I need to create polygons of a specific area based upon random points within bounding polygons, but haven't been able to find a tool able to do all these.

I've looked at growing Theissen polygons, but can't find a way to stop the growth to a specific area.

I've looked at buffering the points, but that doesn't provide a way to grow the polygon to the correct area within the bounding polygons.

I've attached a hand-drawn concept of what I need.

Point Buffer Mock-up

  • I Think you need Python for this. Iterate over each Point and buffer, clip with boundind polygon, check area, rebuffer with smaller/larger width, clip, check area etc. – BERA Mar 20 '18 at 14:09
  • 1
    Could you not do this in steps - run the buffer as a set distance, then run a clip using your bounding polygons and use the output? – MAJ742 Mar 20 '18 at 14:18
  • Ok, re-read the question - you need growth to a specific area, not just clipped to the bounding features so my comment above won't apply. Tricky one! – MAJ742 Mar 20 '18 at 14:55
  • Are all those blue shapes you've drawn supposed to be round (apart from where they run up against the green ones)? Some of them are a bit lumpy. If you're trying to create round buffers (blue) that are contained by the green polygons, BERA's and MAJ742's idea will work: buffer the point, clip the result by the green polygon, repeat as necessary to grow your polygons. – Dan C Mar 20 '18 at 16:22

I use Python and Buffer. Each Point gets buffered, clipped and area is checked. If the difference between clipped area and desired size is more than ok_diff, it will get buffered again with a slightly larger buffer distance and checked again.. When ok it gets appended to output fc. The code can be executed in the Python Window.

import arcpy, math
arcpy.env.overwriteOutput = True

#Change to match your data:
arcpy.env.workspace = r'C:\Default.gdb'
boundries = r'Boundries'
points = r'bufferpoints'
out_feature_class = r'GrowPoints'

#Change to match your desired size of polygon, ok difference and step in buffer radius increase
size = 7500
ok_diff = 50
increment = 1

arcpy.CreateFeatureclass_management(out_path=arcpy.env.workspace, out_name=out_feature_class, 

arcpy.MakeFeatureLayer_management(in_features=boundries, out_layer='blyr')

with arcpy.da.SearchCursor(points,['OID@','SHAPE@']) as cursor:
    for row in cursor:
        bufferstart = math.sqrt((size/math.pi))
        sql = """{0} = {1}""".format(
        arcpy.MakeFeatureLayer_management(in_features=points, out_layer='pointlyr',where_clause=sql)
        arcpy.SelectLayerByLocation_management(in_layer='blyr', overlap_type='INTERSECT', 
        if [i[0] for i in arcpy.da.SearchCursor('blyr','SHAPE@AREA')][0] > size:
            area = 1
            while abs(size-area)>ok_diff:
                print area
                arcpy.Buffer_analysis(in_features='pointlyr', out_feature_class=r'in_memory\point', 
                                     buffer_distance_or_field="{0} Meters".format(bufferstart))
                arcpy.Clip_analysis(in_features=r'in_memory\point', clip_features='blyr',out_feature_class=r'in_memory\clipbuffer')
                area = [i[0] for i in arcpy.da.SearchCursor(r'in_memory\clipbuffer','SHAPE@AREA')][0]

            arcpy.Append_management(inputs=r'in_memory\clipbuffer', target=out_feature_class, schema_type='NO_TEST')
            print 'Impossible to fit buffer inside boundry for point number: ',row[0]

enter image description here

| improve this answer | |
  • 1
    This looks like it will provide exactly what I need. Thanks for sharing the code! – Andrew Strassman Mar 20 '18 at 18:56
  • Set increment as small as possible (only downside is time taken) or it will possibly never leave the while loop if buffererd and clipped size gets as larger than size+ok_diff (as the code is currently written). – BERA Mar 21 '18 at 6:41

Rather than using a buffer I think you need this tool:


Crucially it specifies that...

You can optionally limit the features to be enlarged based on whether they intersect another feature class

I guess if you buffer by a really small amount to give a round polygon feature then use this tool it should do the trick.

Unfortunately it appears to only be available with the 'Production Mapping' extension/licence.

| improve this answer | |

Script below is using bisection method to find solution:

import arcpy, math
from arcpy import env
env.overwriteOutput = True
with arcpy.da.SearchCursor(polygons,(fld,"Shape@")) as cursor:
    for fid,shp in cursor:
curT = arcpy.da.InsertCursor(buffers,"Shape@")
with arcpy.da.SearchCursor(points,("Shape@","NEAR_FID","AREA",)) as cursor:
    for shp, pgonID, target in cursor:
        if target>parentArea:
            L = pow(parentArea/pi,0.5)/5
            H = parent.length
            while True:
                if (H-L)<tolerance:break
                M = (L+H)/2
                if insidePart.area<target:
                else: H=M

Just name your layers in TOC of mxd accordingly. You'll need also to run near tool on points, so your points table looks like that:

enter image description here

Output: enter image description here

Unfortunately arcpy geometry method intersect doesn't do what it should so I was forsed to use cut method to find intersect between buffer and parent polygon.

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