trees What s the number of trees wthn the zone arbtrarly desgned? Pont query Lne query Regon query 3D query Buffer zones Pont query Jordan half-lne theorem 0 Canddate pont A B E Half lne x C D y What do we have n ths pont? Intersecton number wth sdes A pont s nsde f the ntersecton number s odd A pont s outsde f the ntersecton number s even Chapter III: GIS: Data Processng 2

3 Regon query Trench query B E Gas ppe Water ppe A C D What do we have n ths regon? Tap What are the subterraneous engneerng network n ths place? Buffer zones defned by parallels Buffer zone Problem Problem Problem Chapter III: GIS: Data Processng 3

4 Defnton of a buffer zone along a jagged polygon Queres of spatal analyss Optmal pont Optmal zone Optmal path Example: delmtaton of sea terrtoral waters Dstrctng Locatng a new hosptal Optmzaton queres Zone 3 Usually solved by operaton research methods Zone 2 Canddate stes Defnton of one or several crtera Zone 5 Zone 1 Zone 4 Locaton of hndrances Fndng for the optmum Gradent (hll-clmbng) algorthm Mutcrtera methods Chapter III: GIS: Data Processng 4

5 Optmal path n a graph Path n a herarchcal graph A B C1 A B C2 Solved by Djkstra algorthm or varants How to go from A to B? Mnmum path n a polygon Mnmum path n a terran K C J I H G D F A B L A B M E A How to go from A to B? How to go from C to D? B Chapter III: GIS: Data Processng 5

6 Salesman crcut Dstrctng Objectve: fnd a tessellaton followng some crtera A Startng and arrvng pont Example: poltcal electon dstrcts local branch (subsdes) of a company Topologcal queres Example Basc Zones Frst alternatve Query about poston and adjacency of spatal objects Allen and Egenhofer relatons «touch», «ntersect» etc. Object A : nsde: A outsde: A border: δa Second alternatve Thrd alternatve Chapter III: GIS: Data Processng 6

7 Egenhofer Relatons 9 ntersecton Egenhofer Model Object A: A B Object B: nsde : A outsde : A border : δa A A B B nsde : B outsde : B border : δβ A B B B A B A B A B R(A,B) = A A B A B A B A A B A B A B Neghbourng Chapter III: GIS: Data Processng 7

8 Concluson about spatal queres Importance of spatal queres Topology Operaton research Importance of response tme Necessty of ndexng (spatal ndexng) 3.2 Introducton to spatal analyss 1. Interpolaton and extrapolaton 2. Operaton research 3. Spatal analyss by map overlay 4. Smulaton methods 5. Multcrtera analyss 3. Examples 7. Concluson Interpolaton and extrapolaton Varous possbltes of nterpolaton 1. Data Interpolaton 2. Data Extrapolaton 3. Geometrc Inference F(u) F(u) F(u) u u Nearest Value Lnear nterpolaton F(u) u Splne nterpolaton F(u) u Stochastc nterpolaton Interpolated value Model-based nterpolaton u Chapter III: GIS: Data Processng 8

9 Varous possbltes of extrapolaton Geometrc nference: estmaton of alttude of a pont F(u) F(u) F(u) F(u) F(u) Nearest Value (last value) u Lnear extrapolaton u Splne extrapolaton u Stochastc extrapolaton u Model-based extrapolaton u What s the alttude z of ths pont? X Z Y Geometrc nference: geologc layers from borng Calcul of nfluence: Newtonan nterpolaton Terran Inferred layers Lnear nterpolaton Terran Subsol borngs Terran Inferred layers Other nterpolaton , , z r = In whch n = 1 n = z d d d = ( x x ) ( y + y ) If we set 1 p = 2 d We get z r = n = 1 n = 1 r z * p p 2 2 r Chapter III: GIS: Data Processng 9

10 3.2.2 Operaton Research Optmzng a monovarable functon Smplex method Gradent method Optmal path Cost Functon Optmum Cost Functon Local optma Value of x1 gvng the mnmum cost x1 Value of x1 gvng the optmum costs Global Optmum x1 Searchng the optmum of a functon x1 (1) Startng pont (3) Optmum accordng to ths axs; so (4) Second orthogonal drecton drecton x2 (6) False drecton: (5) Optmum (2) Frst drecton U-turn, accordng to ths axs; so orthogonal drecton (7) New drecton (8) Optmum accordng to ths drecton (5) Optmum (6) False drecton: accordng to ths U-turn, axs; so orthogonal drecton «overlay» Spatal Analyss by map overlay Metaphor of the lght table Startng pont (1) (7) Arrvng pont (optmum) (3) (8) (5) (4) (2) (6) Path summary Chapter III: GIS: Data Processng 10

11 Exact overlay Map overlay wth slver polygons Humd Ard Very ard Wheat Corn Oats Humd-Wheat Ard-Corn Very ard-oats Very ard-corn Map A Map B Overlay of A and B Slver polygons Smulaton methods Multcrtera Analyss Monte Carlo Smulaton Statstcal dstrbuton a pror known Usng random numbers Numerous smulatons Computaton of parameters (mean, varance, etc.) Mn f 1( x1, x2, x3,..., xn) Max f 2 ( x1, x2, x3,..., xn) Mn f 3 ( x1, x2, x3,..., xn)... Mn f ( x1, x2, x3,..., xn)... Max f k ( x1, x2, x3,..., xn) etc. Chapter III: GIS: Data Processng 11

12 Multcrtera Optmzaton Examples x3 Space of solutons defned over the varables space f x3 f1 f2 f3 x1 x2 x1 x2 Road rsk Monocrteron Problem Multcrtera Problem f3 Space of solutons defned over the crtera space F M M : Target pont ( pont optmsng all crtera) F : Feasble soluton f2 f1 Crtera space Concluson about Spatal Analyss Importance of spatal analyss ponts lnes zones graphs Chapter III: GIS: Data Processng 12

13 3.3 Spatal ndexng Importance of spatal ndexng Usng quadtrees Usng Peano curves Usng R-tree Indexng n Oracle Conclusons Importance of spatal ndexng Acceleratng system Wthout ndex: Browsng the whole DB (all objects) Very tme-consumng (expensve) Necessty of creatng adapted data structures Indexng n relatonal DB Herarchy of ndces Index level 2 Index level 1 Data Keys Addresses Index level aaaa bbbb cccc dddd eeee gggg hhhh kkkk... Block Block Chapter III: GIS: Data Processng 13

14 3.3.2 Usng quadtree Quadtree 0 E Level 1 0 D 4 8 C 12 Level 2 1 A 4 F 15 G,B Level Usng Peano curves Hlbert and Peano Curves Space-fllng curves Total coverage of the space Impossble wth Eucldan geometry Possble wthn Peanan vson Chapter III: GIS: Data Processng 14

15 Indexng a small terrtory Z-order (Morton codes) 5 E G B Peano keys Sde Objects F 4 1 D A E 0 2 D 1 1 A 4 1 F 8 2 C 15 1 B,G C Usng R-tree Example of an R-tree Tree of rectangles (r-tree) A F G B J K H Amelorated trees (r*-tree) D E M I N C L A B C D E F G H I J K L M N Chapter III: GIS: Data Processng 15

16 Example of an R*-tree Indexng European countres wth Rectangles H A C I F D1 D2 B E G H I A B F D1 C E G D Indexng n Oracle R-tree Quadtree / R-tree Mnmum Boundng Rectangles Indexng prncple Chapter III: GIS: Data Processng 16

17 Quadtree HH codes HHCODEs (Helcal Hyperspatal Codes) Peano key Peano-key based Quadtree (Morton code) Longtude/lattude/alttude/tme Spatal Index Creaton Selectng one ndex Chapter III: GIS: Data Processng 17

18 3.3.6 Conclusons about spatal ndexng Importance of access methods Data Organzaton Evoluton to spato-temporal Evoluton to 3D Evoluton to contnuous phenomena Usng n Oracle 11g (Locator or Spatal) 3.4 Updatng Introducton Alphanumerc Updatng Zonal Updatng and Refnement Global Updatng Mxng two layers Coverage Extenson Conclusons Importance of sources ZONE OROBJECT MODIFICATION Geographc Database newly made measures wth more accurate devces (theodoltes,..) Theodolte GLOBAL REFINEMENT Exstng Database vector and raster format for nstance aeral photos or satellte mages Aeral photos GLOBAL CORRECTIONS varous data producers, usng dfferent bases or standards etc. Satellte mages Scanned maps MULTI-LAYER INTEGRATION COVERAGE EXTENSION Chapter III: GIS: Data Processng 18

19 Toy Database Alphanumerc Updatng PARCEL (#parcel,(#segment) * ) SEGMENT (#segment, (#pont) 2 ) POINT (#pont, x, y) LAST-KEYS (#parcel, #segment, #pont) Usng languages such as SQL UPDATE POINT SET x = 4567, y = 7890 WHERE #pont = 2537; Introducng a new pont nto a segment Prevous segment #pont=120 x=500 y=6820 #pont=121 x=1040 y=6540 #segment=657 Replacng segments #pont=lastpont+1 x=760,y=6640 #segment=last_segment+2 #segment=last_segment+1 DELETE FROM SEGMENT WHERE #segment=657; INSERT INTO POINT VALUES (LAST-KEYS.#pont+1,760,6640); INSERT INTO SEGMENT VALUES (LAST-KEYS.#segment+1,120, LAST-KEYS.#pont+1); INSERT INTO SEGMENT VALUES (LAST-KEYS.#segment+2,121, LAST-KEYS.#pont+1); UPDATE LAST-KEYS SET #segment=old.#segment+2, SET #pont=old.#pont+1; COMMIT; Chapter III: GIS: Data Processng 19

20 Zonal Updatng and Refnement Cadaster database Parcel # 45 Object ntegraton wthout by-effects Parcel # 46 Parcel # 49 Parcel # 50 # 51 Parcel # 48 Cadaster database Updatng wth local modfcaton wthout elastc transformaton Parcel # 45 Parcel # 46 Parcel # 49 Parcel # 50 # 51 Parcel # 48 Updatng wth elastc transformaton Buldng permt fle Insertng new nformaton Updatng wth topologcal modfcatons Old Map Parcel 58 Parcel 56 P 1 P 5 P 6 P 2 P 4 P 3 P 1 P 5 P 2 P 61 P 62 P 4 P 3 P 1 P 5 P 2 P 61 P 62 P 4 P 3 59 Parcel 57 Parcel 60 Project New Road Resultng Map Parcel 56B Parcel 58A New Road Parcel 56A 58B 59B 59A Parcel 57 Parcel 60 (a) (b) (c) Chapter III: GIS: Data Processng 20

21 Global Updatng Rubber-sheetng conventonal rubber-sheetng when a few number of control ponts are provded more sophstcated rubber-sheetng based on several ponts wth constrants global updatng based on aeral photos. Intal map New map Control ponts to move Fxed control ponts Formulae for rubber-sheetng Lnear Rubber-sheetng X = A x + B y + C Y = D x + E y + F Blnear Rubber-sheetng X = A xy + B x + C y + D Y = E xy + F x + G y + H Old map coordnates: x, y New map coordnates : X, Y Example wth aeral photos Before After Chapter III: GIS: Data Processng 21

22 Force-fttng force-ft of a pont (coordnates), force-ft of the length of a segment, force-ft of an angle (especally rght angles), force-replacng of a segment by a new polylne, etc.. Global updatng wth aeral photos Aeral photos taken every two years Updatng the whole urban database Pxel = 8 cm 8 cm A pror model-based reasonng General prncple Aeral photos Aeral photos Global updatng Global updatng Urban Database t Urban Database t+h Urban Database t+2h Chapter III: GIS: Data Processng 22

23 Photos Boundares Homogeneous object Mxng Several Layers Gas-network Database Resultng database before correctons For nstances, streets, gas and water Algnment of coordnates Topologcal problems Water-supply database Resultng database after correctons Chapter III: GIS: Data Processng 23

24 Mxng same nformaton from dfferent sources Examples: two buldngs databases Dutch cadaster Problem: to reconcle the databases Two Topographc Maps (1) Md-scale (TOP10vector) Scale 1 : 10,000 Photogrammetrc mono-plottng 4 year update cycle snap shot database Md-scale (Buldngs) Two Topographc Maps (2) Large-scale (GBKN) Scale 1 : 1,000 Photogrammetrc stereo-plottng Updated contnously Contans hstory Chapter III: GIS: Data Processng 24

25 Large-scale (Buldngs) Correspondences: 1-to-1 Correspondences: n-to-1 Chapter III: GIS: Data Processng 25

26 Correspondences: 1-to-n Correspondences: n-to-m Fndng Correspondng Objects Aggregaton & Flterng (1) Chapter III: GIS: Data Processng 26

27 Aggregaton & Flterng (2) Cartographc Generalzaton Old New Old- New Large-scale Large-scale Generalzed Large-scale + Large-scale Generalzed Adjustment (1) Adjustment (2) Chapter III: GIS: Data Processng 27

28 Coverage Extenson Integraton of new nformaton Same layers or classes of objects Removng of overlaps Problems at the boundary EXISTING DATA BASE INTEGRATION OF NEW INFORMATION UNIFIED DATA BASE NEW INFORMATION TO BE ADDED Map- and Edge- Matchng Necessary Map- and Edge- Matchng Done Reorganzaton at the boundary Cty A Rules Ponts to be forced Boundary accordng to Cty A Swath for the elastc zone Cty A Cty B Boundary accordng to Cty B Cty B Swath for the elastc zone Rule 1: If the boundary segments of A are consdered more accurate than those of B, then keep them (A) and force-ft the boundary segment of B; Rule 2: If boundares are dfferent and both naccurate then take a sort of md-lne and dstort objects neghborng the boundary accordngly. Chapter III: GIS: Data Processng 28

29 Examples of Constrants algnment of streets parallelsm of kerbs or parcel lmts rectangularty of some buldngs Conclusons Importance of updatng Importance of sources Importance of qualty control Geometrc accuracy Topologcal checkng Necessty of nce vsual nterfaces Legslatve aspects Cartography Updatng Queryng 3.5 Conclusons Chapter III: GIS: Data Processng 29