Noriel Christopher C' Tiglao, Dr' Eng

1
Spatial Data Representation and Analysis
Module 3

• Noriel Christopher C. Tiglao, Dr. Eng
• 24 January 4 February 2005
• Statistical Research and Training Center (SRTC)
• Quezon City, Metro Manila

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Presentation Outline

• Introduction
• Spatial Data and Spatial Relationships
• Sampling Reality
• Scales of Measurement
• Data Sources and Errors
• Data Abstraction
• Spatial Data Structures

3
Introduction

• The world is infinitely complex
• The contents of a spatial database represent a
  particular view of the world
• User sees the real world through the medium of
  the database
• The measurements and samples contained in the
  database must present as complete and accurate a
  view of the world as possible

4
Introduction (contd.)

• The contents of the database must be relevant in
  terms of
• themes and characteristics captured
• the time period covered
• the study area

5
Representing Reality

• A database consists of digital representations of
  discrete objects
• The features shown on a map, e.g. lakes,
  benchmarks, contours can be thought of as
  discrete objects
• The contents of a map can be captured in a
  database by turning map features into database
  objects

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Representing Reality (contd.)

• Many of the features shown on a map are
  fictitious and do not exist in the real world
• contours do not really exist, but houses and
  lakes are real objects
• The contents of a spatial database include
• digital versions of real objects, e.g. houses
• digital versions of artificial map features, e.g.
  contours
• artificial objects created for the purposes of
  the database, e.g. pixels

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Data

• Data are facts
• some facts are more important to us than others.
  Some facts are important enough to warrant
  keeping track of them in a formal, organized way
• "Data" is a broad concept that can include things
  such as pictures (binary images), programs, and
  rules
• Informally, data are the things you want to store
  in a database

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Spatial vs. Non-spatial Data

• Spatial data includes location, shape, size, and
  orientation
• Spatial data includes spatial relationships
• Non-spatial data (also called attribute or
  characteristic data) is that information which is
  independent of all geometric considerations

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Spatial vs. Non-spatial Data (contd.)

• It is possible to ignore the distinction between
  spatial and non-spatial data. However, there are
  fundamental differences between them
• spatial data are generally multi-dimensional and
  autocorrelated.
• non-spatial data are generally one-dimensional
  and independent

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Spatial vs. Non-spatial Data (contd.)

• These distinctions put spatial and non-spatial
  data into different philosophical camps with
  far-reaching implications for conceptual,
  processing, and storage issues.
• For example, sorting is perhaps the most common
  and important non-spatial data processing
  function that is performed
• It is not obvious how to even sort locational
  data such that all points end up nearby their
  nearest neighbors

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Spatial Relationships

• Describe the association among different features
  in space
• are visually obvious when data are presented in
  the graphical form
• however, it is difficult to build spatial
  relationships into the information organization
  and data structure of a database

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Spatial Relationships (contd.)

• Difficulty in capturing spatial relationships in
  a database
• there are numerous types of spatial relationships
  possible among features
• recording spatial relationships implicitly
  demands considerable storage space
• computing spatial relationships on-the-fly slows
  down data processing particularly if relationship
  information is required frequently

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Point-Line-Area Relationship Matrix
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Spatial Relationships (contd.)

• Topological
• describes the property of adjacency, connectivity
  and containment of contiguous features
• Proximal
• describes the property of closeness of
  non-contiguous features

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Spatial Relationships (contd.)

• Spatial relationships are very important in
  geographical data processing and modeling
• the objective of information organization and
  data structure is to find a way that will handle
  spatial relationships with the minimum storage
  and computation requirements

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Spatial Data

• Phenomena in the real world can be observed in
  three modes spatial, temporal and thematic
• the spatial mode deals with variation from place
  to place
• the temporal mode deals with variation from time
  to time (one slice to another)
• the thematic mode deals with variation from one
  characteristic to another (one layer to another)

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Spatial Data (contd.)

• All measurable or describable properties of the
  world can be considered to fall into one of these
  modes - place, time and theme
• An exhaustive description of all three modes is
  not possible

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Spatial Data (contd.)

• When observing real-world phenomena we usually
  hold one mode fixed, vary one in a controlled
  manner, and measure the third (Sinton, 1978)
• e.g. using a census of population we could fix a
  time such as 1990, control for location using
  census tracts and measure a theme such as the
  percentage of persons owning automobiles

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Spatial Data (contd.)

• Holding geography fixed and varying time gives
  longitudinal data
• Holding time fixed and varying geography gives
  cross- sectional data
• The modes of information stored in a database
  influence the types of problem solving that can
  be accomplished

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Location

• The spatial mode of information is generally
  called location

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Attributes

• Attributes capture the thematic mode by defining
  different characteristics of objects
• A table showing the attributes of objects is
  called an attribute table
• each object corresponds to a row of the table
• each characteristic or theme corresponds to a
  column of the table
• thus the table shows the thematic and some of the
  spatial modes

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Time

• The temporal mode can be captured in several ways
  
• by specifying the interval of time over which an
  object exists
• by capturing information at certain points in
  time
• by specifying the rates of movement of objects

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Time (contd.)

• Depending on how the temporal mode is captured,
  it may be included in a single attribute table,
  or be represented by series of attribute tables
  on the same objects through time

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Sampling Reality

• Numerical values may be defined with respect to
  nominal, ordinal, interval, or ratio scales of
  measurement
• It is important to recognize the scales of
  measurement used in GIS data as this determines
  the kinds of mathematical operations that can be
  performed on the data

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Sampling Reality (contd.)
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Marathon Example
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Sampling Reality (contd.)

• Distinctions, though important, are not always
  clearly defined
• Is elevation interval or ratio? if the local base
  level is 750 feet, is a mountain at 2000 feet
  twice as high as one at 1000 feet when viewed
  from the valley?
• Many types of geographical data used in GIS
  applications are nominal or ordinal
• Values establish the order of classes, or their
  distinct identity, but rarely intervals or ratios
  

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Sampling Reality (contd.)

• Thus you cannot
• multiply soil type 2 by soil type 3 and get soil
  type 6
• divide urban area by the rank of a city to get a
  meaningful number
• subtract suitability class 1 from suitability
  class 4 to get 3 of anything
• However, you can
• divide population by area (both ratio scales) and
  get population density
• subtract elevation at point a from elevation at
  point b and get difference of elevation

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Multiple Representations

• A data model is essential to represent
  geographical data in a digital database
• There are many different data models
• The same phenomena may be represented in
  different ways, at different scales and with
  different levels of accuracy
• Thus there may be multiple representations of the
  same geographical phenomena

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Multiple Representations (contd.)

• It is difficult to convert from one
  representation to another
• e.g. from a small scale (1250,000) to a large
  scale (110,000)
• Thus it is common to find databases with multiple
  representations of the same phenomenon
• this is wasteful, but techniques to avoid it are
  poorly developed

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Primary Data Sources

• Some of the data in a spatial database may have
  been measured directly
• e.g. by field sampling or remote sensing
• The density of sampling determines the resolution
  of the data
• e.g. samples taken every hour will capture
  hour-to- hour variation, but miss shorter-term
  variation
• e.g. samples taken every 1 km will miss any
  variation at resolutions less than 1 km

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Primary Data Sources (contd.)

• A sample is designed to capture the variation
  present in a larger universe
• e.g. a sample of places should capture the
  variation present at all possible places
• e.g. a sample of times will be designed to
  capture variation at all possible times

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Sampling Approaches

• In a random sample, every place or time is
  equally likely to be chosen
• Systematic samples are chosen according to a
  rule, e.g. every 1 km, but the rule is expected
  to create no bias in the results of analysis,
  i.e. the results would have been similar if a
  truly random sample had been taken

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Sampling Approaches (contd.)

• In a stratified sample, the researcher knows for
  some reason that the universe contains
  significantly different sub-populations, and
  samples within each sub-population in order to
  achieve adequate representation of each
• e.g. we may know that the topography is more
  rugged in one part of the area, and sample more
  densely there to ensure adequate representation
• if a representative sample of the entire universe
  is required, then the subsamples in each
  subpopulation will have to be weighted
  appropriately

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Secondary Data Sources

• Some data may have been obtained from existing
  maps, tables, or other databases
• To be useful, it is important to obtain
  information in addition to the data themselves
• information on the procedures used to collect and
  compile the data
• information on coding schemes, accuracy of
  instruments

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Secondary Data Sources (contd.)

• Unfortunately such information is often not
  available
• a user of a spatial database may not know how the
  data were captured and processed prior to input
• this often leads to misinterpretation, false
  expectations about accuracy

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Data Standards

• Standards may be set to assure uniformity
• within a single data set
• across data sets
• e.g. uniform information about timber types
  throughout the database allows better fire
  fighting methods to be used, or better control of
  insect infestations
• Data capture should be undertaken in standardized
  ways that will assure the widest possible use of
  the information

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Sharing Data

• It is not uncommon for as many as three agencies
  to create databases with, ostensibly, the same
  information
• e.g. a planning agency may map landuse, including
  a forested class
• e.g. the state department of forestry also maps
  forests
• e.g. the wildlife division of the department of
  conservation maps habitat, which includes fields
  and forest

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Sharing Data (contd.)

• Each may digitize their forest class onto
  different GIS systems, using different protocols,
  and with different definitions for the classes of
  forest cover
• this is a waste of time and money
• Sharing information gives it added value
• Sharing basic formats with other information
  providers, such as a department of
  transportation, might make marketing the database
  more profitable

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Errors and Accuracy

• There is a nearly universal tendency to lose
  sight of errors once the data are in digital form
  
• are implanted in databases because of errors in
  the original sources (source errors)
• are added during data capture and storage
  (processing errors)
• occur when data are extracted from the computer
• arise when the various layers of data are
  combined in an analytical exercise

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Errors in Sources

• Are extremely common in non-mapped source data,
  such as locations of wells, or lot descriptions
• Can be caused by doing inventory work from aerial
  photography and misinterpreting images
• Often occur because base maps are relied on too
  heavily

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Classification Errors

• Are common when tabular data are rendered in map
  form
• Simple typing errors may be invisible until
  presented graphically
• More complex classification errors may be due to
  the sampling strategies that produced the
  original data

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Data Capture Errors

• Manual data input induces another set of errors
• Eye-hand coordination varies from operator to
  operator and from time to time
• Data input is a tedious task - it is difficult to
  maintain quality over long periods of time

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Accuracy Standards

• Many agencies may not have established accuracy
  standards for geographical data
• these are more often concerned with accuracy of
  locations of objects than with accuracy of
  attributes
• Higher accuracy requires better source materials
• is the added cost justified by the objectives of
  the study?
• Accuracy standards should be determined by
  considering both the value of information and the
  cost of collection

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Data Abstraction

• Capturing the essential pieces of information to
  describe the spatial phenomenon
• Based on a conceptual model of reality
• Expressed in data models
• Realized by building up of data structures (i.e.
  internal representation of spatial data) using
  database models

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Reality, Conceptual Model and Database
Database (Cyber world)
Reality
Conceptual model
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Data Abstraction Example
Locating objects
Recording attribute info.
Data (1.0, 20.3, 9.0, 12.8, 15.0, 10000.00)
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Data Abstraction Example
Data (1.0, 20.3, 9.0, 12.8, 15.0, 10000.00)
What do you mean by these data?
(1.0, 20.3)
Describing a house for rent
Z15.0
(9.0, 12.8)
Abstraction rule
Monthly rent PhP 10,000.00
Conceptual model of describing house for rent.
Crucial information for data users
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Levels of Data Abstraction
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Data Model vs. Database Model

• Data Model
• Vector methods (feature-based)
• Raster methods (field-based)
• Database Model
• Software implementation of data models
• Metwork, hierarchical and object-oriented
  databases

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Vector Data Model

• Method of representing geographic features by the
  basic graphical elements
• Points
• Lines (arcs)
• Polygons (area)
• They can also be used to construct complex
  features

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Basic Graphical Elements
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Vector Data Model (contd.)

• Related vector data are always organized by
  themes, which are also referred to as layers or
  coverages
• examples of themes geodetic control, base map,
  soil, vegetation cover, land use, transportation,
  drainage and hydrology, political boundaries,
  land parcel and others

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Vector Data Model (contd.)

• For themes covering a very large geographic area,
  the data are always divided into tiles so that
  they can be managed more easily
• a tile is the digital equivalent of an individual
  map in a map series
• a tile is uniquely identified by a file name

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Vector Data Model (contd.)

• A collection of themes of vector data covering
  the same geographic area and serving the common
  needs of a multitude of users constitutes the
  spatial component of a geographical database
• Graphical data captured by imaging devices in
  remote sensing and digital cartography (such as
  multi-spectral scanners, digital cameras and
  image scanners) are made up of a matrix of
  picture elements (pixels) of very fine resolution

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Raster Data Model

• Method of representing geographic features by
  pixels
• A raster pixel is usually a square grid cell but
  there are there are several variants such as
  triangles and hexagons

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Raster Data Model (contd.)

• A raster pixel represents the generalized
  characteristics of an area of specific size on or
  near the surface of the Earth
• the actual ground size depicted by a pixel is
  dependent on the resolution of the data, which
  may range from smaller than a square meter to
  several square kilometers
• Raster data are organized by themes, which is
  also referred to as layers

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Raster Data Model (contd.)

• Raster data covering a large geographic area are
  organized by scenes (for remote sensing images
• The raster method is based on the concept that
  geographic features are represented as surfaces,
  regions or segments

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Vector Data Structure

• Spaghetti
• a direct line-for-line unstructured translation
  of the paper map has very limited practical use
• it is usually an interim data structure for map
  digitizing
• Hierarchical
• a vector data structure developed to facilitate
  data retrieval by separately storing points,
  lines and areas in a logically hierarchical manner

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Spaghetti Data Model and Data Structure
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Hierarchical Data Model and Data Structure
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Vector Data Structure (contd.)

• Topological
• a vector data structure that captures spatial
  relationship by explicitly storing adjacency
  information
• the basic logical feature for line and area
  coverage is a straight line segment
• each individual line segment is defined by the
  coordinates of its end points called nodes

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Topological Data Model and Data Structure
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Raster Data Structure

• Space is subdivided into regular grids of square
  grid cells or other forms of polygonal meshes
  known as picture elements (pixels)
• the location of each cell is defined by its row
  and column numbers
• the area that each cell represents defines the
  spatial resolution of the data
• the position of a geographic feature is only
  recorded to the nearest pixel

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Raster Data Structure (contd.)

• the value stored for each cell indicates the
  types of the object, phenomenon or condition that
  is found in that particular location
• different types of values can be coded integers,
  real numbers and alphabets
• integer values often act as code numbers, which
  are referenced to names in an associated table
  (called the look-up table) or legend
• different attributes at the same cell location
  are stored as separate themes or layers

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Characteristics of Raster Data Structure
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Raster Data Structure (contd.)

• There are several variants to the regular grid
  raster data structure, including
• irregular tessellation (e.g. triangulated
  irregular network (TIN))
• hierarchical tessellation (e.g. quad tree) and
• scan-line

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Representing Fields

• there are many ways of representing fields
• not all are implemented in GIS
• different terminologies exist in different
  disciplines
• Six major representations
• Regular cells
• Rectangular grid of points
• Irregularly spaced points
• Digitized contours
• Polygons
• Triangulated irregular networks (TINs)

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Regular Cells

• Value in each cell is an average, total, or some
  other aggregate property of the field within the
  cell
• the representation defines a value everywhere, so
  is complete
• however, all within-cell variation is lost
• if necessary, it must be reconstructed by some
  method of intelligent guesswork
• e.g. remote sensing data and other kinds of
  digital imagery

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Rectangular grid of points

• e.g. measurements of land surface elevation in a
  digital elevation model (DEM)
• spacing of measurements is critical to accuracy
  of representation
• all variation between sample points is lost
• elevations at other points must be estimated by
  some method of intelligent guesswork (the
  representation is incomplete)

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Irregularly spaced points

• The field's value is defined at a set of sample
  points scattered in the frame
• values of the field at other points must be
  interpolated representation is incomplete
• e.g. weather data, available at scattered weather
  stations
• accuracy depends on the density of points
• it is not clear what measure best defines
  accuracy - density per unit area, minimum
  distance between sample points, maximum distance

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Digitized contours

• The field is represented as a set of isolines,
  each connecting points of constant value
• representation is incomplete
• The scale of measurement of the variable must be
  at least ordinal
• isolines cannot be defined for nominal data
• Each isoline is represented as a polyline
• e.g. data obtained from topographic maps
• Accuracy depends on
• the number of contoured values, or the contour
  interval
• the density of polyline points

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Polygons

• The frame is partitioned into irregular areas
  (volumes for 3 or more dimensions)
• value in each area is an average, total, or some
  other aggregate property of the field within the
  area
• the representation is complete
• all variation within areas is lost
• e.g. data obtained from maps of vegetation cover
  class, soil type

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Polygons (contd.)

• The boundaries of areas are continuously curved
  lines
• represented digitally as polylines - an ordered
  sequence of points connected by straight lines
• the denser the points, the more accurate the
  polyline as a representation of a continuous
  curve
• accuracy depends both on the size of polygons and
  on the density of polyline points
• it is not clear what measure of polygon size -
  average, minimum - best defines accuracy

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Polygons (contd.)

• Every point in the frame lies in exactly one
  polygon
• except for points on the boundaries
• the polygons cannot overlap, must exhaust the
  frame
• they are said to tesselate the space, they form
  an irregular tesselation

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Triangulated irregular networks (TINs)

• the frame is covered with a mesh of irregular
  triangles
• every point lies in exactly one triangle, or on a
  triangle edge
• the value of the field is known at every triangle
  vertex
• within triangles and along edges it is assumed to
  vary linearly
• the representation is complete
• contours drawn across triangles will therefore
  always be straight and parallel
• across triangle edges there will be breaks of
  slope, but not cliffs
• contours will kink at edges

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Triangulated irregular networks (TINs)

• the scale of measurement of the variable must be
  at least interval
• variation within triangles cannot be defined for
  nominal or ordinal variables

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Triangulated irregular networks (TINs)

• Accuracy depends on
• how carefully the vertices were located on the
  surface
• how well the planes defined within each triangle
  fit the actual surface
• the sizes of triangles
• but it is not clear what property of triangle
  size best defines accuracy - average, smallest,
  largest

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Vector and Raster Data Integration

• Recent advances in computer technologies allow
  these two types of data to be used in the same
  applications
• computers are now capable of converting data from
  the vector format to the raster format
  (rasterization) and vice versa (vectorization)
• computers are now able to display vector and
  raster simultaneously
• vector and raster data are largely seen as
  complimentary to, rather than competing against,
  one another in geographic data processing

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Georelational Data Structure

• Was developed to handle geographic data
• It allows the association between spatial
  (graphical) and non-spatial (descriptive) data
• It is the data structure used by many
  vector-based GIS software packages
• Both spatial and non-spatial data are stored in
  relational tables

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Georelational Data Structure (contd.)

• Point, line and polygon data are stored in
  separate feature attribute tables (FAT)
• in the FAT, each entity is assigned a unique
  feature identifier (FID)
• topological information is explicitly stored by
  employing a method similar to the topological
  data structure described above
• non-spatial data are stored in relational tables

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Feature Attribute Table (FAT)
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Georelational Data Structure (contd.)

• Entities in the spatial and non-spatial
  relational tables are linked by the common FIDs
  of entities

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Linking spatial and non-spatial tables
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Data Modeling

• Process of defining real world phenomena or
  geographic features of interest in terms of their
  characteristics and their relationships with one
  another
• it is concerned with different phases of work
  carried out to implement information organization
  and data structure

93
Data Modeling (contd.)

• There are three steps in the data modeling
  process, resulting in a series of progressively
  formalized data models as the form of the
  database becomes more and more rigorously defined
  
• conceptual data modeling - defining in broad and
  generic terms the scope and requirements of a
  database
• logical data modeling - specifying the user's
  view of the database with a clear definition of
  attributes and relationships
• physical data modeling - specifying internal
  storage structure and file organization of the
  database

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Conceptual Data Modeling

• Entity-relationship (E-R) modeling is probably
  the most popular method of conceptual data
  modeling
• It is sometimes referred to as a method of
  semantic data modeling because it used a human
  language-like vocabulary to describe information
  organization

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Conceptual Data Modeling (contd.)

• It involves four aspects of work
• identifying entities
• an entity is defined as a person, a place, an
  event, a thing, etc.
• identifying attributes
• determining relationships
• drawing an entity-relationship diagram (E-R
  diagram)

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Sample E-R Diagram
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Logical Data Modeling

• Comprehensive process by which the conceptual
  data model is consolidated and refined
• the proposed database is reviewed in its entirety
  in order to identify potential problems such as
• irrelevant data that will not be used
• omitted or missing data
• inappropriate representation of entities
• lack of integration between various parts of the
  database
• unsupported applications
• potential additional cost to revise the database

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Logical Data Modeling (contd.)

• The end product of logical data modeling is a
  logical schema
• the logical schema is developed by mapping the
  conceptual data model (such as the E-R diagram)
  to a software-dependent design document

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Logical Schema Example
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Physical Data Modeling

• Database design process by which the actual
  tables that will be used to store the data are
  defined in terms of
• data format - the format of the data that is
  specific to a database management system (DBMS)
• storage requirements - the volume of the database
  
• physical location of data - optimizing system
  performance by minimizing the need to transmit
  data between different storage devices or data
  servers

101
Physical Data Modeling (contd.)

• The end product of physical data modeling is a
  physical schema
• a physical schema is also variably known as data
  dictionary, item definition table, data specific
  table or physical database definition
• it is both software- and hardware specific
• this means the physical schemas for different
  systems look different from one another

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Physical Schema Example
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End