Creating buffer of points with pre-defined area?

Question

I need to create a buffer with a predefined area, my inputs are points, at first I tried it by calculating the area that each buffer may have and then giving the radius as an input, but then I have to dissolve the buffers polygons so the area change.

Is there some tool that can do this?

Answer 1

You can get very accurate estimate by using any root finding algorithm, e.g. bisection.

At given dimensions:

total area of 3 circles is 94247.7796. We can get very close to the same area for dissolved polygon by simply playing with radius:

import arcpy, math
from arcpy import env
resultFC="c:/scratch/scratch.gdb/dissolved"
target=94247.779608
result=arcpy.GetCount_management("POINTS")
nNodes=int(float(result.getOutput(0)))
##find lower limit for radius and set upper one
low=math.pow(target/nNodes/math.pi,0.5)
high=5*low
g=arcpy.Geometry()
iterCount=0
while True:
    if (high-low)<0.01:break
    mid=(high+low)/2
    pgon=arcpy.Buffer_analysis("POINTS",g, mid, "FULL", "ROUND", "ALL")[0]
    curArea=pgon.area
    if curArea<target:low=mid
    else:high=mid
    iterCount+=1
arcpy.AddMessage("\nTarget = {:6.2f}\nArea = {:6.2f}\nRadius = {:6.2f}\nIterations = {}\n".
                 format(target,curArea,mid,iterCount))
arcpy.CopyFeatures_management([pgon],resultFC)

Script messages:

• Target = 94247.78
• Area = 94245.82
• Radius = 110.97
• Iterations = 16

As one can see the difference between target and result is a couple of square meters or 0.002%.