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									            Analysis and Modeling in GIS




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9/2/2009 Ron Briggs, UTDallas   GISC 6381 GIS Fundamentals
                GIS and the Levels of Science
       Description:
       Using GIS to create descriptive models of the world
                --representations of reality as it exists.

       Analysis:
       Using GIS to answer a question or test an hypothesis.
       Often involves creating a new conceptual output layer, (or table or chart),
          the values of which are some transformation of the values in the
          descriptive input layer.
                --e.g. buffer or slope or aspect layers

       Prediction:
       Using GIS capabilities to create a predictive model of a real world
          process, that is, a model capable of reproducing processes and/or
          making predictions or projections as to how the world might appear.
                --e.g. flood models, fire spread models, urban growth models


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9/2/2009 Ron Briggs, UTDallas       GISC 6381 GIS Fundamentals
                     The Analysis Challenge
    • Recognizing which generic GIS analytic capability (or
      combination) can be used to solve your problem:
       – meet an operational need
       – answer a question posed by your boss or your board
       – address a scientific issue and/or test a hypothesis

         Send mailings to property owners potentially affected by a proposed change
           in zoning
         Determine if a crime occurred within a school’s ―drug free zone‖
         Determine the acreage of agricultural, residential, commercial and
           industrial land which will be lost by construction of new highway corridor
         Determine the proportion of a region covered by igneous extrusions
         Do Magnitude 4 or greater sub-oceanic earthquakes occur closer to the
           Pacific coast of South America than of North America?
         Are gas stations or fast food joints closer to freeways?

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9/2/2009 Ron Briggs, UTDallas      GISC 6381 GIS Fundamentals
        Availability of Capabilities in GIS Software
• Descriptive Focus: Basic Desktop GIS packages
    –   Data editing, description and basic analysis
    –   ArcView
    –   Mapinfo
    –   Geomedia
• Analytic Focus: Advanced Professional GIS systems          Capabilities move
    – More sophisticated data editing plus more advanced     „down the chain‟
       analysis                                              over time.
    – ARC/INFO, MapInfo Pro, etc.
    Provided through extra cost Extensions
                                                            In earlier generation
       or professional versions of desktop packages
                                                            GIS systems, use of
• Prediction: Specialized modeling and simulation           advanced applications
    – via scripting/programming within GIS                  often required learning
         » VB and ArcObjects in ArcGIS                      another package with
         » Avenue scripts in ArcView 3.2                    a different user
         » AMLs in Workstation ARC/INFO (v. 7)              interface and
         Write your own or download from ESRI Web site      operating system
    – via specialized packages and/or GISs                  (usually UNIX).
         » 3-D Scientific Visualization packages
         » transportation planning packages e.g TransCAD
         » ERDAS, ER Mapper or similar package for raster
                     Description and Basic Analysis
                                      (Table of Contents)

  • Spatial Operations                                • Attribute Operations
       Vector
       – spatial measurement
                                                            – record selection
       – Centrographic statistics                                   » tabular via SQL
       – buffer analysis                                            » „information clicking‟
       – spatial aggregation                                          with cursor
             » redistricting                                – variable recoding
             » regionalization
             » classification
                                                            – record aggregation
       – Spatial overlays and                               – general statistical
         joins                                                analysis
       Raster
                                                            – table relates and joins
       – neighborhood
         analysis/spatial filtering
       – Raster modeling
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9/2/2009 Ron Briggs, UTDallas          GISC 6381 GIS Fundamentals
                                Spatial operations: Spatial Measurement
  Spatial measurements:
                                                      Comments:
  • distance measures                                 •    Cartesian distance via Pythagorus
       –   between points
       –   from point or raster                                    dij  ( Xi  Xj ) 2  (Yi  Yj ) 2
           to polygon or zone boundary
       –   between polygon centroids                        Used for projected data by ArcMap measure tools
  •   polygon area                                    •    Spherical distance via spherical coordinates
                                                            Cos d = (sin a sin b) + (cos a cos b cos P)
  •   polygon perimeter                                          where:            d = arc distance
  •   polygon shape                                                                a = Latitude of A
                                                                                   b = Latitude of B
  •   volume calculation                                                           P = degrees of long. A to B
                                                            Used for unprojected data by ArcMap measure tools
       – e.g. for earth moving, reservoirs
                                                      •    possible distance metrics:
  • direction determination                                 –   straight line/airline
        – e.g. for smoke plumes                             –   city block/manhattan metric
                                                            –   distance thru network
  ArcGIS geodatabases contain automatic                     –   time/friction thru network
  variables:                                          •    shape often measured by:
  shape.length: line length or                              perimeter                = 1.0 for circle
                 polygon perimeter                        area x 3.54                = 1.13 for square
                                                                                     Large for complex shape
  shape.area: polygon area
                                                      •    Projection affects values!!!
  Automatically updated after editing.
                                                                                    Distances depend on
  For shapefiles, these must be calculated                                          projection.
  e.g. by opening attribute table and applying                                      Perimeter to area ratio
  Calculate Geometry to a column (AV 9.2)
                                                                                    differs
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9/2/2009 Ron Briggs, UTDallas                GISC 6381 GIS Fundamentals
            Spatial operations: Spatial Measurement
  SHAPE      AREA PERIMETER CNTY_ CNTY_ID NAME                        FIPS    Shape Index
  Polygon      0.265    2.729  2605  2605 Anderson                    48001      1.50
  Polygon      0.368    2.564  2545  2545 Andrews                     48003      1.19
  Polygon      0.209    2.171  2680  2680 Angelina                    48005      1.34
  Polygon      0.072    2.642  2899  2899 Aransas                     48007      2.78
  Polygon      0.233    1.941  2335  2335 Archer                      48009      1.14
  Polygon      0.233    1.941  2103  2103 Armstrong                   48011      1.14
  Polygon      0.299    2.278  2870  2870 Atascosa                    48013      1.18
  Polygon
  Polygon       0.224           1.900   2471     2471   Dallas        48113      1.13
  Polygon       0.222           1.889   2481     2481   Dawson        48115      1.13
  Polygon       0.368           2.580   2106     2106   Deaf Smith    48117      1.20
  Polygon       0.072           1.421   2386     2386   Delta         48119      1.50

   Area and Perimeter measures are automatically maintained in the
   attributes table for a Geodatabase or coverage. For a shapefile, you
   need to apply Calculate Geometry to an appropriate column in the
   attribute table (or convert to a geodatabase) .

   The shape index can be calculated from the area and perimeter
   measurements. (Note: shapefile and shape index are unrelated)
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9/2/2009 Ron Briggs, UTDallas            GISC 6381 GIS Fundamentals
     Spatial Measurement: Calculating the Area of a Polygon
10



         Area=(2 x 4)/2=4
                                Area=(3 x 4)=12
                                                                    A              =              B                -              C




                                                       10
                      4,7
                                       7,7


                                                                                                            -




                                                                                                                   5
                                                       5




                                                                                       5
                                                                               =
5




                                                       0
                                       7,3
             2,3                                        0           5              10 0           5         10         0          5       10
         Area=(5 x 1)/2=2.5      6,2
                                                            The actual algorithm used obtains the area of A by
0




     0                      5                     10        calculating the areas of B and C, and then subtracting.
                                                            The actual formulae used is as follows:
     The area of the above
                                                                    
                                                                        i 1
     polygon is 18.5, based on                                          n
                                                                               (X2 - X1) ( Y1  Y2)/2
     dividing it into rectangles                                Its implementation in Excel is shown below.

     and triangles. However,                                    i       X      Y       X2-X1   (Y1+Y2)/2   product         sum
                                                                1       2      3         2        5           10            10
     this is not practical for a                                2
                                                                3
                                                                        4
                                                                        7
                                                                               7
                                                                               7
                                                                                         3
                                                                                         0
                                                                                                  7
                                                                                                  5
                                                                                                              21
                                                                                                              0
                                                                                                                            31
                                                                                                                            31
     complex polygon.                                           4
                                                                5
                                                                        7
                                                                        6
                                                                               3
                                                                               2
                                                                                        -1
                                                                                        -4
                                                                                                 2.5
                                                                                                 2.5
                                                                                                            -2.5
                                                                                                             -10
                                                                                                                           28.5
                                                                                                                           18.5

     Area of triangle =                                                 2      3


              (base x height)/2                                                                                                       8
9/2/2009 Ron Briggs, UTDallas                     GISC 6381 GIS Fundamentals
                                Spatial Operations:
                       Centrographic Statistics
    • Basic descriptors for spatial point distributions
    • Two dimensional (spatial) equivalents of standard descriptive
      statistics (mean, standard deviation) for a single-variable
      distribution
         Measures of Centrality (equivalent to mean)
         – Mean Center and Centroid
         Measures of Dispersion (equivalent to standard deviation or variance)
         – Standard Distance
         – Standard Deviational Ellipse
    • Can be applied to polygons by first obtaining the centroid of
      each polygon
    • Best used in a comparative context to compare one
      distribution (say in 1990, or for males) with another (say in
      2000, or for females)
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9/2/2009 Ron Briggs, UTDallas       GISC 6381 GIS Fundamentals
                        Centroid and Mean Center
 • balancing point for a spatial distribution
                                                                                  n           n
       – analogous to the mean                                            Xi       Yi
       – single point representation for a polygon (centroid)       X  i 1 , Y  i 1
       – single point summary for a point distribution (mean center)       n          n
       – can be weighted by „magnitude‟ at each point (analogous to weighted mean)
       – minimizes squared distances to other points, thus „distant‟ points have bigger
         influence than close points ( Oregon births more impact than Kansas births!)
       – is not the point of “minimum aggregate travel”--this would minimize distances (not
         their square) and can only be identified by approximation.
 • useful for
       – summarizing change over time in a distribution (e.g US pop. centroid every 10 years)
       – placing labels for polygons
 • for weird-shaped polygons,
   centroid may not lie within polygon                                        centroid outside
                                                                               polygon
   Note: many ArcView applications calculate
   only a “psuedo” centroid: the coordinates of the       Can be implemented via:
   bounding box (the extent) of the polygon                ArcToolbox>Spatial Statistics Tools>Measuring
                                                          Geographic Distributions>Mean Center           10
9/2/2009 Ron Briggs, UTDallas              GISC 6381 GIS Fundamentals
    10                                                             Calculating the centroid of a
                                                                   polygon or the mean center of
                         4,7
                                              7,7
                                                                   a set of points.
                                                                                                               (same example data as
                                                                          1        2           3               for area of polygon)
    5




                                                                          2        4           7
                                                                          3        7           7
                                                                          4        7           3                       n                  n


                  2,3
                                              7,3                         5        6           2
                                                                                                                       Xi               Y       i

                                                                                                             X       i 1
                                                                                                                               ,Y       i 1
                                                                       sum         26          22                          n                  n
                                       6,2                          Centroid/MC    5.2         4.4
    0




             0                    5                    10
  10




                                                                  Calculating the weighted mean
                                                                  center. Note how it is pulled
                        4,7
                                             7,7                  toward the high weight point.
                                                              i      X        Y      weight        wX         wY
  5




                                                              1      2        3        3,000         6,000     9,000               n                   n


                                             7,3
                                                              2
                                                              3
                                                                     4
                                                                     7
                                                                              7
                                                                              7
                                                                                        500
                                                                                        400
                                                                                                     2,000
                                                                                                     2,800
                                                                                                               3,500
                                                                                                               2,800               wiXi               wY   i i

                                                                                                                             X   i 1
                                                                                                                                                  ,Y i 1

                                                                                                                                   w                  w
                 2,3                                          4      7        3         100            700       300
                                                              5      6        2         300          1,800       600                          i               i
                                      6,2
                                                             sum     26       22       4,300   13,300        16,200
  0




                                                            w MC                                3.09          3.77
         0                    5                       10
                                                                                                                                                      11
9/2/2009 Ron Briggs, UTDallas                       GISC 6381 GIS Fundamentals
                                       Median Center:
                                       Intersection of a north/south and an east/west
                                       line drawn so half of population lives above
                                       and half below the e/w line, and half lives to
                                       the left and half to the right of the n/s line.
                                       Same as “point of minimum aggregate
                                       travel” the location that would minimize
                                       travel distance if we brought all US residents
                                       straight to one location.
                                       Mean Center:
                                       Balancing point of a weightless map, if equal
                                       weights placed on it at the residence of every
                                       person on census day.
                                       Note: minimizes squared distances. The point
                                       is considerable west of the median center
                                       because of the impact of “squared distance” to
                                       “distant” populations on west coast
                                           For a fascinating discussion of the effect of
                                           population projection see: E. Aboufadel & D.
                                           Austin, A new method for calculating the
                                           mean center of population center of the US
                                           Professional Geographer, February 2006, pp.
Source: US Statistical Abstract 2003
                                           65-69
                      Standard Distance Deviation
      single unit measure of the spread or dispersion of a distribution.

 • Is the spatial equivalent of standard deviation for a single variable
 • Equivalent to the standard deviation of the distance of each point from the mean
   center
 • Given by:
                                 i1 ( Xi  Xc ) 2  i 1 (Yi  Yc ) 2
                                    n                     n


                                                     N
 which by Pythagoras
                                        i1
    reduces to:                            n
                                             diC 2
                                               N

  ---the square root of the average squared distance
 ---essentially the average distance of points from the center
 We can also weight each point and calculate weighted standard distance (analogous
      to weighted mean center.)
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9/2/2009 Ron Briggs, UTDallas    GISC 6381 GIS Fundamentals
           Standard Distance Deviation Example




                                                              10
                                                                                                             Circle with radii=SDD=2.9
                                                                                              4,7
                                                                                                                                 7,7




                                                              5
                                                                                                                                 7,3
                                                                          2,3
               i       X        Y     (X - Xc)2   (Y - Yc)2
                                                                                                                  6,2
               1       2        3        10.2       2.0




                                                              0
               2       4        7         1.4       6.8
               3       7        7         3.2       6.8
                                                                   0                                   5                                           10
               4       7        3         3.2       2.0
                                                                          i           X                  Y              (X - Xc)2      (Y - Yc)2
               5       6        2         0.6       5.8
                                                                          1           2                  3                10.2           2.0
             sum       26       22       18.8       23.2                  2           4                  7                 1.4           6.8
            Centroid   5.2      4.4                                       3           7                  7                 3.2           6.8
                                      sum            42.00                4           7                  3                 3.2           2.0
                                      divide N        8.40                5           6                  2                 0.6           5.8
                                      sq rt           2.90
                                                                        sum           26                22                18.8           23.2
                                                                       Centroid       5.2               4.4
                                                                                                                  sum of sums                 42
                                                                                                                  divide N                   8.4
                                                                                                                  sq rt                     2.90



                                                                                                ( Xi  Xc ) 2  i 1 (Yi  Yc ) 2
                                                                                          n                         n

                                                                              sdd        i 1
                                                                                                              N

                                                                                                                                                        14
9/2/2009 Ron Briggs, UTDallas                       GISC 6381 GIS Fundamentals
  Standard Deviational Ellipse: concept
• Standard distance deviation is a good single
  measure of the dispersion of the incidents around
  the mean center, but it does not capture any
  directional bias
   – doesn‟t capture the shape of the distribution.
• The standard deviation ellipse gives dispersion in
  two dimensions
• Defined by 3 parameters
   – Angle of rotation
   – Dispersion along major axis
   – Dispersion along minor axis
   The major axis defines the
     direction of maximum spread
     of the distribution
   The minor axis is perpendicular to it
     and defines the minimum spread
           Standard Deviational Ellipse: example
                                                             There appears to be
                                                             no major difference
                                                             between the location
                                                             of the software and
                                                             telecommunications
                                                             industry in North
                                                             Texas.




For formulae for its calculation, see
Lee and Wong Statistical Analysis with ArcView GIS pp. 48-49 (1st ed.), pp 203-205 (2nd ed.)
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9/2/2009 Ron Briggs, UTDallas          GISC 6381 GIS Fundamentals
      Spatial Operations: buffer zones
   • region within „x‟ distance units
   • buffer any object: point, line or
     polygon
   • use multiple buffers at progressively            polygon buffer
     greater distances to show gradation
   • may define a „friction‟ or „cost‟ layer      Examples
     so that spread is not linear with            • 200 foot buffer around property
     distance                                        where zoning change requested
   • Implement in Arcview 3.2 with                • 100 ft buffer from stream center
     Theme/Create buffers                            line limiting development
                  in ArcGIS 8 with                • 3 mile zone beyond city
     ArcToolbox>Analysis Tools>Buffer                boundary showing ETJ (extra
                                                     territorial jurisdiction)
point                                             • use to define (or exclude) areas
buffers                           line
                                                     as options (e.g for retail site) or
                                 buffer              for further analysis
                                                  • in conjunction with „friction
                                                     layer‟, simulate spread of fire
                                          Note: only one layer is involved, but the
                                          buffer can be output as a new layer
    Spatial Operations:                  Grouping/combining polygons—is
    spatial aggregation                  applied to one polygon layer only.
• districting/redistricting                Criteria may be:
      – grouping contiguous polygons            –   formal (based on in situ characteristics)
        into districts                              e.g. city neighborhoods
                                                –   functional (based on flows or links):
      – original polygons preserved                 e.g. commuting zones
•    Regionalization (or dissolving)       Groupings may be:
                                                –   contiguous
      – grouping polygons into
                                                –   non-contiguous
        contiguous regions
                                           Boundaries for original polygons:
      – original polygon boundaries             –   may be preserved
        dissolved                               –   may be removed (called dissolving)
• classification                           Examples:
      – grouping polygons into non-        •   elementary school zones to high school
        contiguous regions                     attendance zones (functional districting)
      – original boundaries usually        •   election precincts (or city blocks) into
        dissolved                              legislative districts (formal districting)
      – usually „formal‟ groupings         •   creating police precincts (funct. reg.)
                                           •   creating city neighborhood map (form. reg.)
    Implement in ArcView 9 thru            •   grouping census tracts into market
    ArcToolbox>Generalization>Dissolve         segments--yuppies, nerds, etc (class.)
                                           •   creating soils or zoning map (class)
    Districting: elementary school attendance zones grouped to form
    junior high zones.




     Regionalization: census tracts grouped into neighborhoods




     Classification: cities categorized as central city or suburbs
                    soils classified as igneous, sedimentary, metamorphic
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9/2/2009 Ron Briggs, UTDallas   GISC 6381 GIS Fundamentals
                                Spatial Operations:
                  Spatial Matching: Spatial Joins and Overlays
                                                   Examples
  •   combine two (or more) layers to:
       – select features in one layer, &/or        • assign environmental samples
       – create a new layer                          (points) to census tracts to estimate
  •   used to integrate data having different        exposure per capita (point in
      spatial properties (point v. polygon), or      polygon)
      different boundaries (e.g. zip codes         • identify tracts traversed by freeway
      and census tracts)                             for study of neighborhood blight
  •   can overlay polygons on:                       (polygon on lines)
       – points (point in polygon)                 • integrate census data by block with
       – lines (line on polygon)                     sales data by zip code (polygon on
       – other polygons (polygon on polygon)
                                                     polygon)
       – many different Boolean logic
           combinations possible                   • Clip US roads coverage to just
             » Union (A or B)                        cover Texas (polygon on line)
             » Intersection (A and B)              • Join capital city layer to all city
             » A and not B ; not (A and B)
                                                     layer to calculate distance to
  •   can overlay points on:                         nearest state capital
       – Points, which finds & calculates distance
           to nearest point in other theme
                                                     (point on point)
       – Lines, which calculates distance to
         nearest line                                                                        20
9/2/2009 Ron Briggs, UTDallas            GISC 6381 GIS Fundamentals
                          Example: Spatial Matching:
                            Clipping and Erasing
                          (sometimes referred to as spatial extraction)
   •CLIP - extracts those features from an input        •ERASE - erases the input
   coverage that overlap with a clip coverage.          coverage features that overlap
   This is the most frequently used polygon             with the erase coverage
   overlay command to extract a portion of a
   coverage to create a new coverage.                   polygons.




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9/2/2009 Ron Briggs, UTDallas          GISC 6381 GIS Fundamentals
               Example: Spatial Matching via
            Polygon-on-Polygon Overlay: Union

  Land Use                  a.    b.        c.
                                                             The two layers (land use
                                                             & drainage basins) do not
Drainage         Atlantic
                                       A.                    have common
Basins                           G.                          boundaries. GIS creates
              Gulf
                                                             combined layer with all
                                                             possible combinations,
Combined layer          aA bA             cA                 permitting calculation of
                           bG                                land use by drainage
                     aG                   cG                 basin.
 Note: the definition of Union in GIS is a little different from that in mathematical set
 theory. In set theory, the union contains everything that belongs to any input set, but
 original set membership is lost. In a GIS union, all original set memberships are
 explicitly retained.                                              Another example
 In set theory terms, the outcome
                                                                1 2
 of the above would simply be:                                           3

                                                              GIS Union        Set Theory Union
      Implementing Spatial Matching in ArcGIS 9
Available in three places
• via Selection/Select by Location
     –   this selects features of one layer(s) which relate in some specified spatial manner to the features in another
         layer
     –   if desired, selected features may be saved later to a new theme via Data/Export Data
     –   Individual features are not themselves modified
•   via Spatial Join (right click layer in T of C, select Join/Joins and Relates, then click down arrow in
    first line of Join Data window---see Joining Data in Help for details)
     –   Use for:        points in polygon
                         lines in polygon
                         points on lines (to calculate distance to nearest line)
                         points on points (to calculate distance to “nearest neighbor” point)
     –   operate on tables and normally creates a new table with additional variables, but again does not modify
         spatial features themselves
•   via ArcToolbox
     –   Generally these tools modify geographic feature, thus they create a new layer (e.g. shape file)
     –   Tools are organized into multiple categories

ArcToolbox Examples
• Dissolve features based on an attribute
     –   Combine contiguous polygons and remove common border
     –   ArcToolbox>Generalization>Dissolve
•   Clip one layer based on another
     –   ArcToolbox>Analysis Tools>Extract>Clip
     –   Use one theme to limit features in another theme
         (e.g. limit a Texas road theme to Dallas county only)
•   Intersect two layers (extent limited to common area)
     –   ArcToolbox>Analysis Tools>Overlay>Intersect
     –   Use for polygon on polygon overlay
•   Union two layers (covers full extent of both layers)
     –   ArcToolbox>Analysis Tools>Overlay>Intersect
     –   Use for polygon on polygon overlay
                                Spatial Operations:
              neighborhood analysis/spatial filtering
   • spatial convolution or filter                   • low frequency ( low pass) filter:
      – applied to one raster layer
                                                         mean filter
      – value of each cell replaced by
        some function of the values of                    – cell replaced by the mean for
        itself and the cells (or                            neighborhood
        polygons) surrounding it                          – equivalent to weighting
      – can use „neighborhood‟ or                           (mutiplying) each cell by
        „window‟ of any size                                 1/9 = .11 (in 3x3 case)
               » 3x3 cells (8-connected)
                                                          – smooths the data
               » 5x5, 7x7, etc.
         – differentially weight the cells                – use larger window for greater
           to produce different effects                     smoothing
         – kernel for 3x3 mean filter:                   median filter
               1/9 1/9 1/9                                – use median (middle value)
                                 weights must
               1/9 1/9 1/9
                                 sum to 1.0
                                                            instead of mean
               1/9 1/9 1/9                                – smoothing, especially if data
                                                            has extreme value outliers
                                                                                            24
9/2/2009 Ron Briggs, UTDallas            GISC 6381 GIS Fundamentals
                                    Spatial Operations:
                       spatial filtering -- high pass filter
high frequency (high pass) filter                                 standard deviation filter
    negative weight filter                                          (texture transform)
    – exagerates rather than smooths                              – calculate standard deviation of
       local detail                                                 neighborhood raster values
    – used for edge detection                                     – high SD=high texture/variability
                                                                  – low SD=low texture/variability
cell values (vi ) on                                              – again used for edge detection
each side of edge
                                            filtered values for
                                                                  – neighorhoods spanning border
       2                5                   highlighted pixel       have large SD „cos of
                        1(5)(9)+5(5)(-1)+3(2)(-1) = 14              variability
                       1(2)(9)+5(2)(-1)+3(5)(-1) = -7
                                                     –kernel for example (wi)
                        1(2)(9)+8(2)(-1) = 2
                                                         -1 -1 -1
                          1(5)(9)+8(5)(-1) = 5           -1 9 -1
                              f .v . w                   -1 -1 -1
                                i   i   i                                                              25
9/2/2009 Ron Briggs, UTDallas                  GISC 6381 GIS Fundamentals
                                Spatial Operations:
                                raster–based modelling
• Relating multiple rasters
                                        • Suitability modeling
• Processes may be:                        0     0         1   0        1      0       2
                                                                                       Site
                                                                                                0
                                         soil       slope                   for
    – Local: one cell only                                                             options
                                                                            sale
    – Neighborhood: cells relating      1     0      1   1     1       1               3        2

      to each other in a defined      • Diffusion Modeling
      manner
    – Zonal: cells in a given section                                              System at
                                           Incidence       Probability
    – Global: all cells                    matrix          mask                    time t+1

• ArcGIS implementation:
    – All raster analyses require
                                        • Connectivity Modeling
      either the Spatial Analyst or
      3-D Analyst extensions
                                                 Initial           Connectivity     Resultant
    – Base ArcView can do no                     State             matrix           State
      more than display an image
      (raster) data set
                                                                                                    26
9/2/2009 Ron Briggs, UTDallas         GISC 6381 GIS Fundamentals
      Attribute Operations: record selection or extraction
           --features selected on the map are identified in the table (and visa versa)
  Select by Attribute (tabular)
                                                                    Outputs may be:
  •   Independent selection by clicking table rows:
       – Open Attribute Table & click on grey selection box at      • Simultaneously highlighted
         start of row (hold ctrl for multiple rows)                   records in table, and features
  •   Create SQL query                                                on map
       –     use Selection/Select by Attribute                      • New tables and/or map layers
  •    use table Relates /Joins to select specific data
  Select by Graphic                                            Examples
  • Manually, one point at a time                              • Use SQL query to select all
       – use Select Features tool                                 zip codes with median
  • within a rectangle or an irregular polygon                    incomes above $50,000
       – use Selection/Select by Graphic                          (tabular)
  • within a radius (circle) around a point or points          • identify zip codes within 5
       – use Selection/Select by Location (are wthin distance)    mile radius of several
  Select by Location                                              potential store sites and sum
  • By using another layer                                        household income (graphic)
       – Use Selection/Select by Location                      • show houses for sale on map,
     (same as Spatial Matching discussed previously)              and click to obtain picture and
  Hot Link                                                        additional data on a selected
  • Click on map to „hot link‟ to pictures, graphs, or            house (hot link)
     other maps                                                                                27
9/2/2009 Ron Briggs, UTDallas                GISC 6381 GIS Fundamentals
                  Attribute Operations:
  statistical analysis on one or more columns in table
  • univariate (one variable or column)
        – central tendency: mean, median, mode
        – dispersion: standard deviation, min, max
        – To obtain these statistics in ArcGIS:
              » Right click in T of C and select Open attribute table
              » Right click on column heading and select Statistics
  • bivariate (relating two variables or columns)
        – interval and nominal scale variables: sum or mean by category
              » average crop yield by silt-sand-clay soil types
              » To implement in ArcGIS, proceed as above but use Summarize
        – two interval scale variables: correlation coefficients
              » income by education
              » ArcScripts are available for this on ESRI web site (or use Excel!)
  • multivariate (more than two variables)
        – usually requires external statistical package such as SAS, SPSS, STATA or S-
          PLUS


                                                                                         28
9/2/2009 Ron Briggs, UTDallas              GISC 6381 GIS Fundamentals
              Attribute Operations: variable recoding
• establishing/modifying number of classes and/or their boundaries for
  continuous variable. Options for ArcGIS
      – natural breaks (default)
        (finds inherent inherent groups via Jenks optimization which minimizes the variances
        within each of the classes).
      – quantile (classes contain equal number of records-- Implement in ArcGIS via:
        or equal area under the frequency distribution)              Right click in T of C, select
      – equal interval (user selects # of classes)                   Properties, then Symbology tab
        (equal width classes on variable)
      – Defined interval (user selects width of classes)
                                                                                 (assumes a Normal distribution)
        (equal width classes on variable)
      – standard deviation                                          25% 25%                    Equal area %
                                                             23%               23%
        (categories based on 1,2, etc, SDs               14%      34%     34%      14%          Equal interval %
        above/below mean)
                                                                                              Standard Deviation
      – Manual (user defined)                       -2       -1         0        1         2
                                                                                                Equal interval score
                                                                -.68    0   .68
          » whole numbers (e.g. 2,000)                                                       Equal area score

          » meaningful to phenomena (e.g zero, 32o)
• aggregating categories on a nominal (or ordinal) variable
      – pine and fir into evergreen
No change in number of records (observations).                                                               29
9/2/2009 Ron Briggs, UTDallas                GISC 6381 GIS Fundamentals
                                Attribute Operations:
                                   record aggregation
•   combining two or more records       Fips PMSA_90 PMSA_93 Pop90 Pop95_est Pop90-95% MedInc89 Suburb Name
                                        48085 1920     1920   264036  346232    5.93    46020     1    Collin
    into one, based on common           48113 1920     1920 1852810  1959281    1.09    31605     0    Dallas
    values on a key variable            48121 1920     1920   273525  334070    4.22    36914     1    Denton
•   the attribute equivalent of         48139 1920
                                        48213
                                                       1920
                                                       1920
                                                               85167
                                                               58543
                                                                       94223
                                                                       64293
                                                                                2.03
                                                                                1.87
                                                                                        30553
                                                                                        20747
                                                                                                  1
                                                                                                  1
                                                                                                       Ellis
                                                                                                       Henderson
    regionalization or classification   48231          1920    64343   66972    0.78    25317     1    Hunt
•   equivalent of PROC                  48257 1920     1920    52220   60114    2.88    27280     1    Kaufman
                                        48397 1920     1920    25604   32725    5.30    42417     1    Rockwall
    SUMMARY in SAS                      48221          2800    28981   33384    2.89    31627     1    Hood
•   interval scale variables can be     48251 2800     2800    97165  106181    1.77    30612     1    Johnson
                                        48367 2800     2800    64785   73794    2.65    30592     1    Parker
    aggregated using mean, sum,         48439 2800     2800 1170103  1278606    1.77    32335     0    Tarrant
    max, min, standard deviation,
                                        Source: US Bureau of the Census
    etc. as appropriate
                                        MedInc=Median Household Income. Pop90 as of April 1. Pop95 as of July 1.
•   ordinal and nominal require
    special consideration
                                        Fips   PMSA_90 PMSA_93 Pop90 Pop95_est Pop90-95% MedInc89 Suburb Name
•   example: aggregate county data                       1920 2676248  2957910   2.00     32607     7    Dallas
    to states, or county to CMSA                         2800 1361034  1491965   1.83     31292     3    Fort Worth

Record count decreases (e.g. from 12                                 sum        sum      re-calc.              count
   to 2)                                                                                            average
                                                               Type of processing:                     of
                                                                                                    medians!           30
9/2/2009 Ron Briggs, UTDallas              GISC 6381 GIS Fundamentals
    Attribute Operations: Joining and Relating Tables
                           associating spatial layer to non-spatial table
  Join: one to one, or one to many, relationship appends attributes
  Associate table of country capitals with country layer: only one capital for
     each country (one to one)
   Country Code      Country      Country Code     Capital               Country Code Country                   Capital
        29            France          199          Caracas                    9             UK                  London
        68         Saudi Arabia        96           Manila                    29          France                 Paris
       106             Chad            68          Riyadh                     68       Saudi Arabia             Riyadh
       248            Spain            29           Paris                     96        Philippines              Manila
       199          Venezuela         106        N'Djamena                   106           Chad               N'Djamena
        9               UK             9           London                    199        Venezuela               Caracas
        96          Philippines       248           Madrid                   248           Spain                 Madrid
      Layer Attribute Table            NonSpatial Table                             Layer Attribute Table after Join

  Associate country layer with type of government: one gov. type assigned to
     many countries--but each country has only one gov. type (one to many)
   Gov. Code      Country          Gov. Code             Type                Gov. Code     Country                 Type
         20           France          10          Absolute Monarchy             20          France               Republic
         30          Vietnam          15            Const. Monarchy             30         Vietnam           Communist State
         15             UK            20               Republic                 15            UK             Const. Monarchy
         20         Argentina         30            Communist State             20        Argentina              Republic
         10        Saidi Arabia       45       Parliamentary Democracy          10       Saudi Arabia      Absolute Monarchy
         15          Sweden                                                     15          Sweden           Const. Monarchy
         45          Portugal                                                   45         Portugal     Parliamentary Democracy
      Layer Attribute Table                 NonSpatial Table                          Layer Attribute Table after Join


                                                                                                                                  31
9/2/2009 Ron Briggs, UTDallas                      GISC 6381 GIS Fundamentals
             Single most common error in GIS Analysis
             --intending a one to one join of attribute to spatial table
             --getting a one to many join of attributes to spatial table
                                                                   NAME         FIPS   CODE      POP2000
                                                                Alabama           01    AL           4,447,100
                                                                Alaska            02    AK             626,932
                                                                …..
                                                                Georgia          13     GA           8,186,453
                                                                Hawaii           15     HI           1,211,537
                                                                Idaho            16     ID           1,293,953
                                                                …..
                                                                Wisconsin        55    WI            5,363,675
                                                                Wyoming          56    WY              493,782

                      Spatial                                   51 states              Total    282,421,906

                FID   SHAPE        NAME      FIPS   CODE       POP2000
                 0    Polygon   Alabama        01    AL            4,447,100
                 1    Polygon   Alaska         02    AK              626,932
                                …..
                11    Polygon   Georgia        13    GA             8,186,453
                12
                13
                      Polygon
                      Polygon
                                Hawaii-Hawaii 15
                                Hawaii-Maui    15
                                                     HI
                                                     HI
                                                                    1,211,537
                                                                    1,211,537
                                                                                               After joining
                14    Polygon   Hawaii-Oahu    15    HI             1,211,537
                15    Polygon   Hawaii-Kauai 15      HI             1,211,537                  attribute to
                16    Polygon   Idaho          16    ID             1,293,953
                                …..                                                            spatial data
                53    Polygon   Wisconsin      55    WI             5,363,675
                54    Polygon   Wyoming        56    WY               493,782


                                                     Total   286,056,517
                                                                                                                 32
9/2/2009 Ron Briggs, UTDallas                       GISC 6381 GIS Fundamentals
       Attribute Operations: Joining and Relating Tables
                             associating spatial layer to non-spatial table
                                               (contd.)
  Relate: many to one relationship, attributes not appended
  Associate country layer with its multiple cities (many to one)
      Country Code      Country    Country Code           City
                 29 France             129              Mombasa
                                       129               Nairobi
                 68 Saudi Arabia
                106 Chad                29                Paris        If joined Paris to France, for
                                        29                Lyon
                248 Spain
                199 Venezuela           29              Marseille      example, we lose Lyon and
                                        60              Katmandu
                   9 UK
                                       248               Madrid
                                                                       Marseille, therefore use relate
                 96 Philippines
         Layer Attribute Table         248              Barcelona
                                       248              Valencia
                                             NonSpatial Table


  Note: if we flip these tables we can do a join since there is only one country for
    each city (one to many)

  For both Joins and Relates:
  •      Association exists only in the map document
  •      Underlying files not changed unless export data
                                                                                                         33
9/2/2009 Ron Briggs, UTDallas                       GISC 6381 GIS Fundamentals
           Analysis Options: Advanced & Specialized
                      (Table of Contents)
  Advanced                                         Specialized
  • Proximity/point pattern analysis               • Remote Sensing image
                                                     processing and classification
     – nearest neighbor layer
     – distance matrix layer
                                                   • raster modeling
  • surface analysis                               • 3-D surface modeling
     – cross section creation                      • spatial statistics/statistical
     – visibility/viewshed                           modeling
  • network analysis                               • functionally specialized
     – routing                                           –   transportation modeling
              » shortest path (2 points)                 –   land use modeling
              » travelling salesman (n points)           –   hydrological modeling
     – time districting                                  –   etc.
     – allocation
  • Convex Hull
  • Thiessen Polygon creation
                                                                                       34
9/2/2009 Ron Briggs, UTDallas           GISC 6381 GIS Fundamentals
          Advanced Applications: Proximity Analysis
  Nearest Neighbor
  •   location (distance) relative to nearest             Point Pattern Analysis
      neighbor ( points or polygon centroids)
  •   location (distance) relative to nearest objects           is pattern?
      of selected other types (e.g. to line, or         Random Clustered Dispersed
      point in another layer, or polygon
      boundary)




  Requires only one output column
       – altho generalizable to kth nearest neighbor    Requires the application of
  Full matrix
                                                        Spatial Statistics such as
  •   measure location of each object relative          •Nearest neighbor statistic
      to every other object                             •Moran‟s I
       – requires output matrix with as many
         columns as rows in input table
                                                        which are based on proximity
                                                        of points to each other
                                                        ArcToolbox>Spatial Statistics Tools
                                                                                              35
9/2/2009 Ron Briggs, UTDallas            GISC 6381 GIS Fundamentals
                     Advanced Applications:
                       Network Analysis
                                                  Network-based Districting
        Routing
                                                  •   expand from site along network until
        • shortest path between two                   criteria (time, distance, cost, object
          points                                      count) is reached; then assign area to
                                                      district
             – direction instructions (locating
                                                        – creating market areas, attendance
               hotel from airport)                        zones, etc
        • travelling salesman: shortest                 – essentially network-based buffering
          path connecting n points                Network-based Allocation
             – bus routing, delivery drivers      •   assign locations to the nearest center
                                                      based upon travel thru network
    In all cases, „distance‟ may be                     – assign customers to pizza delivery
    measured in miles, time, cost or                      outlets
    other „friction‟ (e.g pipe diameter           •   draw boundaries (lines of
    for water, sewage, etc.).                         equidistance between 2 centers)
    Arc or node attributes (e.g one-way               based on the above
    streets, no left turn) may also be                 – Network-based market area
    critical.                                             delimitation
                                                       – Essentially, network-based
                                                          polygon tesselation                   36
9/2/2009 Ron Briggs, UTDallas          GISC 6381 GIS Fundamentals
Advanced applications:
                                                  Volumes
  Surface Analysis Cross-section Drawings and along a
                    • elevation (or slope) values
                                                   line
    Slope Transform
                                                • Volume & cut-and-fill calculation
    • fit a plane to the 3 by 3
       neighborhood around every cell, or       • Cross-section easy to produce for
       use a TIN                                   raster, more difficult for vector
    • output layer is the slope (first             especially if uses contours lines
       derivative) of the plane for each        Viewshed/Visibility
       cell                                     • terrain visible from a specific point
    Aspect Transform
                                                • applications
    • direction slope faces: (E-W
                                                     – visual impact of new construction
       oriented ridge has slopes with
       northern and southern aspects)                – select scenic overlooks
    • aspect normally classified into                – Military
       eight 45 degree categories               • Contouring
    • calculate as horizontal component              – Lines joining points of equal
       of the vector perpendicular to the              (vertical) value
       surface                                       – From raster, massed-points or
                                                       breakline data

                                                                                           37
9/2/2009 Ron Briggs, UTDallas        GISC 6381 GIS Fundamentals
  Advanced Applications: Convex Hull
  • Formally: the smallest convex polygon (no
    concave angles) able to contain a set of
    points
  • Informally: a rubber band wrapped around
    a set of points                              No!
  • Just as a centroid is a point representation
    for a polygon, the convex hull is the
    polygon representation for a set of points
  • Go to the following web site for a neat
    application showing how convex hull
    changes as you move points around
             –http://www.cs.princeton.edu/~ah/alg_anim/version1/ConvexHull.html
                                                                                  38
9/2/2009 Ron Briggs, UTDallas       GISC 6381 GIS Fundamentals
                 Advanced Applications:
 Thiessen (Dirichlet, Voronoi) Polgons                                Thiessen Polygons
                                                                       (or proximal regions
        and Delaunay Triangles                                        or proximity polygons)
   •   polygons generated from a point layer such
       that any location within a polygon is closer to
       the enclosed point than to a point within any
       other polygon                                                    A
   •   they divide the space between the points as
       „evenly‟ as possible
   •   used for market area delimitation, rain gauge
       area assignment, contouring via Delaunay
       triangles (DTs), etc.                                             Delaunay Triangles
   •   elevation, slope and aspect of triangle
       calculated from heights of its three corners
   •   DTs are as near equiangular as possible and
       longest side is as short as possible, thus                       A
       minimizes distances for interpolation
             Thiessen neighbors of point A share a common
              boundary. Delauney triangles are formed by
                 joining point to its Thiessen neighbors.
                                                                                        39
9/2/2009 Ron Briggs, UTDallas            GISC 6381 GIS Fundamentals
                      Specialized Applications
    Remote Sensing/Digital Image                     Raster Modeling: 2-D
      Processing                                     • use of direction and friction surfaces to
    • reflectance value (usually 8 bit; 256             develop models for:
      values) collected for each bands                    – spread of pollution
      (wavelength area) in the electro-                   – dispersion of forest fires
      magnetic spectrum                              Surface Modeling: 3-D
         –   1 band for grey scale (Black & white)
                                                          – flood potential
         –   3 for color
                                                          – ground water/reservoir studies
         –   up to 200 or so for „hyperspectral‟          – Viewshed/visibility analysis
         –   permits creation of image
                                                     Spatial Statistics/Econometrics
    •   „spectral signature‟: set of reflectance
        values/ranges over available bands           • analyses on spatial data which explicitly
        typifying a specific phenomena                  incorporates relative location or
                                                        proximity property of observations
         – provides basis for identification of
           phenomena                                      Global (applies to entire study area)
    Location Science/Network Modeling                     – spatial autocorrelation
                                                          – Regressions adjusted for spatial
    • Network based models for optimum                       autocorrelation
       location decisions for (e.g.)                      Local (separately calculated for local areas)
         –   police beats
                                                          – LISA (local indicators of spatial
         –   School attendance zones                         autocorrelation)
         –   Bus routes                                   – Geographically weighted regression
         –   Hazardous material routing
         –   Fire station location        We offer one or more courses on each!
                                                                                                          40
9/2/2009 Ron Briggs, UTDallas              GISC 6381 GIS Fundamentals
     Implementation of Advanced and Specialized Applications
                         in ArcGIS 8/9
   Extensions support many of the Advanced and some Specialized Applications
   • Spatial Analyst extension provides 2-D modeling of GRID (raster) data (AV 3.2 and 8/9)
   • 3-D Analyst extension provides 3-D modeling (AV 3.2 and 8/9)
   • Geostatistical Analyst extension provides interpolation (ArcGis 8/9 only)
   • Network Analyst extension (3.2 only) and ArcLogistics Route (standalone) for routing
      and network analysis
   • Image Analyst extension for remote sensing applications in AV 3.2
        – Leica Image Analysis and Stereo Analyst for ArcGIS 8 (9 version not yet released-Fall ‟04)
   • Spatial Statistics Tools in ArcToolbox provide spatial statistics (centroid, etc..)
   ArcScripts support other Advanced Applications and Specialized Applications
   • ArcScripts (in Visual Basic, C++, etc.) are used to customize ArcGIS 8
        – A variety of scripts available at http://support.esri.com/ >downloads
        – Note: ArcScripts written in Avenue work only in ArcView 3 and will not work in ArcGIS 8/9
        – Many functions previously requiring Avenue scripts for AV 3.2 are built into ArcGIS 8/9
   Specialized Software Packages
   • Remote Sensing packages such as Leica GeoSystems Imagine (formerly ERDAS
      Imagine)
   • For links to some of these packages go to:
      http://www.utdallas.edu/~briggs/other_gis.html
                                                                                                       41
9/2/2009 Ron Briggs, UTDallas            GISC 6381 GIS Fundamentals
                                Appendix

                   Implementing Spatial Analysis in
                          ArcView 3.2/3.3



                                                             42
9/2/2009 Ron Briggs, UTDallas   GISC 6381 GIS Fundamentals
  Implementing Spatial Measurement in ArcView 3.2
  •   Unlike in ArcGIS 8.1 where spatial measurements are provided automatically, in
      AV 3.2 spatial measurement often has to be implemented using Avenue code:
       – in functional expressions
       – in scripts
  •   Using functional expression for areas and lengths:
       – Use Edit/Add field to add a new variable to atttributes of…table called area (or similar)
       – Use Field/calculate and make this variable equal to: [Shape].ReturnArea
       –  Calculation is based on map units irrespective of defined distance units.
       –  If map units are feet, to obtain square miles use: [Shape].ReturnArea/5280/5280
       – If file is a polyline file (arcs), for length of arcs use: [Shape].ReturnLength
  •   Using a Script for areas, perimeters and lengths
       In Project window, select Script and click new button to open script window
       Use Script/load text file to load code from an existing text file
           e.g. arcview\samples\scripts\calcapl.ave will calculate areas, perimeters, lengths
       Click the “check mark” icon to compile the code.
       Open a View and be sure the theme you want processed is active.
       Click on script window then click the Runner icon to run script.
           variables measuring area and perimeter will be added to theme table


                                                                                                     43
9/2/2009 Ron Briggs, UTDallas              GISC 6381 GIS Fundamentals
       Implementing Spatial Matching in ArcView 3.2
   Available in two places (plus additional user extensions such as districting)
   • via Theme/select by theme
        – this selects features of the active theme which relate in some specified spatial manner to
          another theme
        – if desired, selected features may be saved later to a new theme via Theme/convert to shape file
   •   via Geoprocessing Wizard Extension (use File/Extensions to load)
        – this creates a new theme (shape file) & combines attribute tables from 2 or more input themes
        – Six options available for different types of matching
   Options in Geoprocessing Wizard (use View/Geoprocessing Wizard to activate)
   • Dissolve features based on an attribute
        – Use for spatial aggregation/dissolving                     •Scripts and extensions can provide
   •   Merge themes together                                         additional capabilities
        – Use for edge matching                                      •Download from ArcScripts at ESRI
   •   Clip one theme based on another                               http://gis.esri.com/arcscripts/
        – Use one theme to limit features in another theme           scripts.cfm
          (e.g. limit a Texas road theme to Dallas county only)      •Place extensions (.avx) in your
   •   Intersect two themes                                          folder Arcview/ext32
        – Use for polygon on polygon overlay                         •The extension district.avx is good
   •   Union two themes                                              for doing spatial aggregation or
        – Use for polygon on polygon overlay                         “districting”
   •   Assign data by location (Spatial Join)
        – Use for:        points in polygon
                          lines in polygon
                          points on lines (to calculate distance to nearest line)
                          points on points (to calculate distance to “nearest neighbor” point)
                                                                                                      44
9/2/2009 Ron Briggs, UTDallas              GISC 6381 GIS Fundamentals
        Using Extensions and Scripts in ArcView 3.2
 • Obtain copy of script or extension
      – Write yourself with Avenue language
      – Supplied with ArcView in folder: arcview/samples/scripts or arcview/samples/ext
            » Go to ArcView Help/Contents/Sample Scripts and Extensions for documentation
      – Buy from ESRI and other companies
      – Supplied free by ESRI or users and available on ESRI web site at:
          http://arcsripts.esri.com/ Select Avenue language
            » or go to www.esri.com and click Support
            » Be sure to print or download documentation/description
 • To load and use an extension
      – Place .avx file in arcview/ext32 folder
      – Open ArcView, choose File/extensions, place tick next to name, click OK
 • To load and use a script
      In Project window, select Script and click new button to open script window
      Use Script/load text file to load code from existing text file containing avenue code (.ave)
          e.g. \av_gis30\arcview\samples\scripts\calcapl.ave   will calculate areas, perimeters, lengths
      Click the “check mark” icon to compile the code.
      Take steps within ArcView as appropriate for specific script
          e.g. Open a View and be sure the theme you want processed is active.
      Click on script window then click the “Runner" icon to run script.
          e.g. variables measuring area and perimeter will be added to theme table
                                                                                                           45
9/2/2009 Ron Briggs, UTDallas               GISC 6381 GIS Fundamentals
           Some Example Avenue Scripts
                 for ArcView 3
       • Avenue scripts and extensions for AV 3.2 can be downloaded from
         ESRI Web site to do many basic, advanced and specialized
         applications not available in standard products. Some examples are:
             – Addxycoo.ave: adds X,Y coordinates of points (e.g of geocoded
               addresses), or of centroid for polygons, to attributes of … file
             – Polycen.ave: creates point theme containing polygon centroids
             – Dwizard.zip: various districting applications
                   » Use avdist31b which is an update
             – Line.zip: enhanced buffering of lines
             – Nearestneighbor.zip: nearest neighbor analysis
            For more scripts, go to: http://arcsripts.esri.com/ Select Avenue
            language


                                                                                  46
9/2/2009 Ron Briggs, UTDallas            GISC 6381 GIS Fundamentals

								
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