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

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1 Vsal Informaton Systems Pr. Robert Larn GIS: data processng Chapter III Geographc Informaton Systems: Data Processng 3.1 Spatal qeres 3. Introdcton to Spatal nalyss 3.3 Spatal ndexng 3. Updatng 3. Conclsons 3.1 Spatal qeres 1. Example of spatal qeres. Elementary spatal qeres 3. Qeres of spatal analyss. Topologcal qeres. Conclson Example of spatal qeres 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 contres at the border of stra? What are the states crossed by the Msssspp rver? Where s the more pollted zone? Chapter III: GIS: Data Processng 1

2 Vsal Informaton Systems Pr. Robert Larn Example of spatal qery Elementary spatal qeres zone #1 7 zone # 709 zone # 78 zone #3 39 #zone Nmber of trees What s the nmber of trees wthn the zone arbtrarly desgned? Pont qery Lne qery Regon qery 3D qery ffer zones Pont qery Regon qery E E C D y x What do we have n ths pont? C D What do we have n ths regon? Chapter III: GIS: Data Processng

3 Vsal Informaton Systems Pr. Robert Larn Trench qery ffer zones defned by parallels Gas ppe Water ppe Problem Tap What are the sbterraneos engneerng network n ths place? Problem Problem ffer zone Defnton of a bffer zone along a jagged polygon Example: delmtaton of sea terrtoral waters Chapter III: GIS: Data Processng 3

4 Vsal Informaton Systems Pr. Robert Larn Qeres of spatal analyss Optmal pont Locatng a new hosptal Zone 3 Optmal zone Zone Canddate stes Optmal path Zone Zone 1 Zone Locaton of hndrances Dstrctng Optmzaton qeres Optmal path n a graph Usally solved by operaton research methods Defnton of one or several crtera Fndng for the optmm Gradent (hll-clmbng) algorthm Mtcrtera methods Solved by Djkstra algorthm or varants Chapter III: GIS: Data Processng

5 Vsal Informaton Systems Pr. Robert Larn Path n a herarchcal graph Mnmm path n a polygon C1 C K C J I H G D F L M E How to go from to? How to go from to? How to go from C to D? Mnmm path n a terran 3.1. Topologcal qeres Qery abot poston and adjacency of spatal objects llen and Egenhofer relatons «toch», «ntersect» etc. Object : nsde: otsde: border: δ Chapter III: GIS: Data Processng

6 Vsal Informaton Systems Pr. Robert Larn Egenhofer Relatons Conclson abot spatal qeres Importance of spatal qeres Topology Operaton research Importance of response tme Necessty of ndexng (spatal ndexng) 3. Introdcton to spatal analyss 1. Interpolaton and extrapolaton. Operaton research 3. Spatal analyss by map overlay. Smlaton methods. Mltcrtera analyss 3. Examples 7. Conclson Chapter III: GIS: Data Processng

7 Vsal Informaton Systems Pr. Robert Larn 3..1 Interpolaton and extrapolaton Varos possbltes of nterpolaton 1. Data Interpolaton. Data Extrapolaton 3. Geometrc Inference Nearest Vale Lnear nterpolaton Splne nterpolaton Stochastc nterpolaton Interpolated vale Model-based nterpolaton Varos possbltes of extrapolaton Geometrc nference: estmaton of alttde of a pont Nearest Vale (last vale) Lnear extrapolaton Splne extrapolaton Stochastc extrapolaton What s the alttde z of ths pont? Z Y Model-based extrapolaton X Chapter III: GIS: Data Processng 7

8 Vsal Informaton Systems Pr. Robert Larn Geometrc nference: geologc layers from borng Calcl of nflence: Newtonan nterpolaton Terran Inferred layers Lnear nterpolaton Terran Sbsol borngs Terran Inferred layers Other nterpolaton 3 7,, z r = In whch n = 1 n = z d d 1 1 d = ( x x ) ( y + y ) If we set 1 p = d We get z r = n = 1 n = 1 r z * p p r 3.. Operaton Research Optmzng a monovarable fncton Smplex method Gradent method Optmal path Cost Fncton Optmm Cost Fncton Local optma Vale of x1 gvng the mnmm cost x1 Vale of x1 gvng the optmm costs Global Optmm x1 Chapter III: GIS: Data Processng 8

9 Vsal Informaton Systems Pr. Robert Larn Searchng the optmm of a fncton x1 (1) Startng pont (3) Optmm accordng to ths axs; so () Second orthogonal drecton drecton x () False drecton: () Optmm () Frst drecton U-trn, accordng to ths axs; so orthogonal drecton (7) New drecton (8) Optmm accordng to ths drecton () Optmm () False drecton: accordng to ths U-trn, axs; so orthogonal drecton (1) (7) rrvng pont (optmm) Startng pont (8) (3) () () 3.. Mltcrtera nalyss Mn f Max f Mn f... Mn f... Max f etc. 3 1 ( x1, x, x3,..., xn) ( x1, x, x3,..., xn) ( x1, x, x3,..., xn) ( x1, x, x3,..., xn) k ( x1, x, x3,..., xn) () () Path smmary Mltcrtera Optmzaton 3.. Examples x1 x3 Space of soltons defned over the varables space Monocrteron Problem f x x1 x3 f1 f x Mltcrtera Problem f3 Road rsk f3 Space of soltons defned over the crtera space F M M : Target pont ( pont optmsng all crtera) F : Feasble solton f f1 Espace des crtères Chapter III: GIS: Data Processng 9

10 Vsal Informaton Systems Pr. Robert Larn 3..7 Conclson abot Spatal nalyss Importance of spatal analyss ponts lnes zones graphs 3.3 Spatal ndexng Importance of spatal ndexng 3.3. Usng qadtrees Usng Peano crves 3.3. Usng R-tree 3.3. Indexng n Oracle 3.3. Conclsons Importance of spatal ndexng Indexng n relatonal D cceleratng system Wthot ndex: rowsng the whole D (all objects) Very tme-consmng (expensve) Necessty of creatng adapted data strctres Keys ddresses Chapter III: GIS: Data Processng 10

11 Vsal Informaton Systems Pr. Robert Larn Herarchy of ndces 3.3. Usng qadtree Index level Index level 1 Data Index level aaaa bbbb cccc dddd eeee gggg hhhh kkkk... lock lock Qadtree Usng Peano crves 0 E 0 D 8 C 1 1 F 1 G, Level 1 Level Level 3 Space-fllng crves Total Coverage of the space Impossble wth Ecldan geometry Possble wth Peanan vson Chapter III: GIS: Data Processng 11

12 Vsal Informaton Systems Pr. Robert Larn Hlbert and Peano Crves Indexng a small terrtory E G Peano keys Sde Objects F 1 D E 0 D F 8 C 1 1,G 0 8 C 3.3. Usng R-tree Example of an R-tree Tree of rectangles (r-tree) F G J K H melorated trees (r*-tree) D E M I N C L C D E F G H I J K L M N Chapter III: GIS: Data Processng 1

13 Vsal Informaton Systems Pr. Robert Larn Example of an R*-tree 3. Conclsons H C I Cartography Updatng F D1 D Qeryng E G H I F D1 C E G D Chapter III: GIS: Data Processng 13