Hawth's Analysis Tools for ArcGIS

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 Summary

GENERATE RANDOM POINTS TOOL
Input: at least one reference layer (raster or polygon layer)
Output: a point layer of randomly positioned points
Features:

• for raster layers, allows the user to prevent the point from being placed in a NoData cell, and/or uses the values in the raster layer as probability weights for the placement of the random points (see Help section below)
• for polygon reference layers, allows the user to generate a total number of random points, or a constant number per polygon (stratified random points)
• for polygon reference layers, also allows the user to identify areas in which random points are not permitted to occur (in the form of another polygon layer)
• allows the specification of a minimum distance to be enforced between generated points (see Help section below)

Limitations:

• for certain irregularly shaped polygons (where the area of the polygon is small relative to the perimeter) this program will run more slowly
• using a second polygon layer to prevent random points from being placed in some areas will also make the program run more slowly

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 Example

Figures A & B. In this example, an irregularly shaped raster layer is used as the reference layer (A). (Note that NoData cells have been coloured grey in order to display the true extent of the raster layer). 1000 random points (red dots) were generated and the option to prevent them from occurring in NoData cells was activated.

Figures C & D. Here a polygon layer is being used as the reference layer (C) and exactly 5 random points (red dots) per polygon are being generated (D).

 Help

Getting started. At least one polygon or raster layer must be loaded into ArcMap in order to use this tool.

Preventing points from occurring in NoData cells. The greater the proportion of NoData cells in a raster, the longer this tool will take to run. This program generated a true random point within the extent of the raster and THEN tests to see if occurs in a NoData cell. If there are many NoData cells this will clearly result in the rejection of a high proportion of random points, and more time will be needed to meet the quota the user defines. Warning: if your grid is 100% NoData then this program will enter an infinite loop (to force the shutdown of ArcMap, use Task Manager to end the application).

Enforcing a minimum distance between generated points This option is available with all raster and polygon options (including the polygon statified random sampling options), but the implications of using this option can be complex depending on what other options you have switched on. Improperly using this option could result in a biased random sample.

The minimum distance value you supply must be in coordinate system units (e.g. meters for UTM, feet for SPC, etc). This option will simply prevent random points from being placed within this distance of another random point. In the case of stratified random samples, users have the option to enforce the rule across all points (e.g. including across adjacent polygon boundaries), or enforcing the rule only within each strata (i.e. each polygon). In the latter case, it is possible for two random points to be closer than the minimum distance you specify provided they occur in different strata (e.g. adjacent polygons).

There are a number of ways this option can create problems: (1) it may be impossible to generate a certain number of points if the minimum distance you specify is too large relative to the area of the raster/polygon(s), (2) this option can counteract or conflict with the weighted probability distribution raster option. The tool will generate as many points as it is able and then stop if, after 100,000 attempts, it has been unable to generate all the random points under the conditions you have specified. Therefore if you use the minimum distance option it is imperative that you take great care to check that the program has been successful by examining the output.

Note that you can use the Distance Between Points (Within Layer) tool in this toolset to check that the minimum distance has been enforced.

Using a raster layer as a weighted probability distribution. If you check the box "Use raster as a weighted probability distribution", then the values in the raster are used as probabilities of placement such that raster cells with larger values are more likely to have a point placed in them. The probability for each cell is calculated by: (value of cell) / (maximum value). As such, the raster can represent true probabilities (range: 0-1), or can contain any range of numbers that represents the relative probability of occurance between cells. Note that you can use the other options with this tool, including: Prevent points from being located in NoData cells, and Prevent points from occuring in the polygons of the following layer.

Preventing points from occurring in the polygons of another polygon layer. The greater the area in which you prevent points from being placed, the longer the program will take to run. If the polygon layer specified to prevent points from being located in certain areas completely covers the reference polygon layer, then this program will enter an infinite loop.