SANET: A Toolbox for Spatial Analysis on a Networkua.t.u-tokyo.ac.jp/okabelab/atsu/sanet/SANETmanual_Ver.2.0.pdf · A DBF format table which holds the adjacent node number, the link

SANET:

A Toolbox for Spatial Analysis on a Network

Version 2.0 - 040102

Atsuyuki Okabe, Keiichi Okunuki and Shino Shiode

Center for Spatial Information Science University of Tokyo

i

PREFACE

This manual describes how to use SANET: a toolbox for spatial analysis on a network.

SANET is part of the results obtained from the six year (1998-2003) project entitled “Spatial Information Science for Human and Social Sciences” funded by the Grant-In-Aid for Special Field Studies B provided by the Ministry of Education and Science, Japan. The leader is A. Okabe. SANET is developed by A. Okabe, K. Okunuki and S. Shiode with Mathematical Systems Inc.

ACKNOWLEDGEMENTS We express our thanks to Mathematical Systems Inc, in particular, C. Mizuta, K.

Okano and T. Ishitomi, for developing computer programs.

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NOTICE

The authors distribute SANET only to those who agree on the following points. 1. The user will use SANET for nonprofit purposes only. 2. The authors will not bear responsibility for any trouble that the user may meet in the

use of SANET. 3. When the user uses SANET, he/she will report to the authors his/her name, affiliation,

address and e-mail address. 4. When the user publishes any results obtained by using SANET, he/she will explicitly

state in the paper that he/she used SANET. Also, he/she will send a reprint of the paper to the authors.

5. The user will report to the authors any trouble he/she meets in the use of SANET.

(The authors will remove bugs, if any, at their earliest convenience.) The address of the authors is: Atsuyuki OKABE Center for Spatial Information Science c/o Department of Urban Engineering, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan [email protected]

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TABLE OF CONTENS

1. System requirements ............................................................................................................ 1 2. Installation instructions ........................................................................................................ 1 3. General notes ....................................................................................................................... 3 4. Instructions for using SANET.............................................................................................. 4

4.1 Tool_1: Construction of a node adjacency dataset....................................................... 4 4.2 Tool_2: Assignment of a point to the nearest point on a network................................ 9 4.3 Tool_3: Aggregation of attribute values belonging the same item............................. 15 4.4 Tool_4: Generation of a network Voronoi diagram.................................................... 17 4.5 Tool_5: Generation of random points on a network .................................................. 25 4.6 Tool_6: Execution of the network cross K-function method ..................................... 27 4.7 Tool_7: Execution of the network K function method............................................... 32 4.8 Tool_2.1: Partition of a polyline into the line segments constituting the polyline..... 37 4.9 Tool_2.2: Assignment of polygon attributes to the nearest line segment................... 39 4.10 Tool_2.3: Execution of the network nearest neighbor distance method .................. 42 4.11 Tool_2.4: Calculation of polygon centroids ............................................................. 46 4.12 Tool_2.5: Execution of the network Huff model ..................................................... 47

5. References.......................................................................................................................... 52

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1. System requirements Windows NT, 2000, XP ESRI ArcView 8.x

2. Installation instructions

1. Save SANET.zip to any directory. 2. Unzip SANET.zip using WINZIP or any other file compression software. Inside SANET.zip you

will find two files: network_tools_VB.dll and ArcView_tools.dll. 3. Place ArcView_tools.dll under the ArcView Bin directory arcgis¥arcexe81¥Bin in your computer. 4. Place network_tools_VB.dll anywhere you want in your computer. 5. Start ArcMap. 6. In the menu bar of the ArcMap project window, select “Tools”, and proceed to “Customize”. 7. Select “Commands” tag, and click on “Add from file” button, to navigate to a file

network_tools_VB.dll. 8. Click on network_tools_VB.dll, then “Added Objects” window will appear (Figure 1(a)). 9. Click OK in “Added Objects” window. 10. In “Commands” box, you will find the list of 12 tool buttons (Figure 1(b)). 11. Select, and drag and drop these buttons one by one into the menu bar or the view button bar.

Note: This task may be troublesome, but the next version of SANET will provide just one

SANET tool button in which you can select each tool in a drop down list.

12. Press Close. Then, in your menu bar or view button bar on the ArcMap project window, you will find 12 new

buttons (Figure 2).

2

Menu bar View button bar

ArcMap project windowTable of contents

Figure 2: SANET Tools

(a) (b) Figure1: Adding SANET tools to the ArcMap project window

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3. General notes

(1) Network data

Network polylines for the analysis should be connected to each other. If an isolated polyline exists in your prepared data, eliminate it before executing the tools.

(2) Computational time

Since the computational time for each tool may be lengthy, it is preferable to begin with small datasets.

(3) Site map of tools Some tools should be executed after applying other tools. The following is the steps to execute tools. Multi step processing Single step processing

Tool_2.1

Tool 2

Tool_1

Tool_4

Tool_6 Tool_7 Tool_2.3 Tool_2.5

Export points to create a point shapefile

Tool_5 Tool_2.4 Tool_2.2Tool_3

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4. Instructions for using SANET

4.1 Tool_1: Construction of a node adjacency dataset

Tool_1 converts a network polyline shapefile into a dataset that defines the adjacency of nodes. The

output dataset consists of the following three files.

(1) Polyline-point shapefile A point shapefile created by extracting all the points on a network polyline shapefile. The attribute table of the polyline-point shapefile has a field with pointer values pointing record numbers of the adjacent node table (Figure 3(a)(b)).

(2) Adjacent node table

A DBF format table which holds the adjacent node number, the link length and any other attributes field(s) (Figure 3(c)).

(3) Network index file

A text file which contains filenames and relative paths of (i) input network polyline shapefile, (ii) output polyline-point shapefile and (iii) output adjacent node table.

(a) Polylines (b) Attribute table of polyline-point shapefile (c) Adjacent node table

Figure 3: Basic data structure of a network in SANET

Polyline-point

Adjacent node ID Link length Pointer

Record number

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Instructions 1. Add the network polyline shapefile for the analysis to the project window (Figure 4).

Note: When you apply Tool_1, be sure to apply Tool_2.1 beforehand. Polyline parts you use as an input data

in Tool_1 should have no intermediate points.

As a sample datasets, we use network polyline shapefile “ROAD_d”, which consists of 1367 links, and

some types of point data. Each filename is shown in the title of figures.

2. Click button in the menu bar or the view button bar, then the dialogue box of Tool_1

appears (Figure 5).

Figure 5: Dialogue box of Tool_1

(1)

(2)

(3)

(4)

Figure 4: Network polyline shapefile “ROAD_d

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3. Fill in the dialogue box following the instructions below.

(1) Select the network polyline shapefile in the drop down list. (2) You can transfer the attribute field(s) in the network polyline shapefile to the output adjacent

node table, by checking in the check box to the left of “Transfer attribute field(s) to the adjacent table”

(3) If you checked in the check box, select attribute field(s) you want to transfer to the adjacent node table in the “Attribute field(s)” box.

(4) Specify the filename of the output network index file by clicking button and by navigating

to the suitable folder.

4. Press .

Output files (1) Polyline-point shapefile ( filename <input polyline shapefile name _v>*2 )

A point shapefile which holds the entire polyline-points of the network polyline shapefile will be created. It will be automatically added on the map (Figure 6).

(*2: If a file with the same filename already exists, the new file will be saved with a different

filename, such as < _v1>, < _v2>,…)

Figure 6: Polyline-point shapefile “ROAD_d_v” (green points)

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The attribute table of the polyline-point shapefile has fields “NodeID”, “head”, and “x” and “y” (Figure 7). “NodeID” stores ID numbers of polyline-points and “head” stores pointer values pointing record numbers of the adjacent node table. “x” and “y” are coordinates of polyline-points.

(3) Adjacent node table A DBF format file named “< network index file name .atbl.dbf >” will be created ( Figure 8(b) ). Fields “OID”, “AdjPoint” and “Length” will be added automatically. If you checked the “Transfer

attribute field(s) to the adjacent table” check box in the dialogue box, attribute field(s) you selected would also be added to the adjacent node table.

Field “OID” holds the record number of the adjacent node table. “AdjPoint” holds node IDs that are adjacent to nodes in the polyline-point shapefile. “Length” is the link length between two polyline-points. One is in the attribute table of the

polyline-point shapefile and the other is in the adjacent node table. (The unit of lengths is the same as the projected features).

Note: If a field “LENGTH” or “ADJPOINT” existed (irrespective of the size of characters) in the fields you

selected at step (3), it will be saved with the names of “LENG_1” and “ADJ_1” respectively.

Figure 7: Attribute table of polyline -point shapefile “ROAD_d_v”

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(3) Network index file A text format file named “< network Index file name .nidx >” will be created in your specified

folder (Figure 9).

(a) Attribute table of polyline-point

shapefile “ROAD_v” (b) Adjacent node table “REFROAD.atbl.dbf”

Figure 8: Adjacent node table

Figure 9: Network index file “REROAD.nidx”

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4.2 Tool_2: Assignment of a point to the nearest point on a network Tool_2 assigns a point which is not on a network (we call it an original point) to the nearest point on

a network (we call it an access point).

Instructions 1. Prepare the following two input shapefiles and add them on the project window (Figure 11).

(1) Network polyline shapefile. (2) Point shapefile (original points).

2. Click button, then the dialogue box of Tool_2 appears (Figure 12).

Figure 11: Network polyline shapefile “ROAD_d” and point shapefile “BANK_STORE”

Figure 10: Assignment of points to the nearest points on a network

Access points

Original points

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(1) Specify the network index file created in Tool_1. (2) If you want to allocate values in the attribute field(s) of the input adjacent node table

proportional to link lengths, check in the check box.

(3) If you checked in the check box, select attribute field(s) in the “Attribute field(s)(>=1)” box.

Note: In “Attribute field(s)(>=1)” box, all the fields in < network index file.atbl.dbf > file, which is

created in Tool_1 (filename of which is written in the input network index file) ,will be shown.

Do not select field(s) holding characters. It will cause an error.

(4) Select the point shapefile of original points in the drop down list.

(5) Select ID field of the point shapefile.

Note: In “ID field” box, fields except “FID” in the input point shapefile will be shown. Do not select the

field “NodeID” as the ID field. It will cause an error. If you want to select it, change the filename.

ID field should hold identify numbers of original points. These identify numbers will be reflected in “point

access table” (see output files) to identify which original point corresponds to an access point in newly

created polyline-point shapefile.

(6) Specify the filename of the output network index file.


(1)

(2)

(3)

(4)

(5)

(6)

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Note: By clicking icon, you can see the contents of the network index file you selected (Figure 13).

4. Press . After running Tool_2, original points are inserted into the network shapefile, and they become new

polyline-points. Polylines will be cut at the points where original points are inserted.

Output files (1) Network polyline shapefile (file name: < Network Index file>) (Figure 14)

Original points you selected at step (4) will be assigned to the nearest points on the network (Figure 15 is the magnified portion of Figure 14).

Fields you selected in the “Attribute field(s)” box and a new field “Length”, which is physical lengths of links, will be added to the attribute table.

(2) Polyline-point shapefile (file name: < Network Index file _v >)

A point shapefile which holds existing polyline-points and newly added access points will be created (Figure 14).

Fields “NodeID”, “head”, “x” and “y” will be added to the attribute table.

Figure13: Contents of the network index file

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Note: If an access point is extremely close to an existing polyline-point or an already added new access point,

an additional access point will not be created. As the result, in the output polyline-point shapefile, multiple

original points may be assigned to one polyline-point or one access point.

(3) Point access table (file name: < Network Index file _r.dbf >) (Figure 16)

A DBF format file which has fields “OID”, “<field name of ID field> ” which you selected at step (5), and “NodeID”. “<field name of ID field>” holds the identify numbers of the original points, and “NodeID” holds node ID numbers of the corresponding polyline-point in the new polyline-point shapefile.

Figure 14: Network polyline shapefile “REFROAD_PT” and polyline-point shapefile “REFROAD_PT_v” (green points)

Figure 15: Correspondence of original points and access points

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(4) Adjacent node table <network index file .atbl.dbf > (Figure 17) New fields “OID”, “AdjPoint”, and “Length” will be added. All the attribute field(s) in the input adjacent node table will also be added to the output adjacent

node table. Values in field(s) you selected at step (3) of instructions will be allocated proportional to the link lengths.

Note: If a field “LENGTH” or “ADJPOINT” existed in the fields you selected in the “Attribute field(s)” box,

they will be saved with the names of “LENG_1” and “ADJP_1” respectively. Similarly, if a field “LENG_1”

or “ADJP_1” was in the fields you selected, they will be saved with the names of “LENG_2” and “ADJP_2”

respectively. But values in those fields (they are lengths and adjacent point IDs) are updated in fields

“Length” and “Adjpoint” in the adjacent node table, so you do not need to use values of “LENG_1”,

“LENG_2”, “ADLP_1”, “ADJP_2”.

Figure 16: Point access table “REFROAD_PT_r”

Figure 17: Relationship between three tables: point access table “REFROAD_PT_r“, attribute table of polyline-point shapefile “REFROAD_PT_v“, and adjacent node table “REFROAD_PT.atbl.dbf”

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In Figure 17, the original point 44 has become the polyline-point 1233. In the attribute table of polyline-point shapefile, polyline-point 1233 is pointing the record number 2810 of the adjacent node table, which shows the polyline-point 1233 is adjacent to two polyline-points, 278 and 230 (Figure 15).

(5) Network index file (Figure18).

Export a point shapefile To apply K function (Tool_6,Tool_7), nearest neighbor method (Tool_2.3), and the Huff model tools

(Tool_2.5), you need to create a new shapefile of access points, select all access points in the output polyline-point shapefile of Tool_2 and export them to create another shapefile consisting of points on the network.

Figure 18: Network index file “REFROAD_PT.nidx”

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4.3 Tool_3: Aggregation of attribute values belonging the same item Tool_3 does not conduct a map based operation, but conduct table calculation using DBF format

files. Tool_3 aggregates values in the input table file in terms in the values of designated attribute field. In the case of the example shown in Figure 19, Tool_3 sums “Population” values in the records that

have the same values in the field “Area_ID”.

Instructions

1.Click button, then the first dialogue box appears (Figure 20).

2. Specify the filenames of

(1) Input file (DBF format) (2) Output file (DBF format)

3. Press , then the second dialogue box appears (Figure 21).

(a) Input table (b) Output table Figure 19: Field aggregation

Figure 20: First dialogue box of Tool_3

(1)

(2)

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(1) Select “ID” field in the drop down list. Records having the same value in this field becomes one record in the output file.

(2) Select at least one field(s). Values in the field(s) are aggregated in terms of the field selected above.

5. Press .

(1)

(2)

Figure 21: Second dialogue box of Tool_3

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4.4 Tool_4: Generation of a network Voronoi diagram Tool_4 constructs a Voronoi diagram based on a set of Voronoi points (we call them generator points

or generators) on a network.

Instructions 1. Prepare the following two input shapefiles and add them on the project window (Figure 22). (1) Network polyline shapefile

(2) Polyline-point shapefile created as an output file of Tool_2, which includes generator points as new polyline-points (access points). (Do not export access points as a new shapefile).

2. Click , then a dialogue box appears (Figure 23).

Figure 22: Network shapefile “ROAD_d” and polyline-point shapefile ‘’REFROAD_PT_v”

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(1) Specify the network index file created as the output file of Tool_2. (2) Select the polyline-point shapefile created as the output file of Tool_2. (3) Distance from a generator point to a location on a network is measured using physical link lengths

or values in an attribute field (ex. time distances, costs, or any other weighted values). Check in either check box. If you checked in “by values in an attribute field” check box, select an attribute field in the drop down list.

(4) If you want to allocate values in attribute field(s) in the input adjacent node table proportional to link lengths, check in the check box and select attribute field(s) in “Attribute field(s)” box. They will be added to the output adjacent node table.

(5) Specify the filename of the output network index file.

4. In the ArcMap table of contents, right-click on the polyline-point shapefile to make it active.

5. Open the attribute table of the polyline-point shapefile.

6. Select the records of generator points in the attribute table, to make them active (Figure 24).


(1)

(2)

(3)

(4)

(5)

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7. Press .

Output files (1) Polyline-point shapefile < Network Index file _v> (Figure 25)

Collision points and boundary points will be added in this file (Figure 27). Collision point is a point which has more than two different routes with the same shortest path distances toward one generator point. On the other hand, boundary point is a point which has the same length of shortest path distances to two or more different generator points. More than two Voronoi regions are connected to each other at a boundary point.

Note: As to the details of collision points and boundary points, please refer Okabe and Okunuki (2001).

In the attribute table of this file, collision points and boundary points are identified with the value of

1 in fields “C_Point” and “BoundPoint” respectively. (Figure 26) The polyline-point shapefile has two pointer fields, “head” and “phead”. The former points the

record number of the adjacent node table, the latter points the record number of the nearest path table.

Figure 24: Polyline-point shapefile and activated generator points in “REFROAD_PT_v”

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Figure26: Attribute table of Polyline-point shapes “VORTREE v”

Collision points

Boundary points

Figure25: Polyline-point shapefile “VORTREE_v”

Figure27: Locations of boundary points (left) and collision points (right) (marked in light blue)

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(2) Network polyline shapefile < filename: network index file > (Figure 28). In the attribute table of this file, field “NN_Gene” will be created, which holds ID numbers of the

nearest generator points. Note: To display polylines in different colors in terms of the nearest generators, double click on the

polyline shapefile in the table of contents, and “Layer Property Box” will appear. Click “Symbol” in the menu bar and double click “Category” in the “Show” box to the left. Select “NN_Gene” in the “Field” dropdown list. Click “Add All” and then, click “Apply”.

(3) Adjacent node table < network index file .atbl.dbf> (Figure 29) Polyline-point 1926 is pointing the record number 4196 of the adjacent node table. It means two

polyline-points 697 and 1498 are adjacent to the polyline-point 1926. New fields “OID”, “AdjPoint”, and “Length” will be added. All the attribute field(s) in the input adjacent node table will also be added to the output adjacent

node table. Values in field(s) you selected will be allocated proportional to the link lengths.

Figure 28: Network polyline shapefile “VORTREE“

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(4) Nearest path table < network index file _p.dbf > (Figure 30)

Nearest path table is a DBF format file containing fields “NN_Gene”, “PreNode” and “PathDist”. “NN_Gene” holds identify numbers of the nearest generator points. “PreNode” holds the predecessor polyline-points along the shortest paths toward the nearest generator points. “PathDist” holds the shortest path distances to the nearest generator points.

Figure 30: Nearest path table “VORTREE_p.dbf”

Figure 29: Attribute table of polyline-point shapefile “VORTREE_v” and adjacent node table “VORTREE.atbl.dbf”

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(5) Generator points shapefile < filename: Network Index file _g> (Figure 31) All the generator points are extracted from the input polyline-point shapefile, to make a point

shapefile.

(6) Adjacent node table of generator points <Generator point shapefile_g.gatb.dbf > (Figure 32) The table shows adjacency of generator points. Field “SPDist“ denotes the shortest path distance between two generators, and field “Adj_Gene”

shows the ID number of the adjacent generators. Generator point shapefile has a field “ghead” which points record numbers of the adjacent node

table of generator points. Field “NodeID” stores the existing ID numbers as polyline-points. For example, node 1199 is incident to six generators 1208, 1196, 1203, 1201, 1204, and 1200 (Figure 31 and 32).

Figure 31: Generator points labeled with their NodeIDs

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(7) Network index file

Figure 32: Generator point shapefile “VORTREE_g” and the adjacent node table of generator points “VOROTREE_g_gatb”

Figure33: Network index file

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4.5 Tool_5: Generation of random points on a network Tool_5 generates random points according to the Poisson point process on the network (i.e. the

probability of a point being placed on a unit line segment on a network is the same regardless of the location of the segment).

Instructions 1. Add the network polyline shapefile to the project window (Figure 34).

2. Click button, then a dialogue box appears (Figure 35).

Figure 34: Network shapefile “ROAD_d”

Figure 35: Dialogue box in Tool_5

(1)

(2)

(3)

(4)

26


(1) Select the polyline shapefile in the drop down list. (2) Type the number of random points to be generated. (3) Distances on the network are measured using physical link lengths or values in an attribute field.

Check in either check box. If you checked in “by values in an attribute field” check box, select an attribute field in the drop down list of “Attribute field”.

(4) Specify the filename of the output random point shapefile.

4. Press . After computation, another dialogue box appears with a message of “Add created point shapefile in

the map?”.

5. Press button if you want to add the created random point shapefile on the project window.

Output file Random point shapefile (Figure 36).

Figure 36: Output point shapefile “RANDOM” (1000 green points)

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4.6 Tool_6: Execution of the network cross K-function method Tool_6 is to detect the locational tendency whether points (of Type A) are independently and

randomly distributed with respect to a set of fixed points (of Type B) by cross K function method. We call type A points non-basic points, and type B points basic points.

Instructions 1. Add the following three input shapefiles on the project window (Figure 37).

(1) Network polyline shapefile (2) Basic point shapefile (3) Non-basic point shapefile Note: All points in file (2) and (3) should be located on the network (1). If they are not on the network, apply

Tool_2 and export access points to create a point shapefile which consists of points on the network.

2. Click , then the dialogue box appears (Figure 38).

Figure 37: Network polyline shapefile “ROAD_d”, basic point shapefile “STORE_ON” and non-basic point shapefile “BANK_ON”

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(1) Specify the network polyline shapefile along which shortest path distances from basic points to non-basic points are calculated.

(2) Select the basic point shapefile in the drop down list. (3) Select the non-basic point shapefile in the drop down list. (4) Distance from a basic point to a non-basic point on a network is measured using physical link

lengths or values in an attribute field. Check in either check box. If you checked in “by values in an attribute field” check box, select an attribute field in the drop down list.

(5) Specify the filename of the output table file.

4. Press .

Output files Two DBF format output files will be created. You can read in them using any spreadsheet application (ex. Microsoft Excel) to aggregate data and

to display graphs.

(1) Observed K function table (filename: < table file _o.dbf> ) (Figure 39) A table contains observed cumulative numbers of non-basic points with respect to the shortest-path

(1)

(2)

(3)

(4)

(5)


29

distance from basic points. Fields “OID”, “Distance” and “SumPoints” are created. “Distance” is the shortest path distance from basic points. “SumPoints” shows the number of

cumulative points located within a distance from basic points. Since Tool_6 counts all the non-basic points from basic points, value of “SumPoints” amounts to < #

of basic points * # of non-basic points >.

Figure 40 is the observed K function curve created by setting “Distance” as x-axis and “SumPoints” as y-axis.

Figure 39: Observed K function table

Figure 40: Observed K function curve

(m)

Points

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(2) Expected K function table (filename: < table file_e.dbf > ) (Figure 41) This is a table to make an expected cross K-function curve.

Fields “OID”, “FromDist”, “ToDist” and “Links” are created. “FromDist” and “ToDist” are the

starting value and the ending value of OID’th interval distance. “Links” is the number of links existing within each interval distance.

To make the expected K function curve to overlay with the observed K function curve, you should

derive the expected numbers of cumulative points. First, get the total distance of the network links in your network data. Second, calculate the expected numbers of cumulative points. The expected number of points

= (ToDist – FromDist) * Links * (number of non-basic points) / (total distance of network links) The expected numbers of cumulative points can be derived by accumulating the expected numbers

of points. Setting “ToDist” as x-axis and “Links” as y-axis, you can get a graph of expected K function curve

(Figure 43).

Figure 41: Expected K function table

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Figure 44 is the overlay of Figure 40 and Figure 43. If the observed curve is to the left of the expected curve like Figure 44, it shows the non-basic points

tend to locate near the basic points. On the other hand, if the observed curve is to the right of the expected curve, it shows the basic points and the non-basic points tend to locate apart.

Note: The current version of SANET doesn’t have a function to calculate the confidence interval of

cross K-function, but it can be theoretically obtained from the binomial distribution. (The authors can send you a MS Excel format spreadsheet to conduct this calculation.)

Figure 43: Expected K function curve

(m)

Points

Figure 44: Overlay of the observed and expected k function curves

(m)

Points

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4.7 Tool_7: Execution of the network K function method Tool_7 is to test the randomness of one type of point distribution on a network by K function

method. The tool derives upper and lower 5% confidence interval of K function by Monte Carlo simulations.

Instructions 1. Add the following two data sets on the project window (Figure 45). (1) Network polyline shapefile (2) Point shapefile

Note: If point shapefile (2) is not located on the network, apply Tool_2 and exported access points

assigned on a network to create a point shapefile which consists of points on a network.

2. Click button, then a dialogue box appears (Figure 46).

Figure 45: Network polyline shapefile “ROAD_d” and point shapefile “BANK_ON”

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(1) Specify the network polyline shapefile along which distances between points are measured. (2) Select the point shapefile in the drop down list. (3) Distance from a point to another point on a network is measured using physical link lengths or

values in an attribute field. Check the either check box. If you checked in “by values in an attribute field” check box, select an attribute field in the drop down list of “Attribute field”.

(4) Specify the filename of the output table. (5) Type the number of simulations. (6) Type the interval distance to create an output table. (The unit of distance is the same as

projected features).

4. Press .

Output files (1) Observed K-function table ( filename: < table file _o.dbf> ) (Figure 47)

A DBF format file having three fields “OID”, “Distance” and “SumPoinsts“ will be created.


(1)

(2)

(3)

(4)

(5)

(6)

34

“SumPoints” holds cumulative numbers of points located within shortest-path distances (they are shown in “Distance” field) from the points.

You can get the observed K function curve by setting “Distance” as x-axis and “SumPoints” as

y-axis. (2) Expected K function table ( filename: < table file _e.dbf> ) (Figure 49)

An expected K function curve and 5% confidence interval will be derived by Monte Carlo simulations.

Figure 47: Observed K function table

Figure 48: Graph of observed K function curve

(m)

Points

35

The table holds fields “FromDist”, “ToDist”, “Max”, “Min”, “Mean”, “UP5”, and “LW5”. “FromDist” and “ToDist” are the starting value and the ending value of OID’th interval of

distance. “Max”, “Min”, “Mean”, “UP5” and “LW5” are the maximal, minimal, mean, upper 5%, and lower 5% number of cumulative points located within each interval distance.

Figure 50 is the graph of K function curve created by setting “ToDist” as x-axis, and mean, upper

5% and lower 5% cumulative points as y-axis.

Figure 49: Expected K function table

Figure 50: Confidence interval of expected K function curve

Mean

LW5%

UP5%

(m)

Points

36

Figure 51 is the overlay of Figure 48 and Figure 50. Interpretation of the graph is similar to the case of cross K function. If the observed curve is to the left of the upper 5% K function curve, it shows the observed points

significantly locate near each other. On the other hand, if the observed curve is to the right of the lower 5% K function curve, it shows the observed points significantly locate apart.

Figure 51: Overlay of the observed and expected K function curves

(m)

Points

37

4.8 Tool_2.1: Partition of a polyline into the line segments constituting the polyline

Tool_2.1 devides a polyline part into link(s). A link consists of a line and two end points. Be sure to apply Tool_2.1 before applying Tool_1.

Instructions 1.Add the network polyline shapefile on the project window. 2. Click Tool_2.1 button, then a dialogue box appears (Figure 53).


(1)

(2)

(3)

Figure 53: Dialogue box of Tool_2.1

(a) A polyline part (b) Three links Figure 52: Conversion of a polyline

38

(1) Select the network polyline shapefile in the drop down list. (2) If you want to allocate values in attribute field(s) proportional to link lengths, check in the check

box.

(3) If you checked in the check box, select field(s) in “Attribute field(s)” box.

4. Press . Note: All the attribute field(s) in (1) will be shown in the output network polyline shapefile. Fields

you did not selected at (3) will be transferred with the same values.

Output file A network polyline shapefile named <nework polyline shapefile _d> will be created in the same

directory as the input shapefile. If a file with the same filename exists, the ouput file will be saved with another filename, such as

<nework polyline shapefile_d1>, <nework polyline shapefile_d2>… .

39

4.9 Tool_2.2: Assignment of polygon attributes to the nearest line segment Tool_2.2 allocates attribute values in polygons to their nearest links. The method of allocation is as follows,

1. Divide polygons into grids. You can specify the grid size in the dialogue box. 2. Allocate polygon attributes proportional to the grid size and assign them to each grid’s

attribute table. (Peripheral areas which have not become proper grids are included in the nearest proper grids).

3. Transfer grid attributes to their nearest network links. 4. Aggregate assigned attribute values in terms of links.

Instructions 1. Add the following input shapefiles to the project window.

(1) Network polyline shapefile. (2) Polygon shapefile with a field of ID number.

Note: Apply ‘Intersect’ to the polygon and the polyline shapefiles before running Tool2_2 using “Geo

processing wizard” in ArcMap.

In the menu bar, click on ‘Tools’ button and select ‘Geo Processing wizard’, then the Geo Processing

window appears. Check ‘Intersect two layers’ check box and proceed to the next window. In the next

window, select the polyline shapefile at ‘1. Select the input layer to intersect’ box. Select the polygon

shapefile at ‘2. Select a polygon overlay layer’.

Applying intersect, polylines are cut at intersections with polygons, and all the attributes in the polygon

Network

Polygon B Polygon A

40

shapefile will be transferred to the polyline shapefile, as well as polygon ID numbers.

2. Click Tool_2.2 button, then the dialogue appears (Figure 54).


(1) Specify the polygon shapefile. (2) Select the ID field of polygon shapefile in the drop down list. Note: ID field is a field that has polygon identify numbers.

(3) Select attribute fields of the polygon shapefile that you want to transfer to the links. (4) Select the network polyline shapefile on which polygon attributes are to be transferred. (5) If you would like to assign polygon attributes only to the links which has the same ID numbers

even if it is not the nearest links (it means that a polygon attributes are assigned to a link which is included in the same polygon), check in the check box. (If you do not check in the box, attributes will be allocated to the nearest links).

(6) Select ID field of the network polyline shapefile, which is transferred on the network polyline by intersecting.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Figure54: Dialogue box of Tool_2.2

41

Note: Two “ID fields” asked to specify the values in the dialogue box correspond to the fields which contain

polygon identify numbers. They exist in either shapefiles, polygon and polyline shapefile.

(7) Input the grid size, the unit of which is the same as the currently projected features. If you have not specified the unit, you will see “Unknown Units” on the dialogue box.

(8) Specify the output filename.

4. Press .

Output file Polyline shapefile < new polyline shapefile name> will be created. Attribute field(s) you selected at step (3) will be added to this shapefile. If the field with the same

field name already exists, a field with the name of < new field name 1> will be created.

42

4.10 Tool_2.3: Execution of the network nearest neighbor distance method Tool_2.3 is to investigate points (of Type A) are independently and randomly distributed with

respect to a set of fixed points (of Type B). We call type A points non-basic points, and type B points basic points. If basic points and non-basic points are the different, we call this type of nearest neighbor method ‘conditional nearest neighbor method’. On the other hand, if basic points and non-basic points are the same, we call such type of nearest neighbor method just ‘nearest neighbor method’. Tool_2.3 can deal with either type of nearest neighbor methods.

Instructions 1. Add the following two input shapefiles on the project window. (Figure 55)

(1) Network polyline shapefile (2) Point shapefile(s)

2. Click Tool_2.3 button, then the dialogue box appears (Figure 56).

Figure55: Network Polyline shapefile “ROAD_d“, basic point shapefile, “STORE_ON”, and non-basic point shapefile “BANK_ON”

43


(1) Specify the polyline shapefile on which the shortest path distances between points are calculated. (2) Select the basic point shapefile in the drop down list. (3) Select the non-basic point shapefile in the drop down list.

Note: If you want to investigate the locational tendency of one type of points by applying the normal nearest

neighbor method, select the same point shapefile for (2) and (3).

(4) If you specified the same file for (2) and (3), check in the check box. (5) Specify the filename of a nearest neighbor distance table (6) Specify the filename of a pointer table to nearest neighbor points (7) Specify the filename of a frequency distribution table (8) Input the interval distance for making a frequency distribution table and a cumulative distribution

table.

4. Press .


(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

44

Output files and graphs Three DBF format output files and two graphs will be created.

(1) Nearest neighbor distance table (Figure 57) Fields “NN_Node” and “PathDist” are created. The former holds node numbers of the nearest points

from basic points. The latter holds the shortest path distances between two points.

(2) Pointer table to nearest neighbor points (Figure 58) Fields “NodeID” and “head” are created. The former holds the node numbers of basic points. The

latter holds the pointer values pointing record numbers of “Nearest neighbor distance table”.

(3) Frequency distribution table (Figure 59) Fields “FromDist”, “ToDist”, “frequency”, and “SumPoints” are created. Difference between values in “ToDist” and “FromDist” is the interval distance you specified in the

dialogue box. “frequency” holds the frequency distribution of the observed numbers of non-basic points within interval distances of basic points.

“SumPoints” holds the cumulative numbers of values of “frequency”, which means cumulative

Figure57: Nearest neighbor distance table “NND.dbf”

Figure58: Pointer table to nearest neighbor points “NNP.dbf”

45

frequency distribution of the observed number of non-basic points.

(4) Frequency distribution graph < Pointer table to nearest neighbor points.grf > and cumulative frequency distribution graph < Pointer table to nearest neighbor points_c.grf >

(Figure 60) These are the graphs made from the frequency distribution table.

Note: The current version of SANET doesn’t have a function to calculate the confidence interval of these

two nearest neighbor methods. It will be included in the next version of SANET.

Figure59: Frequency distribution table “NNF.dbf”

Figure60: Frequency distribution graph NNP.grf and Cumulative distribution graph NNP_c.grf

46

4.11 Tool_2.4: Calculation of polygon centroids Tool_2.4 calculates centroids for polygons (we call it a representative point) and create a new point

shapefile.

Instructions 1. Add the polygon shapefile on the project window. 2. Click Tool_2.4 button, then the dialogue box appears (Figure 61). 3. Select the polygon shapefile in the drop down list.

4. Press .

Output file Point shapefile named <polygon shapefile .rep> will be created. All the attribute fields of the input polygon shapefile are transferred to their representative points.


47

4.12 Tool_2.5: Execution of the network Huff model Tool_2.5 estimates the demand of supply points using the Huff model.

Instructions If point shapefile (2) and (3) are not located on the network (1), apply Tool_2 first and export points

assigned on a network to create a point shapefile which consists of points on a network. 1. Add the following three input shapefiles on the project window (Figure 62). (1) Network polyline shapefile created in Tool_2 as an output polyline shapefile. (2) Supply point shapefile (3) Demand point shapefile

Supply points should have an attribute field which holds any attractiveness values, such as sales

volumes and areas of stores. Demand points should also have an attribute field which holds any demand values, such as the numbers of family members and purchasing powers of customers.

2. Click Tool_2.5 button, then the dialogue box appears (Figure 63).

Figure62: Network polyline shapefile “Huff_supply_demand”, supply point shapefile “SUPPLY” labeled with supply amounts and demand point shapefile “DEMAND”

48


(1) Specify the polyline shapefile along which distances from supply points to demand points are measured.

(2) Select the supply point shapefile in a drop down list. (3) Select the attractiveness field in the attribute fields of the supply point shapefile. (4) Select the demand point shapefile in the drop down list. (5) Select the demand field in the attribute fields of the demand point shapefile. (6) Input lambda value. (As for the appropriate value, refer to the probability function below)(For

the dataset in Figure 62, 0.01 was used for lambda value).

4. Press .

Note: Probability Pij that a consumer at a demand point i chooses a supply point j is represented as

∑ −

−=j

dijAjdijAjPij

) exp( ) exp(

λλ

where, Aj : Attractiveness value (amount of supply) of a supply point j, dij : Distance from a consumer i to a supply point j.


(1)

(2)

(3)

(4)

(5)

(6)

49

Output files Three output files with information about the territories of demand points are created.

(1) Network polyline shapefile <network polyline shapefile _nn> (Figure 64) Fields “ID”, “Supply_ID”, “Max_Prob” and “Min_Prob” will be created. “ID” is the link ID. “Supply_ID” holds the supply point that the probability of being selected by a

consumer located on the link is the largest (Links colored in terms of “Supply ID” are shown in Figure 67).

“Max_Prob” and “Min_Prob” are maximum and minimum probabilities that a customer on the link selects one of the supply points.

(2) Polyline-point shapefile <network polyline shapefile _nn_v> (Figure 65) This point shapefile consists of polyline-points on the network, collision points, demand points and supply points.

Fields “Demand”, “Supply_ID”, “Distance”, “Dom_Demand”, “Max_Prob”, and “Min_Prob” will be created.

“Demand” is the amount of demand, which is the same as in the demand point shapefile. Polyline points and collision points have values of 0 and –1 respectively in this field.

“Supply_ID” holds supply point IDs that the probability of being selected by a consumer located at the point is the largest (Points colored in terms of “Supply ID” are shown in Figure 67).

“Distance” holds the distances to the supply points in “Supply_ID” field from points. “Dom_Demand” is the total amount of demand that each supply point has acquired. Points other

Figure 64: Network polyline shapefile “Huff_supply_demand_nn”

50

than supply points has 0 values in this field. “Max_Prob” and “Min_Prob” are maximum and minimum probabilities that a customer located at

the point selects one of the supply points.

(3) Choice probability table <network polyline shapefile _nn_prob.dbf> (Figure 66) A DBF format table file holding the fields “NodeID” and more than one field(s) of “<ID number of

supply point>” will be created. “NodeID” is ID number of each demand point as a Polyline-point of the output point shapefile (2). The number of fields “<ID number of supply point>” would be the number of the supply points. In the field of each “<ID number of supply point>”, probabilities that consumers at their demand

points select each supply point are stored.

Figure 65: Polyline-point shapefile “Huff_supply_demand_nn_v”

Figure 66: Choice probability table

51

Figure 67: Territories of dominant supply points

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5. References

Aho, A.V., Hopcroft, J.E. and Ullman, J.D. (1974) The Design and Analysis of Computer Algorithms, Reading,

Massachusetts: Addison-Wesley.

Bailey, T.C., and Gatrell A.C. (1995) Interactive Spatial Data Analysis, Harlow: Longman.

Buxton, T. (1992) “GIS Expected to Micromarketing Challenge”, GIS World, Vol.5, No.1, pp.70-72.

Egenhofer, M. and Franzosa, R. (1991) “Point-Set Topological Spatial Relations”, International Journal of

Geographical Information Systems 5 (2): 161-174.

Kato, T., Sadahiro, U., Shiode, S. and Okabe, A. (2003) “Analysis of the spatial distribution of vending

machines using GIS”, Papers and Proceedings of Geographic Information Systems Association,Vol.12,

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Morita, M.and Okunuki, K. (2003) “A study on the edge effects in analyzing a point pattern on a network”,

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Morita, M., Okunuki, K. and Okabe, A. (2001) "A Market Area Analysis on a Network Using GIS: A Case

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Miller, H.J. (1999) “Measuring Space-time Accessibility Benefits within Transportation Networks: Basic Theory

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Okabe, A., Boots, B., Sugihara, K. and Chiu, S. N. (2000) Spatial Tessellations: Concepts and Applications of

Voronoi Diagrams, (2nd edition), Chichester: John Wiley.

Okabe, A. and Kitamura, M. (1996) "A Computational Method for Market Area Analysis on a Network",

Geographical Analysis, Vol.28, No.4, pp.330-349.

Okabe, A. and Miki, F. (1984) "A Conditional Nearest-Neighbor Spatial Association Measure for the Analysis of

Conditional Locational Interdependence", Environment and Planning A, Vol.16, pp.163-171.

Okabe, A. and Okunuki, K. (2001) "A computational method for estimating the demand of retail stores on a

street network and its implementation in GIS", Transactions in GIS, Vol.5, No.3, pp.209-220.

Okabe, A. and Shiode, S. (2003) “Cell Count Method on a Network with SANET”, Center for Spatial

Information Science, University of Tokyo, Discussion paper No.59.

Okabe, A. and Yamada, I. (2001) "The K-function method on a network and its computational implementation"

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Okabe, A., Yomono, H. and Kitamura, M. (1995) "Statistical Analysis of the Distribution of Points on a

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AAG Annual Meeting, Los Angeles, CA.

Documents

SANET: A Toolbox for Spatial Analysis on a Networkua.t.u-tokyo.ac.jp/okabelab/atsu/sanet/SANETmanual_Ver.2.0.pdf · A DBF format table which holds the adjacent node number, the link