Transcript Maps as Numbers

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 Information
Geographic Information
Theme
Time
Space
Points
Nominal
Ordinal
Interval
Ratio
Lines
Areas
Volumes
(A Start at) a Typology of Thematic
Maps
fixed
controlled
measured
geological time
theme
location
map
census datatime
location theme
weather
location time
theme
report
tide table theme location time
Geographic Data Models
Vector and Raster - two main families
 Representation of geographic
information:

– Raster: location controlled, attribute
measured
 values
3
43
are stored in ordered array, so that
position in the array defines geographic
location
12 3
45
21
3
5
(v1,v2)
–
Vector:
attribute
controlled,
location
15 40 2 15
24
V
measured
10
64
 geographic
coordinates are stored separately
from attributes, connected with Identifiers
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 nominalscale field denoting land cover class.
The mixed pixel problem
Water dominates
Winner takes all
Edges separate
W W
G
W G
G
W
E
G
W W
G
W W
G
W
E
G
W W
G
W G
G
E
E
G
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 runlength encoding and quad trees.
Rasters and vectors can be flat files
… if they are simple
Vector-based line
Raster-based line
Flat File
4753456
4753436
4753462
4753432
4753405
4753401
4753462
4753398
623412
623424
623478
623482
623429
623508
623555
623634
Flat File
0000000000000000
0001100000100000
1010100001010000
1100100001010000
0000100010001000
0000100010000100
0001000100000010
0010000100000001
0111001000000001
0000111000000000
0000000000000000
Compacting Raster

from simple matrix to...
...run-length encoding
...row differences encoding, TIFF
...Quadtrees, Morton numbers
0
203
1
3
1
21
Vector - Land Records
Surveyed feature
20.37’
26.23’
13
12
30.5’
26.23’
GIS
Survey
Link
/
Survey point
/
/
/
/
/
9
Computation
Vector 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)
(x5,y5)
(x4,y4)
(x6,y6)
Vector Data Structure Alternatives 2

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
1
2
3
5
4
– 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...
Topology

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
3
n2
2
A
1
n1
B
Topological Arcs File
Arc
1
From To PL PR n1x n1y n2x n2y
n1 n2 A B x y
x y
13
11
2
12
10
7
POLYGON “A” 5
9
4
2
1
6
3
8
1
1xy
2xy
3xy
4xy
5xy
6xy
7xy
8xy
9xy
10 x y
11 x y
12 x y
13 x y
Points File
Arc/node map data structure with files
File of Arcs by Polygon
A: 1,2, Area, Attributes
1 1,2,3,4,5,6,7
2 1,8,9,10,11,12,13,7
Arcs File
Tracking Topological Relationships

Connectivity
– nodes bound chains
– chains bound polygons
in turn,
– chains are bounded by nodes
– polygons are bounded by chains
Node table
ID
1
2
3
4
1
III
2
B
3
IV
A
I
U
II
V
C
VI
4
Point table
ID
a
b
c
d
…
Chains
<list>
<list>
<list>
<list>
Polygon table
ID Chains
A
<list>
B
<list>
C
<list>
U
<list>
Coord
<x,y>
<x,y>
<x,y>
<x,y>
<…>
Chain table
ID
I
II
III
IV
V
VI
Vertices
<list>
<list>
<list>
<list>
<list>
<list>
From
1
1
1
3
4
2
To
4
2
3
2
3
4
Left
A
U
B
B
A
U
Right
U
B
A
C
C
C
Typical Digitizing Situations
this is ideal, but...
undershoot,
and what to do
overshoot, and what
to do with it
Planar Enforcement Is Not Enough
• Interrelationships between semantic and spatial
structures
Each string is marked with
left and right labels
Trying to assemble polygons
from these strings: there may
be more than one label
“to the left” of all strings
forming a closed polygon…
a standard topological error...
However, these labels may
be in container relationship
in a domain map
Automatic labeling results…
3
4
1
2
Special Cases: 1
B: basal nucleus of
Meynert (C0004788)
 LGP: lateral globus
pallidus, C0262267
 Basal nucleus cells (B) are
within LGP, but their
precise locations not
known  polygon is
coded LGP, B is a
secondary descriptor

Special Cases: 3




DG: dentate gyrus, C0152314
PoDG: polymorph layer of the dentate gyrus
CA1: field CA1 of hippocampus (C0019564)
All of them have a common parent:
hippocampus  a common parent is used
to label polygon; polylines are labeled
separately