Representation of spatial data
This presentation is the property of its rightful owner.
Sponsored Links
1 / 43

Representation of spatial data PowerPoint PPT Presentation


  • 101 Views
  • Uploaded on
  • Presentation posted in: General

Representation of spatial data. GIS thematic layers, raster and vector, conversi on , subdivisi on representation, continu ous data: contours, DEMs, TINs. Thematic map la yers. Separate storage of data according to them e : map la yers

Download Presentation

Representation of spatial data

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Representation of spatial data

Representation of spatial data

GIS thematic layers, raster and vector, conversion, subdivision representation, continuous data: contours, DEMs, TINs


Thematic map la yers

Thematic map layers

  • Separatestorageof data according to theme: map layers

  • GIS typically use tens to hundreds of map layers

  • For example: municipality borders, land use, cadastral boundaries, water pipes, churches, etc.


Example map layers

Examplemap layers

Census data, 1995

(U.S.A.)


Geometr y topolog y and attribute s

Geometry, topologyand attributes

  • Geometry: coordinates

  • Topology: adjacency relations of objects

  • Attributes: properties, values

Example: CountrymapofSouth America

Geometry: coordinatesof the bordersTopology: whichcountries border which Attributes: namesofcountries, population, etc.


Representati on of geometr y

Representationof geometry

  • Twomain approaches: raster and vector

  • Can also be mixed in a GIS, anymap layer

  • Conversion raster-vector and vice versa possible

  • Representationdepends ontype of data, way ofacquisition, desired operations, etc.


Raster structur e

Rasterstructure

  • Division of space intoequal-size cells (squares, pixels)

  • Themegives cellsavalue (nominal, ordinal, interval, ratio, vector, …)

  • Cellsshould not contain any furtherspatialinformation (more detail)


Data in raster f orm

Data in raster form

Point object in

raster form

Line object in

raster form

Plane object in

raster form


Raster maps

Raster maps


Raster pros and cons

Simple structure

Simple operations

Obtained after scanning, remote sensing

Less suitablefor point and line objects: representationdoes not follow intuition

Networkanalysisdifficult

Not adaptive: no difference in detail possible in different regions

Eitherexpensive in memory, orlittle precision

Not obtained after digitizing

Raster: pros and cons


Raster memory reduction

Raster: memory reduction

  • Run-length encoding: no 2-dim array but coding start pixel withvalue and lengthofrun

  • Block encoding: 2-dim version

  • Disadvantage: makes structureand operationsmuch morecomplex

(34,67) forest 9

(34,67) forest 4,6


Vector structur e

Vectorstructure

  • Objectsstored as points, linesandareas

  • Points have coordinates; linesconnect points; areas are delimited by lines

  • Attributesare stored with the objects (point, line orareal)


Vector pros and cons

Elegant structure; fits withboth point, lineand areal objects

Small storage consumption

Precise

Adaptive: additional controlpointspossible

Network and clusteranalysispossible

Obtained after digitizing

Relatively complex

Map overlay and buffer computation complex

Vector: pros and cons


Vector representation of a region

Vector representation of a region

  • Not necessarily simply-connected:

    • NL has islands

    • NL has holes(Baarle-Nassau / Baarle-Hertog); there are even regions in these holes


Representation of subdivisions

Representation of subdivisions


Subdivisi on s spaghetti model

Subdivisions: spaghetti model

  • Every chain is represented by a list with coordinate pairs

  • Splitnodesare doubly stored

  • Areas are not present explicitly

C1

C2

C5

C4

C3

C6

C1: (..,..), (..,..), (..,..), ...

C2: (..,..), (..,..), (..,..), ...

C3: (..,..), (..,..), (..,..), ...


Subdivisi on s polygon ring structur e

Subdivisions: polygon ringstructure

  • Every area is represented by a list with coordinate pairs

  • Controlpointsare doublystored

  • Neighbor areas aredifficult to determine

  • Consistency is difficult to maintain

P1

P2

P3

P1: (..,..), (..,..), (..,..), ...

P2: (..,..), (..,..), (..,..), ...

P3: (..,..), (..,..), (..,..), ...


Subdivisi on s topologic al structur e

Subdivisions: topological structure

  • Nodes are objectswith coordinates

  • Edges are connectionsof nodes

  • Sequences of edges along polygon boundaries form cycles

  • Polygons are objects that can access their boundaries

Doubly-connected edge list


Subdivisi on s topologic al structur e1

Subdivisions: topological structure

  • Edges are split into directed half-edges

  • Half-edges have pointers to

    • Twin half-edge

    • Origin vertex

    • Next and Prev half-edges of incident polygon

    • Incident polygon

  • Polygons have pointers to half-edges, one in each bounding cycle

Origin

polygon

Twin

Prev

Next

polygon


Subdivisi on s topologic al chain structur e

Subdivisions: topologicalchain structure

  • Splitting nodes are objectswith coordinates

  • Chains are connections of splitting nodes and contain zero or morenodes with coordinates

  • Sequences of chains along polygon boundaries formcycles

  • Polygonsare objects that can access their boundaries

half-chains

Doubly-connected chain list


Vector structure s

Memory Duplication Polygon Topology

retrieve retrieve

Vectorstructures

Spaghetti +++-- -Polygon ring ---++ -DC edge list --++- +DC chain list +++++ ++


Raster vector conversi on

Raster-vector conversion

E.g. for data integration

  • Vector-to-raster: Like in computer graphics: scan-conversionof lines, etc.

  • Raster-to-vector: Consider pixel sides between pixels with different values as boundary and put in vectorrepresentation Thinning, line simplification


Thinning

Thinning

Raster-vector

conversion

Thinning


Lin e simplificati on

Line simplification

  • Douglas-Peucker algorithm from 1973

  • Input: chainp1, …, pnanderror

p1

pn


Dp algorit h m

DP-algorithm

  • Draw line segmentbetween first and last point

  • If all points in between are within error: ready

  • Otherwise, determine farthest point and recursively continueon the part until farthest point and the part afterfarthest point


Dp algorit h m1

DP-algorithm

DP-standard(i, j, )

Determine farthest point pkbetween piandpj

Ifdistance(pk, pi pj) > then DP-standard(i, k, )

DP-standard(k, j, )

Return the concatenationof

the simplifications


Representation of spatial data


Representation of spatial data


Properties of the dp algorit h m

Properties of the DP-algorithm

  • DP-algorithm does not minimizethe number of points in the simplification

DP-algorithm

Optimal


Properties of the dp algorit h m1

Properties of the DP-algorithm

  • Determining farthest point takesO(n) time

  • Whole algorithm takesT(n) = T(m) + T(n-m+1) + O(n),T(2) = O(1) time,splitting in m and n-m+1 points

  • “Fair” split givesO(n log n) time

  • Worst case gives quadratic time


Properties of the dp algorit h m2

Properties of the DP-algorithm

  • DP-algorithm may giveself-intersections in the output

Solution: test output forself-intersectionsand continue adding controlpoints if necessary


Improved dp algorit h m

Improved DP-algorithm

DP-improved(i, j, )

Simp = DP-standard(i, j, )

V = set ofintersecting segmentsofSimpRepeat

For all segments s  VRefine(s) in SimpDo 1 refinementà la DP by adding the farthest pointV = set of intersecting segmentsofSimpUntilV is empty


Continu ous data representati on

Continuous data representation

Digital Elevation Model (DEM)

  • Data on interval or ratio measurement scale

  • Data values of points near by will usually be not very different

  • Representation is necessarily an approximation:finite representation of information with infinite detail

  • Raster (1x) or vector (2x)


Elevation model s

Elevation models

Raster

Vector

Vector

21

20

21

20

15

19

20

25

10

10

(Elevation) grid

Contourlinemodel

Triangulation(TIN; triangulatedirregular network)


Grid elevation model

Grid elevation model


Tin elevation model

TIN elevation model


Elevation model s1

Elevation models

  • Contourmodel well-suited for visualisation, not for representation or storage

  • Interpretations grid:- elevation whole cel: not a continuous model- elevation middle cel: interpolation needed; how?

  • Advantage grid: simple storage, operations simple too

  • Advantage TIN: more efficient in storage, adaptive


Interpolation for grid

20+18+18+22

= 19.5

4

Interpolation for grid

20

20

18

18

22

18

18

22

18

20

Linear interpolation; saddle point problem

18

22

20

20

18

18

22

22

18

18

Linear interpolation;additional point

Non-linear

interpolation


Topologic al tin structur e

Topological TIN structure

  • With explicit vertex and triangle representation

t2

w

t3

t1

t1

t2

t

t

v

u

u

w

t3

v

x, y-coordinatesandelevation


Topologic al tin structur e1

Topological TIN structure

  • With explicit vertex and triangle representation

t2

w

t3

t1

t1

t2

t

t

v

u

u

w

t3

v

Because t1 has pointers to two the same vertices as t, we can determine their shared edge, even though it is not represented explicitly


Topologic al tin structur e2

t

Topological TIN structure

  • With explicit vertex and triangle representation

w

w

t1

t2

t2

t1

t

v

u

t3

v

u

t3


Topologic al tin structur e3

w

t1

e1

t

u

e3

Topological TIN structure

  • Alternatively, edges have an explicit representation too

w

t1

t2

t

e1

e2

e2

e3

v

u

t3


Summary representation

Summary representation

  • Objects have geometry and attributes, at least the attributes are in a database

  • Geometry can be stored in raster or vector form; each has advantages and disadvantages

  • Important geometric types of representations are those for subdivisions and for elevation models

  • For subdivisions, the doubly-connected chain list is the most suitable structure

  • For elevation models, grids or TINs are most useful


  • Login