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Spatial Data Models and Spatial Data Models and StructureStructure
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Part 1: Basic Geographic Part 1: Basic Geographic ConceptsConcepts
• Real world -> Digital Environment– GIS data represent a simplified view of
physical phenomena
• These data contain:– Locational Information– Non-spatial attributes
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SymbolizationSymbolization
• In a GIS, we represent real world phenomena in a digital format
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VocabularyVocabulary
• Real-World Entities or Phenomena• Data Objects• Cartographic Objects
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TerminologyTerminology
• Entities or Phenomenon -- real world features to be represented in a database
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TerminologyTerminology
• Data Objects -- digital representations of entities or phenomena
Pasture
Road
House
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TerminologyTerminology• Cartographic Objects -- real-world entities as depicted on maps
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Real World Real World Data Objects Data Objects
• Attributes– Information about object (e.g., characteristics)
• Location/Spatial information– Coordinates– May contain elevation information
• Time– When collected/created– Why? Objects may have different attributes over
time
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Real World Real World Cartographic Cartographic ObjectsObjects
• Real world objects differ in:– Size– Shape– Color– Pattern
• These differences affect how these objects are represented on maps
• Where possible the cartographic objects (i.e., map symbols) can relate to the entities they are representing (e.g., water = blue)
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TopologyTopology
• The spatial relationships between data objects
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Conceptualizing TopologyConceptualizing Topology
• Primary– Adjacency– Connectivity– Containment
• Secondary– Direction– Proximity (distance)
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AdjacencyAdjacency
SpringfieldSpringfield
ShelbyvilleShelbyville
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ConnectivityConnectivity
These roads are connected at the black points.
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ContainmentContainment
Moe’sMoe’s
Kwik-E-MartKwik-E-Mart
NuclearNuclearPlantPlant
SpringfieldSpringfield
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DirectionDirection
Moe’s is Northeast of Moe’s is Northeast of the Kwik-E-Martthe Kwik-E-Mart
The nuclear plant is The nuclear plant is Southeast of the Kwik-E-Southeast of the Kwik-E-MartMart
Moe’sMoe’s
Kwik-E-MartKwik-E-Mart
NuclearNuclearPlantPlant
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ProximityProximity
Homer lives near NedHomer lives near Ned
Homer lives far from Homer lives far from GrampaGrampa
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Complex Case: OverlapComplex Case: Overlap
SpringfieldSpringfield
Blue Lake
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• Entities in the real world are represented as one of the following in a GIS:– Raster data
• Pixels in an array
– Vector data• Points• Lines• Areas (or polygons)
Part 2: GIS Data ModelsPart 2: GIS Data Models
Key concept!
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• “The continuous field view represents the real world as a finite number of variables, each one defined at every possible position. “
• “The discrete object view represents the geographic world as objects with well-defined boundaries in otherwise empty space. “
Continuous & DiscreteContinuous & Discrete
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Continuous & DiscreteContinuous & Discrete
• Some data types may be presented as either discrete or continuous– Example
• Population at a point (discrete) • Population density surface for an area
(continuous)
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Continuous & Continuous & Discrete Discrete
• Continuous – Data values distributed across a surface
w/out interruption – Key words: What varies and how smooth? – Examples: elevation, temperature
• Discrete– with well-defined boundaries in otherwise
empty space– Examples
• Points: Town, power pole• Lines: Highway, stream• Areas: U.S. Counties, national parks
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Continuous or Discrete?Continuous or Discrete?
www.regional.org.au/au/asa/2003/i/6/walcott.htm
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Continuous & DiscreteContinuous & Discrete
• In computer databases – Raster data models represent
continuous data– Vector data model are used for discrete
objects
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Cell (x,y)
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 8 3 9
3 5 3 3 1
7 5 4 3 9
2 2 4 5 2
Cell value
Cell size = resolution
columns
row
sRaster Data ModelRaster Data Model
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Raster data exampleRaster data example
Elevation data: each cell contains a number representing the elevation of that cell.
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Part 3: The vector data model
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Vector Data ObjectsVector Data Objects
Geographic building blocks
• Points
– 0 dimensional
• Lines
– 1 dimensional
• Polygons
– 2 dimensional
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Spatial ObjectsSpatial 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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Object example: oak tree
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Thought question: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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– 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?
Thought questions:Thought questions:
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point line polygon(area)
(x,y)
(x,y)
(x,y)(x,y) (x,y)
(x,y)
(x,y)
(x,y)(x,y)
(x,y)
The vector data objects
• 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
(x,y)
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Vector Data Storage in Computers: Points
Points Data Storage
+1+2 +3
+4
Point ID Coordinates
1 1, 12 4, 23 6, 2 4 2, 4
0
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(x1,y1)
(x2,y2)
(x3,y3)
②
①
Line # Coordinates ① (x1, y1) (x2,y2)
② (x2,y2) (x3,y3)
Note: In GIS, this is considered a line (a connected set of individual lines).
Vector Data Storage in Computers: Lines(Sometimes called arcs)
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(x1,y1)
(x2,y2)
(x3,y3)
(x4,y4)
(x6,y6)
(x5,y5)
① ②
Polygon # Coordinates ① (x1,y1) (x2,y2) (x3,y3) (x4,y4)
② (x3,y3) (x4,y4) (x5,y5) (x6,y6)
Vector Data Storage in Computers: Polygons
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The Arc-Node Data Structure
The arc-node structure allows efficient data storage for vector dataBenefit:
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 nodesdefining the shape of an arc are called vertices. Nodes and vertices are represented as x, y coordinates.
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1
65
2
4
3
①②③
Arc: , , ① ② ③ Nodes: 2, 5Vertices: 1, 6 for arc ① 3, 4 for arc ②
Arc # Start Node Vertices End Node
1 2 1,6 52 2 3,4 53 2 5
Polygon arc listA , ① ③B , ② ③
A B
Points1 x1,y12 x2,y23 x3,y34 x4,y45 x5,y56 x6,y6
The Arc-Node Data Structure
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Topology defines spatial relationships. The arc-node data structure supports three major topological concepts:
Connectivity: Arcs connect to each other at nodesArea definition: Arcs that connect to surround an area define a polygonContiguity: Arcs have direction and left and right sides
Arc-Node Data Structure: enables topology definitionenables topology definition
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Topology: Connectivity
10 11 12
13 14
15
⑤
① ②
③
④
Arc From-Node To-Node1 10 112 11 123 11 134 13 155 13 14
Arc-node list
Connected arcs are determined by searching through the list for common node numbers.
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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Topology: Area Definition
BC
D
E
1
2
3
4
5
67
8
9
Polygon Arc List B 1,5,8,4 C 2,6,9,5 D 6,3,4,7 E 9,7,8
Polygon-Arc Topology
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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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 ArcFrom-Node To-Node
Direction
left
right
BC
D
E
1
2
3
4
5
67
8
9
Arc Left Right Polygon Polygon5 C B9 E C10 ? ? 1 ? ?