SpatialAnalysisandModeling(GIST4302/5302)

Guofeng CaoDepartmentofGeosciences

TexasTechUniversity

DatabaseFundaments

Review:BitsandBytes

Datastoredinacomputersystemismeasuredinbits eachbit recordsoneoftwopossiblestates

0(off,false) 1(on,true)

Bits areamalgamatedintobytes(8bits) Eachbyte representsasinglecharacter Acharactermaybeencodedusing7bits withanextrabit usedasasignofpositiveornegative

Question:CanIusebytetorepresenttheelevationoftheEverestinmeters?

Megabytes(2^20bytes)

Database

Adatabase isacollectionofdataorganizedinsuchawaythatacomputercanefficientlystoreandretrievedata Arepositoryofdatathatislogicallyrelated

Adatabaseiscreatedandmaintainedusingageneralpurposepieceofsoftwarecalledadatabasemanagementsystem(DBMS)

CommonDatabaseApplications

Home/officedatabase Simpleapplications(e.g.,restaurantmenus)

Commercialdatabase Storetheinformationforbusinesses(e.g.customers,employees)

Engineeringdatabase Usedtostoreengineeringdesigns(e.g.CAD)

Imageandmultimediadatabase Storeimage,audio,videodata

Geodatabase/spatialdatabase Storeacombinationofspatialandnonspatialdata

TheRelationalModel Therelationalmodelisoneofthemostcommonlyusedarchitectureindatabase Arelationaldatabase isacollectionofrelations,oftenjustcalledtables

Eachrelationhasasetofattributes Thedataintherelationisstructuredasasetofrows,oftencalledtuples

Eachtupleconsistsofdataitemsforeachattribute Eachcell inatuplecontainsasinglevalue Arelationaldatabasemanagementsystem(RDBMS)isthesoftwarethatmanagesarelationaldatabase

AnExampleRelation

Relation Attribute

TupleDataitem

Relations Arelation isbasicallyatable Arelationschemeisthesetofattributenamesandthedomain

(datatype)foreachattributename Adatabasescheme isasetofrelationschemes Inarelation:

Eachtuplecontainsasmanyvaluesasthereareattributesintherelationscheme

Eachdataitemisdrawnfromthedomainforitsattribute Theorderoftuplesisnotsignificant Tuplesinarelationarealldistinctfromeachother

Thedegree ofarelationisitsnumberofcolumns Thecardinality ofarelationisthenumberoftuples

RelationScheme Acandidatekey isanattributeorminimalsetofattributesthatwilluniquelyidentifyeachtupleinarelation

Onecandidatekeyisusuallychoseasaprimarykey

OperationsonRelations

Fundamentalrelationaloperators: Union,intersection,difference,productandrestrict:usualsetoperations,butrequirebothoperandshavethesameschema

Selection:pickingcertainrows Projection:pickingcertaincolumns Join:compositionsofrelations

Together,theseoperationsandthewaytheyarecombinediscalledrelationalalgebra combined: Analgebrawhoseoperandsarerelationsorvariablesthatrepresentrelations

ProjectOperator Theproject operatorisunary

Itoutputsanewrelationthathasasubsetofattributes

Identicaltuplesintheoutputrelationarecoalesced

Relation Sells:bar beer priceChimys Bud 2.50Chimys Miller 2.75Crickets Bud 2.50Crickets Miller 3.00

Prices := PROJbeer,price(Sells):beer priceBud 2.50Miller 2.75Miller 3.00

SelectOperator

Theselectoperatorisunary Itoutputsanewrelationthathasasubsetoftuples Aconditionspecifiesthosetuplesthatarerequired

Relation Sells:bar beer priceChimys Bud 2.50Chimys Miller 2.75Crickets Bud 2.50Crickets Miller 3.00

ChimyMenu := SELECTbar=Chimys(Sells):bar beer priceChimys Bud 2.50Chimys Miller 2.75

JoinOperator

Thejoin operatorisbinary Itoutputsthecombinedrelationwheretuplesagreeonaspecified

attribute(naturaljoin)Sells(bar, beer, price ) Bars(bar, address)

Chimys Bud 2.50 Chimys 2417 Broadway St.Chimys Miller 2.75 Cricekts 2412 Broadway St.Crickets Bud 2.50Crickets Coors 3.00

BarInfo := Sells JOIN BarsNote Bars.name has become Bars.bar to make the naturaljoin work.

BarInfo(bar, beer, price, address )

Chimys Bud 2.50 2417 Broadway St.Chimys Milller 2.75 2417 Broadway St.Crickets Bud 2.50 2412 Broadway St.Crickets Coors 3.00 2412 Broadway St.

JoinOperator

Joinisthemosttimeconsumingofallrelationaloperatorstocompute Ingeneral,relationaloperatorsmaynotbearbitrarilyreordered(leftjoin,rightjoin)

Queryoptimizationaimstofindanefficientwayofprocessingqueries,forexamplereorderingtoproduceequivalentbutmoreefficientqueries

ComplexRelationalOperatorExample

HowtofindthelocationsthatsellBud?Sells(bar, beer, price ) Bars(bar, address)

Chimys Bud 2.50 Chimys 2417 Broadway St.Chimys Miller 2.75 Cricekts 2412 Broadway St.Crickets Bud 2.50Crickets Coors 3.00

Step 2 BarInfo(beer, address )

Bud 2417 Broadway St.Milller 2417 Broadway St.Bud 2412 Broadway St.Coors 2412 Broadway St.

Step 1 BarInfo(bar, beer, price, address )

Chimys Bud 2.50 2417 Broadway St.Chimys Milller 2.75 2417 Broadway St.Crickets Bud 2.50 2412 Broadway St.Crickets Coors 3.00 2412 Broadway St.

SQLinOneSlide StructuredQueryLanguage Thestandardforrelationaldatabasemanagementsystems(RDBMS)

Example:

Select * from Sells where bar=Chimys Select * from Sells where bar=Chimys orderby price

asc

Relation Sells:bar beer priceChimys Bud 2.50Chimys Miller 2.75Crickets Bud 2.50Crickets Miller 3.00

ChimyMenu := SELECTbar=Chimys(Sells):bar beer priceChimys Bud 2.50Chimys Miller 2.75

RelationalDatabasesandSpatialdata

Severalissuespreventunmodifieddatabasesbeingusefulforspatialdata Structureofspatialdatadoesnotnaturallyfitwithtables Performanceisimpairedbytheneedtoperformmultiplejoinswith

spatialdata Indexesarenonspatialinaconventionalrelationaldatabase

AnextensibleRDBMSofferssomesolutionstotheseproblemswith userdefineddatatypes userdefinedoperations userdefinedindexesandaccessmethods activedatabasefunctions(e.g.,triggers)

RepresentationofSpatialData

RepresentationofSpatialDataModels

Objectbasedmodel: treatsthespaceaspopulatedbydiscrete,identifiableentitieseachwithageospatialreference Buildingsorroadsfitintothisview GISSoftwares:ArcGIS

Fieldbasedmodel: treatsgeographicinformationascollectionsofspatialdistributions Distributionmaybeformalizedasamathematicalfunctionfromaspatial

frameworktoanattributedomain Patternsoftopographicaltitudes,rainfall,andtemperaturefitneatlyinto

thisview. GISSoftware:Grass

RelationalModels Tuplesrecordingannualweatherconditionsatdifferentlocations

The field-based and object-based approaches are attempts to impose structure and pattern on such data.

ObjectbasedApproach Clumpsarelationassingleorgroupsoftuples

Certaingroupsofmeasurementsofclimaticvariablescanbegroupedtogetherintoafinitesetoftypes

ObjectbasedExample

Fieldbasedapproach

Treatsinformationasacollectionoffields Eachfield definesthespatialvariationofanattributeasafunctionfromthesetoflocationstoanattributedomain

ObjectbasedApproach

Entity

Objectbasedmodelsdecomposeaninformationspaceintoobjectsorentities

Anentitymustbe: Identifiable Relevant(beofinterest) Describable(havecharacteristics)

Theframeofspatialreferenceisprovidedbytheentitiesthemselves

Example:Houseobject

Hasseveralattributes,suchasregistrationdate,address,ownerandboundary,whicharethemselvesobjects

Example:GISanalysis ForItalyscapitalcity,Rome,calculatethetotallengthoftheRiverTiberwhichlieswithin2.5kmoftheColosseum FirstweneedtomodeltherelevantpartsofRomeasobjects

Operationlength willactonarc,andintersect willapplytoformthepieceofthearc incommonwiththedisc

Example:GISanalysisAprocessofdiscretizationmustconverttheobjectstotypesthatarecomputationallytractable

Acirclemayberepresentedasadiscretepolygonalarea,arcsbychainsoflinesegments,andpointsmaybeembeddedinsomediscretespace

PrimitiveObjects

EuclideanSpace:coordinatized modelofspace Transformsspatialpropertiesintopropertiesoftuplesofrealnumbers

Coordinateframeconsistsofafixed,distinguishedpoint(origin)andapairoforthogonallines(axes),intersectingintheorigin

Pointobjects Lineobjects Polygonalobjects

Polygonalobjects Convexity

Visibilitybetweenpointsx,y,andz

Example:Triangulation

Everysimplepolygonhasatriangulation.Anytriangulationofasimplepolygonwithnverticesconsistsofexactlyn 2triangles

ArtGalleryProblem Howmanycamerasareneededtoguardagalleryandhowshouldtheybe

placed? UpperboundN/3

Related:ConvexHull

Related:Voronoi Diagram Voronoi DiagramonRoadNetwork

JohnSnow,PumpsandCholeraOutbreak

PrimitiveGISOperations inEuclideanspaces

Length,bearing,area Howmanywaysyoucanthinkoftocalculatetheareaofapolygon? Howtotestwhichsideofapointcorrespondingtoaline?

Distancebetweenobjects(points,lines,polygons) Distancecouldbeambiguous,e.g.,whatisthedifferencefromLubbocktoDallas(from

citycenterorcityboundary?). Centroid

Notnecessarilywithinintheboundaryofpolygon Pointinpolygon

Raycastingmethod Pointonline

area Buffer Intersection/overlay

Intopologicalspaces Spatialrelations(within,touch,cover,)

Areaofasimplepolygon

Notethattheareamaybepositiveornegative Infact,area(pqr)=area(qpr) Ifp istotheleftofqr thentheareaispositive,ifp istotherightofqr thentheareaisnegative

Pointinpolygon Determiningwhetherapointisinsideapolygonisoneof

themostfundamentaloperationsinaspatialdatabase Semilinemethod(raycasting):checksforoddoreven

numbersofintersectionsofasemilinewithpolygon Windingmethod:sumsbearingsfrompointtopolygon

vertices

PrimitiveGISoperations:Overlay

Union Intersect Erase Identity Update SpatialJoin SymmetricalDifference

Overlay

Union Computesageometricunionoftheinputfeatures.Allfeaturesandtheirattributeswillbewrittentotheoutputfeatureclass.

Overlay

Intersect Computesageometricintersectionoftheinputfeatures.Featuresorportionsoffeatureswhichoverlapinalllayersand/orfeatureclasseswillbewrittentotheoutputfeatureclass.

Overlay

Erase CreatesafeatureclassbyoverlayingtheInputFeatureswiththepolygonsoftheEraseFeatures.Onlythoseportionsoftheinputfeaturesfallingoutsidetheerasefeaturesoutsideboundariesarecopiedtotheoutputfeatureclass

Overlay

Identity Computesageometricintersectionoftheinputfeaturesandidentityfeatures.Theinputfeaturesorportionsthereofthatoverlapidentityfeatureswillgettheattributesofthoseidentityfeatures

Overlay

Update ComputesageometricintersectionoftheInputFeaturesandUpdateFeatures.Theattributesandgeometryoftheinputfeaturesareupdatedbytheupdatefeaturesintheoutputfeatureclass.

Overlay

Symmetricaldifference Featuresorportionsoffeaturesintheinputandupdatefeaturesthatdonotoverlapwillbewrittentotheoutputfeatureclass.

Overlay Spatialjoin

Joinsattributesfromonefeaturetoanotherbasedonthespatialrelationship.Thetargetfeaturesandthejoinedattributesfromthejoinfeaturesarewrittentotheoutputfeatureclass.

QuizInputFeature OverlayFeature

Whichofthefollowingistheresultofidentity,intersect,symmetricaldifference,unionandupdaterespectively?

A B C D E

Buffer

Primitiveoperators youmightalreadyrealizedthattheseprimitiveoperatorsareoftenusedcollaborativelywitheachother,andotheranalyticalmethods(e.g.,dissolve,surfaceanalysis,interpolation)thatwewillintroduceinthecominglectures.

Topologicalspatialoperations:spatialrelationship

Objecttypeswithanassumedunderlyingtopologyarepoint,arc,loop andarea

Operations: boundary,interior,closure andconnected aredefinedintheusualmanner

components returnsthesetofmaximalconnectedcomponentsofanarea

extremes actsoneachobjectoftypearcandreturnsthepairofpointsofthearcthatconstituteitsendpoints

iswithin providesarelationshipbetweenapointandasimpleloop,returningtrueifthepointisenclosedbytheloop

TopologicalspatialoperationsforareasXmeets Y ifX andYtouchexternallyinacommonportionoftheirboundaries

X overlaps Y ifX andYimpingeintoeachothersinteriors

Topologicalspatialoperationsforareas

X isinside Y ifX isasubsetofYandX,Y donotshareacommonportionofboundary

X covers Y ifY isasubsetofX andX,Y touchexternallyinacommonportionoftheirboundaries

Topologicalspatialoperations Thereareaninfinitenumberofpossibletopologicalrelationshipsthatareavailablebetweenobjectsoftypecell

http://resources.esri.com/help/9.3/ArcGISDesktop/com/Gp_ToolRef/Data_Management_toolbox/select_by_location_colon_graphical_examples.htm

ContainvsCONTAINS_CLEMENTINI: theresultsofCONTAINS_CLEMENTINIwillbeidenticaltoCONTAINSwiththeexceptionthatifthefeatureintheSelectingFeatureslayerisentirelyontheboundaryoftheInputFeatureLayer,withnopartofthecontainedfeatureproperlyinsidethefeatureintheInputFeatureLayer,theinputfeaturewillnotbeselected.

Spaghetti

Spaghettidatastructurerepresentsaplanarconfigurationofpoints,arcs,andareas

Geometryisrepresentedasasetoflistsofstraightlinesegments

Spaghetti example

Eachpolygonalareaisrepresentedbyitsboundaryloop

Eachloopisdiscretizedasaclosedpolyline Eachpolylineisrepresentedasalistofpoints

A:[1,2,3,4,21,22,23,26,27,28,20,19,18,17]B:[4,5,6,7,8,25,24,23,22,21]C:[8,9,10,11,12,13,29,28,27,26,23,24,25]D:[17,18,19,20,28,29,13,14,15,16]

Issues

ThereisNO explicitrepresentationofthetopologicalinterrelationshipsoftheconfiguration,suchasadjacency

Dataconsistenceissues Silverpolygons Dataredundancy

NAA:nodearcarea

Eachdirectedarchasexactlyonestartandoneendnode.

Eachnodemustbethestartnodeorendnode(maybeboth)ofatleastonedirectedarc.

Eachareaisboundedbyoneormoredirectedarcs. Directedarcsmayintersectonlyattheirendnodes. Eachdirectedarchasexactlyoneareaonitsrightandoneareaonitsleft.

Eachareamustbetheleftareaorrightarea(maybeboth)ofatleastonedirectedarc.

NAA:planardecompositionArc Begin End Left Right

a 1 2 A X

b 4 1 B X

c 3 4 C X

d 2 3 D X

e 5 1 A B

f 4 5 C B

g 6 2 D A

h 5 6 C A

i 3 6 D C

FieldbasedApproach

Spatialfields IfthespatialframeworkisaEuclideanplaneandtheattributedomainisasubsetofthesetofrealnumbers; TheEuclideanplaneplaystheroleofthehorizontalxyplane Thespatialfield valuesgivethezcoordinates,orheightsabove

theplane

Imagine placing a square grid over a region and measuring aspects of the climate at each node of the grid. Different fields would then associate locations with values from each of the measured attribute domains.

RegionalClimateVariations

Propertiesoftheattributedomain Theattributedomainmaycontainvalueswhichare

commonlyclassifiedintofourlevelsofmeasurement Nominalattribute:simplelabels;qualitative;cannotbe

ordered;andarithmeticoperatorsarenotpermissible Ordinalattribute:orderedlabels;qualitative;andcannotbe

subjectedtoarithmeticoperators,apartfromordering Intervalattributes:quantitiesonascalewithoutanyfixed

point;canbecomparedforsize,withthemagnitudeofthedifferencebeingmeaningful;theratiooftwointervalattributesvaluesisnotmeaningful

Ratioattributes:quantitiesonascalewithrespecttoafixedpoint;cansupportawiderangeofarithmeticaloperations,includingaddition,subtraction,multiplication,anddivision

Continuousanddifferentiablefields

Continuous field:smallchangesinlocationleadstosmallchangesinthecorrespondingattributevalue

Differentiable field:rateofchange(slope)isdefinedeverywhere

Spatialframeworkandattributedomainmustbecontinuousforboththesetypesoffields

Everydifferentiablefieldmustalsobecontinuous,butnoteverycontinuousfieldisdifferentiable

Onedimensionalexamples Fieldsmaybeplottedasagraphofattributevalueagainstspatialframework

Continuous and differentiable; the slope of the curve can be defined at every point

OnedimensionalexamplesThe field is continuous (the graph is connected) but not

everywhere differentiable. There is an ambiguity in the slope, with two choices at the articulation point between the two

straight line segments.

Continuous and not differentiable; the slope of the curve cannot be defined at one or more points

OnedimensionalexamplesThe graph is not connected and so the field in not continuous

and not differentiable.

Not continuous and not differentiable

Twodimensionalexamples

Theslopeisdependentontheparticularlocationandonthebearingatthatlocation

Isotropicfields Afieldwhosepropertiesareindependentofdirectioniscalledanisotropicfield

Considertraveltimeinaspatialframework ThetimefromXtoanypointYisdependentonlyuponthedistancebetweenXandYandindependentofthebearingofYfromX

Anisotropicfields Afieldwhosepropertiesaredependentondirectioniscalledananisotropicfield.

SupposethereisahighspeedlinkAB ForpointsnearB itwouldbebetter,iftravelingfromX, totraveltoA,takethelink,andcontinueonfromB tothedestination

Thedirectiontothedestinationisimportant

Spatialautocorrelation

SpatialautocorrelationisaquantitativeexpressionofToblersfirstlawofgeography(1970) Everythingisrelatedtoeverythingelse,butnearthingsaremore

relatedthandistantthing Spatialautocorrelationmeasuresthedegreeofclusteringofvaluesin

aspatialfield

Alsotermedasspatialdependency,spatialpattern,spatialcontext,spatialsimilarity,spatialdissimilarity

Autocorrelation

Ifthereisnoapparentrelationshipbetweenattributevalueandlocationthenthereiszerospatialautocorrelation

Iflikevaluestendtobelocatedawayfromeachother,thenthereisnegativespatialautocorrelation

If like values tend to cluster together, then the field exhibits high positive spatial autocorrelation

RepresentationsofSpatialFields

Points Contours Raster/Lattice Triangulation(DelaunayTrangulation)

Example

Contourlinesandraster

Example

Trangulations

SideNote:DelaunayTriangulationandVoronoi Diagram

DualGraph

Operationsonfields

Afieldoperationtakesasinputoneormorefieldsandreturnsaresultantfield

Thesystemofpossibleoperationsonfieldsinafieldbasedmodelisreferredtoasmapalgebra

Threemainclassesofoperations Local Focal Zonal

Neighborhoodfunction GivenaspatialframeworkF,aneighborhoodfunction

n isafunctionthatassociateswitheachlocationx asetoflocationsthatareneartox

Localoperations Localoperation:actsupononeormorespatialfieldstoproduceanewfield

Thevalueofthenewfieldatanylocationisdependentonthevaluesoftheinputfieldfunctionatthatlocation isanybinaryoperation

Focaloperations Focaloperation:the

attributevaluederivedatalocationxmaydependontheattributesoftheinputspatialfieldfunctionsatxandtheattributesofthesefunctionsintheneighborhoodn(x)ofx

Zonaloperations Zonaloperation:aggregatesvaluesofafieldoverasetofzones(arisingingeneralfromanotherfieldfunction)inthespatialframework

Foreachlocationx:FindtheZoneZi inwhichxiscontainedComputethevaluesofthefieldfunctionfappliedtoeachpointinZiDeriveasinglevalue(x)ofthenewfieldfromthevaluescomputedinstep2

Summary:Objectbasedvs Fieldbasedmodels

Objectbasedmodels: Greaterprecision Lessredundantinformation(smallerstoragefootprints)

Complexdatastructures Fieldbasedmodels:

Simplerdatastructures Moreredundantinformation(largerstoragefootprints)

Lessprecision Rasterisfaster,butvectoriscorrector

Endofthistopic