Spatial Data Models and Structure

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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


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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


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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• 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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• 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

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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 ? ?

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Spatial Data Models and Structure