1Lecture 2 1

L2 –Data ModelsCh. 2, pp 25-53

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1.2 , 4 .75 .8 , 3 .68 .9 , 7 .2..

Real W or ldDat a M odel Dat a

S t r uct ur e

Phenomena/entities that exist in the realworld

An abstraction, relevant phenomena and properties

Computer Representation

Machine Code

10011101

00110110

10110100

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Data Model

• The spatial data model provides a formal means of representing and manipulating spatially-referenced information.

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http://webhelp.esri.com/arcgisserver/9.3/java/index.htm#geodatabases/an_over-776141322.htm

Thematic Layers• A logical

separation of data according to theme.

• Each layer reflects a particular use or characteristic.

• Overlays.

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Coordinates

• Coordinates are used to define the location and extent of our geographic object.

• Coordinates are either (x,y) or (x,y,z).

• Polygon [(8,10), (14,5), (5,15), (1, 8), (3,12), (8,10)]

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Coordinate Data

• Latitude & Longitude– Origin (intersection of

the Equator and Greenwich meridian)

• Spherical Coordinates– Deg., min., sec. (DMS)– Decimal degrees (DD)

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Conversion

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368.5833

3600

57

60

4868

360060

SECMIN

DEGDD

Convert: 68o 48’ 57” to decimal degrees:

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Types of Attribute Data• Attribute data record the non-spatial characteristics of an

entity.• Attributes have values

– Observed – Measured

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Llbean.com

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Measurement of Attributes

• Physical scientists define measurement as the comparison of an object to a standard object.

• They define two types of measurements– Extensive/Fundamental Properties (feet)– Derived – by combining extensive properties

(feet/second)

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Stevens’ Levels of Measurement

• Social scientists weren’t satisfied with this classification

• Stanley Stevens (1946) proposed a framework for measurement types based upon “levels of measurement”.

• He defined measurement as being the assignment of classes or scores to phenomena according to a set of rules.

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Stevens’ Levels of Measurement

• There are four basic levels according to Stevens: – Nominal – provides descriptive information.– Ordinal – implies a rank order.– Interval – implies order and difference in

magnitude.– Ratio - implies order and difference in

magnitude and has an absolute 0.

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Ordinal

• Ordinal Measurement sorts objects in an order or ranked category.

• For example, the order of finish in a race, someone gets first place, second place, third place, and so on.

• Each object gets categorized based on its position relative to others, ordinal would not measure when, but where in relation to others.

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Ordinal

• You can do comparisons:– If A>B and B>C then the correct increasing

order is C, B, A; i.e., establish order

• You can establish equality between two orders.

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Interval

• Interval Measurement puts the object on a number line, so instead of just knowing where, someone finished in relation to others, would also know when, they finished.

• But, the number line does not have a zero value, the number line starts arbitrarily.

• It would be like writing the times of finish by just looking at a watch, and noting the time they came in. You would know how long between each runner, but not how long the race took over all.

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Interval

• Operations include:– Count– Equality– Order– Addition and Subtraction

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Ratio

• Ratio Measurement adds the how long, the number line gets a zero value.

• So you would know how long and when, and where each runner comes in.

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Ratio

• Operations:– Count– Equality– Order– Addition and Subtraction– Multiplication and Division– Higher order operations

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Additional Levels of Measurement

• Nicholas Chrisman includes several more in his textbook "Exploring Geographic Information Systems."

• I will add those here:– Absolute scales – scales bounded on both ends like

probability– Cyclical measures – angular measure– Counts are misfits. They are not continuous, but

otherwise behave as a ratio scale– Graded membership in categories – Fuzzy set theory;

i.e., not all membership within a class must be equal.

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Common Spatial Data Models

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Raster & Vector Image

http://www4.ncsu.edu/~hmitaso/gmslab/hohen2/w2elev10.gif

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Vector & Raster

• Vector is better at representing discrete features.

• Raster is better at representing continuous features

• A project may contain both vector and raster layers.

• Spatial operations can only be performed on one type of layer.

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Vector & Raster (cont’d)

• The best data model for a given layer depends upon the operations, the experience and the views of the user.

• No decision is final, as one can be converted to the other.

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Other Data Models

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Vector Data Raster Data

Non-topological Topological

Simple DataHigher-level Data

TIN Regions Dynamic Segmentation

Spatial Data

    

 

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Vector Terminology

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Polygon Inclusions

• Areas in polygons that are part of the polygon, but different from the rest of the polygon: e.g. Islands in a lake.

• Solutions:– Create separate polygons for each inclusion.– Create an attribute column for coding

inclusions.

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Vector TopologyTopology – geometric properties that to not change with shape: Adjacency, Connectivity, Containment

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Topology in the object data model is a set of rules and software tools to define spatial relationships an behaviors, such as:– Polygons must not overlap within a dataset.– Lines must not overlap themselves within a

data set.

Topology

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PointsPoint ID X Y 1 32.7 45.6 2 76.3 19.5 3 22.7 15.8etc…..

1 2

3 4

Organization

Lines6

9

1

239

AB

C Line Begin End ID Point Point A 6 9 B 9 1 C 239 1etc…..

Polygons

13

22

41954

11

12

52

53

PolygonID Lines

A 11, 12, 52, 53, 54

B 52, 53, 9, 41, 22, 13

Three Types of Vector Features

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Advantages of Topology

• Maintain correct data spatial relationship (Find errors)

• Efficient data storage (quickly process large data sets)

• Facilitate spatial analysis (Network analysis, Adjacent area analysis, overlay analysis

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Encoding Topological Primitives

Polygon Bounding Arcs

A (e,f,g,i,j) (h) (k)

B (a,b,c,-i)

C (-c,d,-j)

D (-k)

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Arc Bounding Nodes Left Poly Right Poly

a 1,2 - B

b 2,3 - B

c 3,5 C B

d 3,4 - C

…

k 9,9 D A

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Nodes Co-bounding Arcs

1 a,i,-g

2 -a,b

3 -b,d,c

4 -j,d,e

5 -c,j,-i

6 -e,f

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Raster Coordinates

• Coordinate of upper (lower) left corner.

• Cell size (Width, Height) – usually square

• (Row, Column)

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http://www.codeproject.com/Articles/44389/Build-a-Desktop-GIS-Application-Using-MapWinGIS

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Calculation

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(16,23)

10

10

27)10(523

56)10(416

y

x

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Raster – The Storage Space/Resolution Tradeoff

Decreasing the Cell Size by one-halfcauses aFour-fold increase in the storage space required

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Rasters – Discrete or Continuous Features

discrete continuous

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Raster – The Mixed Pixel Problem

Landcover map –Two classes, land or water

Cell A is straightforward

What category to assignFor B, C, or D?

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Raster Feature & Attribute Tables

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Raster Feature & Attribute Tables

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Raster Feature & Attribute Tables

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Raster vs. Vector

• Most current GIS packages have both raster and vector capabilities.

• A project may use both spatial data models, but they cannot be combined for analysis.

• They are usually better adapted for handling one over the other.

• There are advantages and disadvantages to each.

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Raster vs Vector 

Characteristics Positional Precision

 Attribute Precision

 Analytical Capabilities   Data Structures

 Storage Requirements Coordinate conversion Network Analyses

 Output Quality

   

 Can be Precise

 Defined by cell size

 Poor for continuous data

 Good for continuous data

Good for spatial query, adjacency, area, shape analyses. Poor for continuous data. Most analyses limited to intersections. Slower overlays.

Spatial query more difficult, good for local neighborhoods, continuous variable modeling. Rapid overlays.

 Often complex

 Often quite simple

 Relatively small

 Often quite large

 Usually well-supported

 Often difficult, slow

 Easily handled

 Often difficult

 Very good, map like

 Fair to poor - aliasing

Vector Raster

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No Decision is Final – We Can Convert

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Triangulated Irregular Networks

• TINs

• Typically used to represent elevations.

• Require x,y & z coordinates.

• A TIN forms a connected network of triangles (Delaunay triangles)

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BUILDING A TIN

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TIN Parts

Points – sample locations

Edges – connecting lines

Facets – triangles, “faces”

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TIN – Triangle Formation

TIN triangles defined such that

•Three points on a circle•Circles are empty – they don’t contain another point

These are convergent circles

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Digital Elevation Models

• DEM is point based with elevation at center of a cell.

• Each file contains– Elevation, – Header: units, min/max elev, proj, accuracy

• Four types– 7.5 minute DEM (30 or 10 meter)– 30 minute DEM (60 meter)– 1 degree DEM (100 meter)– Alaska DEMs

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DEM

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http://rylincolnblaisdell.blogspot.com/2010_12_01_archive.html

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Figure 3.31 Examples of true 3D data structuresSources: (a) Rockware Inc., with permission; (b) Centre for Advanced Spatial Analysis (CASA), University College London, with permission

Modeling in the Third Dimension

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3 D Demo

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Modeling the Fourth Dimension

Four temporal attributes:

1. Generation time

2. Duration time

3. Temporal significance

4. Temporal scale

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Possible Changes of Spatiotemporal Relationships over Time

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Time Slider Demo

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Animation Demo

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