1. UNC at Chapel Hill, Gregory Taff
Geography 70
Spatial Data Models and Structure
11/18/2018
UNC at Chapel Hill, Gregory Taff

2. Representing the Real World
Map
Since GIS is based on the model of a map, we have covered elements of maps up to this point.
If you remember back a few lectures, I said that the three elements of a map are scale, projection and symbolization.
We’ve talked about scale.
We’ve covered projection and the elements that go along with it: geodesy and coordinate systems
Now, we come to symbolization.
11/18/2018
UNC at Chapel Hill, Gregory Taff

3. UNC at Chapel Hill, Gregory Taff
Symbolization
In a GIS, we represent real world phenomena in a digital format
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UNC at Chapel Hill, Gregory Taff

4. UNC at Chapel Hill, Gregory Taff
Vocabulary
Entity
Data objects
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UNC at Chapel Hill, Gregory Taff

5. UNC at Chapel Hill, Gregory Taff
Terminology
Entity -- a real world phenomenon to be represented in a database
There are some terms that you need to know that help describe how this real world-to-digital data conversion takes place.
Real world phenomena are known as entities.
Some entities might be:
Buildings
Forest
Roads
Coastline
Pastures
Pasture boundaries
Entities are the geographic objects in the real world that we want to represent in the GIS.
Now keep in mind, like I’ve talked about before, there are two components to geographic data: location and attributes.
We may create a representation of this road by drawing a line and assigning real world coordinates to it.
However, there are features, information, attributes of the road that also need to be assigned. Speed limit and surface type may be important attributes. Keep this in mind as I go along here.
11/18/2018
UNC at Chapel Hill, Gregory Taff

6. UNC at Chapel Hill, Gregory Taff
Terminology
Data Object -- digital representation of an entity
Pasture
So you have your Entities, your real world objects that you want to put into the GIS.
Entities are represented by Data Objects.
A data object is…
House
Road
11/18/2018
UNC at Chapel Hill, Gregory Taff

7. UNC at Chapel Hill, Gregory Taff
Summary
Data objects represent entities in a GIS.
So to summarize, you have a data model that is made up of data objects, each of which represents a real world entity.
11/18/2018
UNC at Chapel Hill, Gregory Taff

8. UNC at Chapel Hill, Gregory Taff
Topology
The relationships between data objects in space.
This relationship between objects in space, whether conceptually or logically, is known as topology.
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UNC at Chapel Hill, Gregory Taff

9. Conceptualizing Topology
Adjacency
Connectivity
Containment
Direction
Proximity
Overlap
There are three primary components of topology. They are adjacency, connectivity and containment.
There are also two other components that are important, but I consider them secondary components of topology. They are direction and proximity
Can anybody give me a definition of adjacency? Just give it a shot. It’s not a special definition.
How about connectivity?
OK. What about containment?
Direction is easy. Everyone knows where north is, right? Or do you? I’m going to do a quick test. I’m going to ask you which direction north is in from here. I will mention four landmarks around here. Everyone put your heads down.
Now raise your hand if you think the Carolina Inn is north of here.
Raise your hand if you think the Post Office downtown is north of here.
Raise your hand if you think the Forest Theater is north.
Raise your hand if you think Kenan Stadium is north. (Tally votes)
See, not everyone inherently knows directions. When objects have a topological relationship, their direction in relation to each other can be determined.
OK. Now, how about a definition of proximity.
Good. Now, I’m going to go through these using an example that everyone should be familiar with. And I have to give credit where credit is due. John Spencer came up with these examples and I’m borrowing them from him.
11/18/2018
UNC at Chapel Hill, Gregory Taff

10. UNC at Chapel Hill, Gregory Taff
Adjacency
Springfield
Shelbyville
Adjacency – this relationship describes whether or not two objects are next to one another
In this example, Springfield and Shelbyville are adjacent.
In the real world, France and Germany are adjacent; France and England are not.
11/18/2018
UNC at Chapel Hill, Gregory Taff

11. UNC at Chapel Hill, Gregory Taff
Connectivity
Connectivity – are two objects connected?
Here, Springfield is connected to South Springfield.
Real World #1 (lines): Franklin St and Columbia are connected. They intersect.
Real World #2 (areas): Chapel Hill and Raleigh are connected by I-40
Are they adjacent? No.
But, Springfield and South Springfield are both connected and adjacent. So what is the difference, if any?
Well, let’s take this adjacency vs. connectivity a step further. I may confuse you on this, but I just want to try and reinforce this idea. But it may only confuse you further.
Think back to before the fall of the Berlin Wall.
West Berlin and East Berlin were adjacent. But were they connected? Well, yes, there was a gate through the wall, but without the proper papers, you could not pass through it. So, for the majority of Berliners, the two cities were not connected. But they were definitely adjacent.
Now, let’s think of England and France. They are definitely not adjacent. The English Channel separates them. But they are connected. We can say they are physically connected, because the Chunnel (the underwater tunnel) connects them.
These roads are connected at the black points.
11/18/2018
UNC at Chapel Hill, Gregory Taff

12. UNC at Chapel Hill, Gregory Taff
Containment
Springfield
Moe’s
Kwik-E-Mart
Connectivity – describes objects that may be wholly contained within an area
Springfield contains Moe’s, the Kwik-E-Mart, and the Nuclear Plant
Real World: University Lake is contained within the area of Orange County
Nuclear
Plant
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UNC at Chapel Hill, Gregory Taff

13. UNC at Chapel Hill, Gregory Taff
Direction
Moe’s
Kwik-E-Mart
Nuclear
Plant
Moe’s is Northeast of the Kwik-E-Mart
The nuclear plant is Southeast of the Kwik-E-Mart
Direction. This is a human derived attribute. Direction is relative. Therefore, it is an important conceptual part of topology, but as you will see in a minute, it is not an important logical part of topology.
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UNC at Chapel Hill, Gregory Taff

14. UNC at Chapel Hill, Gregory Taff
Proximity
Homer lives near Ned
Homer lives far from Grampa
Proximity – how near certain objects are to each other, or far away from each other they are
This is another relative measure. Once again, it is conceptual, not logical.
It is also a derived measure. A GIS does not inherently know which objects are near each other. It is a subjective determination.
Real Sesame Street kind of stuff, but they are important measures used in geography
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UNC at Chapel Hill, Gregory Taff

15. UNC at Chapel Hill, Gregory Taff
Overlap
Blue Lake
Springfield
Adjacency – this relationship describes whether or not two objects are next to one another
In this example, Springfield and Shelbyville are adjacent.
In the real world, France and Germany are adjacent; France and England are not.
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UNC at Chapel Hill, Gregory Taff

16. UNC at Chapel Hill, Gregory Taff
Review
Topology
The relationships between data objects in space.
This relationship between objects in space, whether conceptually or logically, is known as topology.
11/18/2018
UNC at Chapel Hill, Gregory Taff

17. UNC at Chapel Hill, Gregory Taff
2 GIS Data Models
Entities in the real world are represented as one of the following in a GIS:
Vector data:
Points
Lines
Areas (or polygons)
Raster data
Pixels in an array
Key concept!
11/18/2018
UNC at Chapel Hill, Gregory Taff

18. Raster data model (details later)
The raster data model represents the Earth’s surface as a two-dimensional array of grid cells, with each cell having an associated value: 1 2 3 5 8 4 6 9 7
Cell (x,y)
Cell value
rows
Cell size = resolution
columns
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UNC at Chapel Hill, Gregory Taff

19. UNC at Chapel Hill, Gregory Taff
Raster data example
Elevation data: each cell contains a number representing the elevation of that cell.
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UNC at Chapel Hill, Gregory Taff

20. UNC at Chapel Hill, Gregory Taff
The vector data model
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UNC at Chapel Hill, Gregory Taff

21. Vector Data Objects Geographic building blocks Points Lines Polygons
0 dimensional
Lines
1 dimensional
Polygons
2 dimensional
The vector model is composed of three basic spatial objects, known as geographic primitives.
They are known as this because they are the basis of geographic entities.
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UNC at Chapel Hill, Gregory Taff

22. UNC at Chapel Hill, Gregory Taff
Spatial Objects
Data objects in the vector data model can be:
A point can represent:
Tree, airport, a city, street intersection, a movie theater, a benchmark
A line is a data object, made up of a connected sequence of points. It can represent:
Roads, rivers, regional boundaries, fences, hedgerows, power lines
A polygon is an enclosed area. Examples:
A census tract, Saunders building, boundary of Chapel Hill, a lake, a watershed, a city
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UNC at Chapel Hill, Gregory Taff

23. UNC at Chapel Hill, Gregory Taff
Object example: oak tree
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UNC at Chapel Hill, Gregory Taff

24. UNC at Chapel Hill, Gregory Taff
Thought question:
How are you going to represent the California OAK tree in digital format?
A point? A polygon? Or a pixel?
It will depend on:
Scale of observation
Purpose of your research
The type of data you have access to in the GIS
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UNC at Chapel Hill, Gregory Taff

25. UNC at Chapel Hill, Gregory Taff
Thought questions:
When do you want to represent Chapel Hill as a polygon object instead of a point object?
When do you want to represent a river as a polygon instead of a line?
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UNC at Chapel Hill, Gregory Taff

26. UNC at Chapel Hill, Gregory Taff
The vector data objects
(x,y)
(x,y)
(x,y)
(x,y)
(x,y)
(x,y)
(x,y)
(x,y)
(x,y)
(x,y)
(x,y)
point
line
polygon(area)
The vector data model represents geographic features similar to the way maps do
A point: recorded by a pair of (x,y) coordinates.
A line: recorded by joining more than one point,
A polygon: recorded by a joining multiple points that enclose an area
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UNC at Chapel Hill, Gregory Taff

27. UNC at Chapel Hill, Gregory Taff
Vector Data Storage in Computers: Points
Data Storage
Points
Point ID Coordinates +4
, 1
, 2
, 2
, 4 +2 +3 +1
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UNC at Chapel Hill, Gregory Taff

28. UNC at Chapel Hill, Gregory Taff
Vector Data Storage in Computers: Lines
(Sometimes called arcs)
Line # Coordinates
① (x1, y1)
(x2,y2)
② (x2,y2)
(x3,y3)
(x1,y1)
(x2,y2)
(x3,y3) ② ①
Note: In GIS, this is considered a line (a connected set of individual lines).
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UNC at Chapel Hill, Gregory Taff

29. UNC at Chapel Hill, Gregory Taff
Vector Data Storage in Computers: Polygons
Polygon # Coordinates
① (x1,y1)
(x2,y2)
(x3,y3)
(x4,y4)
② (x3,y3)
(x5,y5)
(x6,y6)
(x1,y1)
(x2,y2)
(x3,y3)
(x4,y4)
(x6,y6)
(x5,y5) ① ②
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UNC at Chapel Hill, Gregory Taff

30. UNC at Chapel Hill, Gregory Taff
The Arc-Node Data Structure
Benefit:
The arc-node structure allows efficient data storage for vector data
How does it work?
It stores data so that nodes construct arcs, and arcs construct polygons
Nodes define the two endpoints of an arc. They may or may not connect
two or more arcs.
An arc is the line segment between two nodes. The points between two nodes
defining the shape of an arc are called vertices. Nodes and vertices are
represented as x, y coordinates.
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UNC at Chapel Hill, Gregory Taff

31. UNC at Chapel Hill, Gregory Taff
The Arc-Node Data Structure 2 3
Arc: ①, ②, ③
Nodes: 2, 5
Vertices: 1, 6 for arc ①
3, 4 for arc ② 1 ③ B ② A ① 4 5 6
Arc # Start Node Vertices End Node , ,
Points
1 x1,y1
2 x2,y2
3 x3,y3
x4,y4
5 x5,y5
6 x6,y6
Polygon arc list
A ①, ③
B ②, ③
11/18/2018
UNC at Chapel Hill, Gregory Taff

32. Arc-Node Data Structure: enables Topology definition
Topology defines spatial relationships. The arc-node data structure supports
three major topological concepts:
Connectivity:
Arcs connect to each other at nodes
Area definition:
Arcs that connect to surround an area define a polygon
Contiguity:
Arcs have direction and left and right sides
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UNC at Chapel Hill, Gregory Taff

33. UNC at Chapel Hill, Gregory Taff
Topology: Connectivity
Connected arcs are determined by searching through the list for common
node numbers.
Arc-node list 10 11 12 ① ②
Arc From-Node To-Node ③ ⑤ 13 14 ④ 15
Because of the common node 11, arcs 1, 2, and 3 all intersect. The computer
can determine that it is possible to travel along arc 1 and turn onto arc 3. But it
is not possible to turn directly from arc 1 to arc 5.
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UNC at Chapel Hill, Gregory Taff

34. UNC at Chapel Hill, Gregory Taff
Topology: Area Definition
Polygon-Arc Topology 1 8 B
Polygon Arc List
B ,5,8,4
C ,6,9,5
D ,3,4,7
E ,7,8 5 C 4 2 E 9 D 6 7 3
Polygons are simply the list of arcs defining its boundary, arc coordinates
are stored only once, therefore, reducing the amount of data and ensuring
that the boundaries of adjacent polygons don’t overlap
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UNC at Chapel Hill, Gregory Taff

35. UNC at Chapel Hill, Gregory Taff
Topology: Contiguity
Two geographic features which share a boundary are called
adjacent. Contiguity is the topological concept which allows
the vector data model to determine adjacency.
An Arc
left
From-Node
To-Node
right
Direction 1 8 B
Arc Left Right
Polygon Polygon
C B
E C
? ?
? ? 5 C 4 2 E 9 D 6 7 3
11/18/2018
UNC at Chapel Hill, Gregory Taff