[GIS] How to create one random point per grid cell? (i.e., systematic sampling with randomly placed points)

arcgis-desktoppointsamplingvector-grid

Using ArcMap, I have used the Fishnet tool to create a grid of 1km squares. I am looking to create random points so that there is one (randomly placed) point per grid cell, with a minimum distance of 150m between points. (for reference, see "Systematic Sampling with Random Point Placement about halfway down at http://www.quantdec.com/sample/ )

I understand I can use the Fishnet tool to place points in the center of the cells; however, I am looking for a random point distribution, with the only constraints being the minimum distance between and points limited to 1 per cell.

Also, there is a a layer with which I would like the points to overlap with. Once the points are generated, I know I can use the Intersect Tool to ensure the points remaining intersect with this layer; however, I am hoping to create as many points as possible and a lot of non-intersecting points will be lost if I do this.

To give you an idea, here is an image of a small area of what I am working with enter image description here

Best Answer

If you have ArcInfo, 3D or Spatial analyst, you can use the create random point tool to generate your points.

First I would start with the intersection between your fishnet and a dissolve of your other feature class. This will give you one multipart polygon per grid cell including some of the yellow polygons.

Then you can place one point for each of the resulting feature classes using the optional parameters of "create random points"(take the result of the intersection as constraining_feature_class and set the number of points = 1).

As a remark, I would not use the 150 m constraint if I were you because you already have a lot of constraints, but you can use a "minimum_allowed_distance" parameter to avoid points falling at less than 150 m from each other.

If you don't have the appropriate licence, have a look at Geospatial Modelling Environment(previously Hawth's tools) and their geostratrandompnts tool

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[GIS] How to generate random points with minimum distances between points in multiple polygons

In ArcGIS, this can be done with Create random point if you have spatial analyst or 3D analyst or Advanced(ArcInfo) licence

select each shapefile as "constraining_feature_class" and set the "minimum_allowed_distance"to 250 m.

In QGIS, from what I know, you can use "Vector ‣ Research Tools ‣ Random points" with a constraining feature class, but not for distance. Again, you can use this tool in a loop to add points one by one until you reach the required number.

On the other hand, a solution for simple random sampling with distance contraint is to recursively add your random point and erase the buffer around your random point from the feature class until all your features are completely erased. As mentioned by @Whuber, this will not optimize the number of sample points, but you can control the number of points per strata.

Finally, the optimal number of points with a distance constraint can be achieved by systematic sampling : create a grid (with fishnet) with evenly spaced points (in your case 250 m) and randomly select a rotation angle and shift value betwen 0 and 250 in X and Y direction. This will optimize the number of point samples (and you could randomly subselect some points to reach a given number inside each startum). However, note that systematic sample could be biased because of the spatial autocorrelation.

[GIS] Creating Random Points that respect minimal distance across features / strata using ArcGIS for Desktop

I had initially posted the question on geonet. The matter being rather urgent, I posted the question here as well when I didn't recieve an answer there. In the meantime, Xander Bakker posted an excellent script that solves the problem neatly. The full answer can be view here, this is the section that solves the problem (with some slight modifications from me).

import arcpy
import random
import math

def main(path,fc_pol,fc_pnt,fc_mp,min_dist,number_of_points):
    # path = path for the input and output data
    # fc_pol = name of the input polygon shapefile
    # fc_pnt = name of the output point shapefile
    # fc_mp = name of the output point shapefile, used for visualization it and some manual checking
    arcpy.env.overwriteOutput = True

    arcpy.CreateFeatureclass_management(path, fc_pnt, "POINT")
    arcpy.CreateFeatureclass_management(path, fc_mp, "POINT")
    lst_all_pnts = []
    lst_mp = []
    cnt_pol = 0
    with arcpy.da.SearchCursor(path+fc_pol, "SHAPE@") as curs:
        for row in curs:
            cnt_pol += 1
            # print "polygon: {0}".format(cnt_pol)
            polygon = row[0]
            lst_pnts = []
            sr = polygon.spatialReference
            # create points inside polygons
            while len(lst_pnts) < number_of_points:
                print " - len(lst_pnts)={0}".format(len(lst_pnts))
                lst_pnts, bln_ok = add_random_point(lst_pnts, lst_all_pnts, polygon, min_dist)
                if bln_ok == False:
                    # saturation reached
                    print "saturation reached"
                    break
            # write points
            if len(lst_pnts) > 0:
                mp = create_multipoint(lst_pnts, sr)
                lst_mp.append(mp)
                lst_all_pnts.extend(lst_pnts)

    # create outputs
    sr = polygon.spatialReference
    lst_pntgeom = create_pointgeometry_list(lst_all_pnts, sr)
    arcpy.CopyFeatures_management(lst_pntgeom, path + fc_pnt)
    arcpy.CopyFeatures_management(lst_mp, path + fc_mp)

Best Answer

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