topic Re: Creating wedge-shaped territories in Geoprocessing Questions

Creating wedge-shaped territories

JuanetteWillis — Tue, 19 Jan 2016 15:02:26 GMT

Good morning, I am trying to create new territories for our inspectors based on the number of locations to be inspected. Our office is centrally located in the county. We are wanting to have wedge-shaped territories radiating from our office, like pieces of a pie. Any suggestions on how to have the GIS assist with the division?

Thanks,

Juanette

Re: Creating wedge-shaped territories

WesMiller — Tue, 19 Jan 2016 15:10:43 GMT

Do you have an advanced license? You could put a point at the center of each proposed area then use Create Thiessen Polygons—Help | ArcGIS for Desktop to create the polys.

Re: Creating wedge-shaped territories

JuanetteWillis — Tue, 19 Jan 2016 15:32:10 GMT

Unfortunately no, I do not have an advanced license. Just basic ArcMap 10.1 with the Spatial Analyst extension.

Re: Creating wedge-shaped territories

ChrisDonohue__GISP — Tue, 19 Jan 2016 15:44:25 GMT

Just wanted to toss out a couple of ideas, though it may be more elaborate than you want:

1. Most of the inspections will likely require transiting a street network. If points could be established at the center of each "territory" (see the idea by Wes Miller , then if you have access to the Network Analyst Extension, you could run a Location Allocation to refine the territories.

ArcGIS Help 10.1 - Network Analyst

2. In terms of figuring out where to place the "center" of each territory, there may possibly be a way to derive those centers using the Geostatsical Analyst Extension. However, I'm not super-familair with this extension, so we'd need someone who is to chime in here.

ArcGIS Help 10.1

Chris Donohue, GISP

Re: Creating wedge-shaped territories

WesMiller — Tue, 19 Jan 2016 15:46:02 GMT

When i did districts for my codes enforcement inspectors i used the Districting for ArcGIS | Overview the tool is intended for political boundaries but i used five years of historical inspection data to create a balanced set of districts.

Re: Creating wedge-shaped territories

XanderBakker — Tue, 19 Jan 2016 15:48:38 GMT

I haven't tried the tool yet, but Dan Patterson published a tool to calculate Thiessen polygons with a Basic license: http://www.arcgis.com/home/item.html?id=6e9bc6cbf93d4939b2eb04ff8519be47

Re: Creating wedge-shaped territories

ChrisDonohue__GISP — Tue, 19 Jan 2016 15:53:59 GMT

Question - what data is available to use in dividing up the territories? Any chance you have point data showing each inspection?

Also, let me add in who probably has several ideas on how to solve your original proposal:

Dan Patterson

EDIT: Xander Bakker beat me to it. I need to learn how to type faster......

Chris Donohue, GISP

Re: Creating wedge-shaped territories

JuanetteWillis — Tue, 19 Jan 2016 15:55:03 GMT

I did not know about this add-on. It shows potential. Since this is for inspecting restaurants, hotels, pools etc. I do have a specific set of locations.

Re: Creating wedge-shaped territories

JuanetteWillis — Tue, 19 Jan 2016 15:56:48 GMT

Thanks Chris. This is for inspecting restaurants, pools, hotels etc so I will have point data as soon as I finish cleaning up the geocoding. 🙂

Re: Creating wedge-shaped territories

DanPatterson_Retired — Tue, 19 Jan 2016 16:21:26 GMT

Several possibilities...

If you have an origin point (office) and destination points (the other stuff), you can create points that radiate from the origin to the destination quite easily. BUT, your map may look like this which isn't too helpful but looks really cool in color.

2. You could artificially create a circle to overlay your area and divide into the desired number of sectors needed and sample your points within each sector

3. You could use the network analyst extension (aka the not free extension) and produce a service area AND shortest route to the destinations from the office and divide it up as in step 2. It might look like the above, but there might be fewer lines since the same road could be used to go from the different points (ie from point 59 to 99 to 26 might be the shortest, so you reduce 3 lines to 1, if they were connected by a road.)

4. other ideas pending... a nice screen grab would help fine-tune the above

Re: Creating wedge-shaped territories

JuanetteWillis — Tue, 19 Jan 2016 16:37:59 GMT

Here is a quick screen grab. The star is our office and the dots are locations to be inspected.

Re: Creating wedge-shaped territories

DanPatterson_Retired — Tue, 19 Jan 2016 16:58:43 GMT

A circle division would be unduly cruel to just about everyone particularly if the slices of the circle were equal. Since the intent...I hope... is to be fair and minimize clients, drive times and total costs, I am leaning more towards a Network Analyst solution.

In any event, it would be fairly easy and quick to solve if you just wanted to do something like quarter the distribution knowing full well that each quarter would have an unequal number of places to visit and the aspects of drive time and cost would be pretty well thrown out the window.

So back to you again...

do you have the network analyst extension?
could you live with straight line distances and directions as in my previous figure?
how many slices do you need?

Re: Creating wedge-shaped territories

XanderBakker — Tue, 19 Jan 2016 17:26:01 GMT

... and if you don't have access to the Network Analyst, you could do this in ArcGIS Online, if you have some credits to burn. Plan Routes—ArcGIS Online Help | ArcGIS can help to assign each point to an inspector. This will not create polygons, but will assign each point to a route (or vehicle = inspector).

I believe that a max of 200 points will be assigned per vehicle and each "vehicle/inspector" will burn 1 credit. If there are 1000 points and you have 5 inspectors, 5 routes will be calculated and you will consume 5 credits. So that's not a big thing (no need to take a second mortgage on your house)

Re: Creating wedge-shaped territories

JuanetteWillis — Tue, 19 Jan 2016 18:59:08 GMT

To answer your questions, Dan.

I do not have Network Analyst. Just basic ArcMap 10.1 with the Spatial Analyst extension.
I can live with the straight line distances and directions. The main goal is to distribute the number of locations to visit. We know that the distances and routes will vary but it is hoped that each inspector will get some locations near the office and some farther. That is hoped to even out the driving burden. Some will have further to drive but others will have to deal with more traffic.
I am looking for 19 territories plus 6 which will only be about half the number of locations.

I do appreciate all your thoughts and insight into this problem.

Re: Creating wedge-shaped territories

DanPatterson_Retired — Tue, 19 Jan 2016 21:39:32 GMT

The earlier suggestion of Theissen polygons or voronoi diagrams you didn't respond to (see Xander's earlier post). Is another potential route to take. It would require some work to cluster you data into logical areas rather than just the individual points. The Triangulation tools I wrote produces for Voronoi diagram and Delauney triangulation which may be of use. http://www.arcgis.com/home/item.html?id=6e9bc6cbf93d4939b2eb04ff8519be47

Re: Creating wedge-shaped territories

XanderBakker — Wed, 20 Jan 2016 03:58:31 GMT

Interesting what you can do with wedges...

Precision is off (not much intelligence in the definition of the cut-off angles), but I'm getting somewhere... Will try to post some code tomorrow.

Re: Creating wedge-shaped territories

DanPatterson_Retired — Sat, 11 Dec 2021 10:35:38 GMT

Xander Bakker forgot about this one... only got so far... I am sure you are using numpy too and could use a distraction

import numpy as np
import pylab as plt
angle = [np.deg2rad(i) for i in range(-180,180,30)]
R= 100
Xs = R*np.cos(angle)        # X values
Ys = R*np.sin(angle)        # Y values
pnts = np.round(np.array(zip(Xs,Ys)), 3)  # create the points
print("{}".format(pnts))
# center point and mean distance
XY_c = np.array([0.0,0.0])  # create a center point
Xc, Yc = XY_c.flatten()      # pull out values separately
#
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
circ = plt.Circle((Xc, Yc), radius=R, color='w',lw=2,alpha=.5)
ax.add_patch(circ)
plt.axis('equal')
plt.scatter(Xs,Ys)
plt.show()

Now just change the radius, give it a real center, connect the center to the points as triangles and you have a big circle for intersection or select by attributes (distractions... distractions... )

[[-100.      -0.   ]
[ -86.603  -50.   ]
[ -50.     -86.603]
[   0.    -100.   ]
[  50.     -86.603]
[  86.603  -50.   ]
[ 100.       0.   ]
[  86.603   50.   ]
[  50.      86.603]
[   0.     100.   ]
[ -50.      86.603]
[ -86.603   50.   ]]

ADDENDUM

c =np.array([0,0])
p = np.array([[c,pnts[i-1],pnts,c] for i in range(1,len(pnts))])
>>> print(p)
[[[   0.       0.   ]
  [-100.      -0.   ]
  [ -86.603  -50.   ]
  [   0.       0.   ]]

 [[   0.       0.   ]
  [ -86.603  -50.   ]
  [ -50.     -86.603]
  [   0.       0.   ]]
etc

should get you polys which can be "Arc'ed" into shape

Re: Creating wedge-shaped territories

XanderBakker — Wed, 20 Jan 2016 12:35:37 GMT

Cool! I should have used numpy, but didn't, since I'm not that experienced in it as you are ...

So what I did still has a lot of room for enhancement and fails to create the last wedge. Not sure why, and I don't have the time to look into it. I will post what I have and if anyone wants to play around with it, please do and post back if you get a decent result.

I drew a polygon with the area and created some random points (4400). Additionally I create another point featureclass with the point representing the office.

The code works as follows:

pnt_off is the point geometry of the office
it creates a list of slices (19*2 and 6*1) representing the 19 large and 6 smaller areas to be created
It loops through the slices
- for each slice it starts to create the wedge using small angle steps
- it creates a polygon of the wedge and counts the points inside
- it is is close enough or higher than the number of points searched for it breaks and add the polygon to a list
- at the end it writes the list of wedges (polygons) to a featureclass
I manually did a union with the area, selected those records where the FID_Area <> -1 and joined the points to the wedges to count the results.

I´m getting an error when I try to activate the advanced editor, so I will post the code later...

Re: Creating wedge-shaped territories

XanderBakker — Sat, 11 Dec 2021 10:35:40 GMT

Code used:

import arcpy
import math
import os

def main():
    arcpy.env.overwriteOutput = True

    fc_off = r"D:\Xander\GeoNet\Wedges2\data.gdb\Office"
    fc_pnt = r"D:\Xander\GeoNet\Wedges2\data.gdb\RandomPoints"
    fc_tst = r"D:\Xander\GeoNet\Wedges2\data.gdb\test07"

    sr = arcpy.Describe(fc_pnt).spatialReference
    ws, name = os.path.split(fc_pnt)

    pnt_off = arcpy.da.SearchCursor(fc_off, ("SHAPE@")).next()[0]
    cnt_pts = Count(fc_pnt)

    radius = 6000 # value higher than the max distance of point to office
    slices = [2] * 19 + [1] * 6 # create the slices and corresponding sizes
    tol = 3 # a tolerance value (will stop if current value >= serach value - tolerance)
    steps = 1000 # number of steps (each bearing is 360 / steps)

    lst, lst_pols  = [], []
    i = 0
    last_step = 0
    for s in slices:
        i += 1
        print "Slice: {0},   Size: {1}".format(i, s)
        print "Percentage: {0}%,  Points: {1}".format(round(float(s)/sum(slices)*100, 2), round(float(s)/sum(slices) * cnt_pts,0))
        max_pnts = round(float(s)/sum(slices) * cnt_pts,0)

        for step in range(last_step, steps):
            bearing = float(step) / float(steps) * 360
            print " - bearing: {0}".format(round(bearing,2))
            pnt = getPoint(pnt_off.firstPoint, bearing, radius)

            if step == last_step:
                # create list of first points
                pnt0 = arcpy.Point(pnt.X, pnt.Y)
                lst = [pnt_off.firstPoint, arcpy.Point(pnt.X, pnt.Y), pnt_off.firstPoint]
            else:
                # update list, create polygon and count points in polygon
                lst.insert(len(lst)-1, arcpy.Point(pnt.X, pnt.Y))
                polygon = arcpy.Polygon(arcpy.Array(lst), sr)
                cnt = CountInPolygon(fc_pnt, polygon, ws)
                print "   - point count: {0}".format(cnt)
                last_step = step
                if cnt >= max_pnts - tol:
                    print "     - add wedge"
                    lst_pols.append(polygon)
                    break

    # add last polygon
    lst.insert(len(lst)-1, arcpy.Point(pnt0.X, pnt0.Y))
    polygon = arcpy.Polygon(arcpy.Array(lst), sr)
    print "     - add last wedge"
    lst_pols.append(polygon)

    # create polygon and count
    arcpy.CopyFeatures_management(lst_pols, fc_tst)

def getPoint(pnt, bearing, radius):
    angle = math.radians(90 - bearing)
    dist_x, dist_y = (radius * math.cos(angle), radius * math.sin(angle))
    return arcpy.Point(pnt.X + dist_x, pnt.Y + dist_y)

def Count(fc):
    return int(arcpy.GetCount_management(fc).getOutput(0))

def CountInPolygon(fc_pnt, polygon, ws):
    arcpy.env.overwriteOutput = True
    fc_tmp = "IN_MEMORY\polygon"
    arcpy.CopyFeatures_management([polygon], fc_tmp)
    arcpy.MakeFeatureLayer_management(fc_tmp, "pol", None, ws)
    arcpy.MakeFeatureLayer_management(fc_pnt, "pnts", None, ws)
    arcpy.SelectLayerByLocation_management("pnts", "INTERSECT", "pol")
    return Count("pnts")

if __name__ == '__main__':
    main()

Re: Creating wedge-shaped territories

JuanetteWillis — Wed, 20 Jan 2016 14:03:09 GMT

Oh my...this is all great and has my mind spinning with the various possibilities. I am still deep in the depths of hand placing the last couple of hundred locations that didn't geocode. But I am really looking forward to trying at least a couple of these ideas. I have not used code before in ArcMap but am excited about the possibilities. Unfortunately GIS is only a tiny portion of my job duties (and one that I specifically sought out myself) so I don't get near enough time to work on much beyond the basics. I do really appreciate all this input and frankly am a bit in awe of the great responses. Thank you so much. (And feel free to keep additional ideas coming if you are so inspired.)