GIS - - the best way

to create ugly maps

FAST

GIS - - the best way

to create ugly maps

FAST

More bad maps…

Representing and Transforming

• Graphic symbols• size, symbology, value, saturation, shape, arrangement,

texture, focus

• Classification procedures are used to ease user interpretation • Natural, quantile, equal interval, s.d.

• Cartogram transformations distort area or distance for some specific reason

More examples: US Transportation Survey

Components of Geographic InformationComponents of Geographic Information

Geographic InformationGeographic Information

ThemeTheme TimeTime SpaceSpace

NominalNominal

OrdinalOrdinal

IntervalInterval

RatioRatio

PointsPoints LinesLines AreasAreas VolumesVolumes

(A Start at) a Typology of Thematic Maps(A Start at) a Typology of Thematic Maps

fixed controlled measured

geological time theme location

map

census data time location theme

weather location time theme

report

tide table theme location time

flood hydro. location time theme

grid cell data time location theme

Vector and Raster - two main families Representation of geographic information:

– Raster: location controlled, attribute measured values are stored in ordered array, so that position in the array defines geographic

location

– Vector: attribute controlled, location measured geographic coordinates are stored separately from attributes, connected with Identifiers

Geographic Data ModelsGeographic Data Models

V

(v1,v2)3 43 12 3 45

15 40 2 15 24

21 3 5 10 64

Rasters• How to represent phenomena conceived as fields or

discrete objects?• Raster

• Divide the world into square cells• Register the corners to the Earth• Represent discrete objects as collections of one or more cells• Represent fields by assigning attribute values to cells• More commonly used to represent fields than discrete objects

• Characteristics:• Pixel size

• The size of the cell or picture element, defining the level of spatial detail• All variation within pixels is lost

• Assignment scheme• The value of a cell may be an average over the cell, or a total within the

cell, or max, or min, or the commonest value in the cell, or presence/absence, or…

• It may also be the value found at the cell’s central point, or systematic analigned

Legend

Mixed conifer

Douglas fir

Oak savannah

Grassland

Raster representation. Each color represents a different value of a nominal-

scale field denoting land cover class.

The mixed pixel problem

W GW

W W G

W W G

W GG

W W G

W G G

W GE

W E G

E E G

Water dominates Winner takes all Edges separate

RASTERS…

• Each cell can be owned by only one feature.• Rasters are easy to understand, easy to read and

write, and easy to draw on the screen. A grid or raster maps directly onto an array.

• Grids are poor at representing points, lines and areas, but good at surfaces.

• Grids are a natural representation for scanned or remotely sensed data.

• Grids suffer from the mixed pixel problem.• Grid compression techniques used in GIS are run-

length encoding and quad trees.

Rasters and vectors can be flat files … if they are simple

Vector-based line

Raster-based line

4753456 6234124753436 6234244753462 6234784753432 6234824753405 6234294753401 6235084753462 6235554753398 623634

00000000000000000001100000100000101010000101000011001000010100000000100010001000000010001000010000010001000000100010000100000001011100100000000100001110000000000000000000000000

Flat File

Flat File

Compacting RasterCompacting Raster

from simple matrix to...

...run-length encoding

...row differences encoding, TIFF

...Quadtrees, Morton numbers

10

3203

1

21

Vector - Land Records

GIS

Survey

9/

/

/ / /

/

30.5’ 26.23’

20.37’ 26.23’

45.8

1’

45.8

1’

35.4

4’

R 10’

12 13

Survey point

Computation

Link

Surveyed feature

Vector Data Structure Alternatives 1Vector Data Structure Alternatives 1 Development trends:

– increasing complexity, refining logic– making geographic relationships EXPLICIT

Spaghetti files (1974...)– the original CIA format– lines and points which the

reader must organize

Polygon loops (location lists):– polygons stored as objects, polygon

shading is easy, IF CORRECT!– problems: common line defined twice;

slivers between adjacent polygons because boundaries not necessarily the same

(x1,y1)

(x2,y2)(x3,y3)

(x4,y4)

(x5,y5)(x6,y6)

Point dictionary– polygon descriptions refer to lists of fixed

points with coordinates (point dictionaries)

– similar to polygon loops, but instead of coordinates of vertices in polygon descriptions - IDs of vertices

Topological data structure– Organizes Points, Lines, and Areas as

Nodes, Chains, and Polygons– The model: nodes bound chains, chains co-bound polygons;

chains co-bound nodes, polygons co-bound chains...

– the structure stores topological relationships between nodes, chains, and polygons; these relationships are used in defining chains through nodes, polygons through chains, etc.

– Provides for contiguity, better quality control...

Vector Data Structure Alternatives 2Vector Data Structure Alternatives 2

1

23

4

5

TopologyTopology

TOPOLOGY: study of basic spatial relationships based on intuitive notions of space (those not requiring numerical measurements); fundamental level of mathematics of space;

Topology IS NOT topography– TOPOGRAPHY: measurement/representation of earth

elevation and related features (a form of general/ reference map)

Why topology in cartography/GIS– lines are coded once - avoids redundancy– data quality issue: [topo]-logical consistency

Basic arc topology

n1

n2

123 A

B

Arc From To PL PR n1x n1y n2x n2y1 n1 n2 A B x y x y

Topological Arcs File

Arc/node map data structure with files

1 1,2,3,4,5,6,7

Arcs File

POLYGON “A”

A: 1,2, Area, Attributes

File of Arcs by Polygon

1

23

4

5

6

7

8

9

10

1112

13 1 x y2 x y3 x y4 x y5 x y6 x y7 x y8 x y9 x y10 x y11 x y12 x y13 x y

Po

ints

Fil

e

1

2

2 1,8,9,10,11,12,13,7

Tracking Topological RelationshipsTracking Topological Relationships

Connectivity– nodes bound chains– chains bound polygons

in turn,– chains are bounded by nodes– polygons are bounded by chains

A

B

C

1

2

3

4

I

II

III

IV

U

V

VI

ID Vertices From To Left RightI <list> 1 4 A UII <list> 1 2 U BIII <list> 1 3 B AIV <list> 3 2 B CV <list> 4 3 A CVI <list> 2 4 U C

ID Chains1 <list>2 <list>3 <list>4 <list>

ID ChainsA <list>B <list>C <list>U <list>

Chain table

Node table

Polygon table

ID Coorda <x,y>b <x,y>c <x,y>d <x,y>… <…>

Point table

Typical Digitizing SituationsTypical Digitizing Situations

this is ideal, but...

overshoot, and what to do with it

undershoot, and what to do

• Interrelationships between semantic and spatial structures

Each string is marked withleft and right labelsTrying to assemble polygonsfrom these strings: there maybe more than one label “to the left” of all strings forming a closed polygon…a standard topological error...

However, these labels maybe in container relationship in a domain map

Planar Enforcement Is Not Enough

AutomaticAutomatic labeling results…labeling results…

12

3

4

Special Cases: 1Special Cases: 1

B: basal nucleus of Meynert B: basal nucleus of Meynert (C0004788)(C0004788)

LGP: lateral globus pallidus, LGP: lateral globus pallidus, C0262267C0262267

Basal nucleus cells (B) are Basal nucleus cells (B) are within LGP, but their precise within LGP, but their precise locations not known locations not known polygon is coded LGP, B is a polygon is coded LGP, B is a secondary descriptorsecondary descriptor

SpecialSpecial Cases: 3Cases: 3

DG: dentate gyrus, C0152314DG: dentate gyrus, C0152314 PoDG: polymorph layer of the dentate PoDG: polymorph layer of the dentate

gyrusgyrus CA1: field CA1 of hippocampus CA1: field CA1 of hippocampus

(C0019564)(C0019564) All of them have a common parent: All of them have a common parent:

hippocampus hippocampus a common parent is a common parent is used to label polygon; polylines are used to label polygon; polylines are labeled separatelylabeled separately