Identify number of buffer around a point within a polygon

[CraigRattigan]

Hi, I'm new to ArcGIS. I am in the process of completing part of dissertation project looking at the potential of low carbon energy as an alternative to a proposed nuclear development, as part of this I have designated suitable locations for which wind turbines can be constructed. However each of these turbines have a set distance needing to be separated by so a buffer zone and the consequent buffer circle have been estimated at 70685 sq m;

1. Is there a tool which could estimate the number of buffered points which could be situated inside a polygons (Mock-up shown in attached picture

2. Slightly more confusing, the buffer zones can theoretically cross the polygon boundary so is there an appropriate tool for both of these points

Any help would be greatly appreciated

[DanPatterson_Retired · Accepted solution]

I think one problem is that you potential containment area where one can place things, it pretty specific and probably the result of a variety of constraints.  The placement of the turbines is pretty convoluted...

• the blades can't touch (pretty reasonable)
• the footprint has to be inside the containment area
• the turbines can overhang
• you want to optimize packing

You want to be looking for 'packing' algorithms (like circles in rectangles etc, or hexagons in rectangles)

A hexagon could be used if you make the short radius equal to your minimum diameter.  Hexagons can be used to emulate circles obviously, you just have to be careful about the diameter used.  The difficulty arises in your containment area.  if it could be generalized outwards, like with a convex hull (CH) or a minimum area bounding rectangle (MABR ... includes rotation), then it might be a bit simpler, since you could get the orientation of the CH or MABR, overlay an oriented hexagon and fiddle with their placement until optimized (not an easy task however).

In short, your constraints need to be looked, and the method of boundary delineation addressed in order to determine the optimal packing.  Which is why you can never get multipart purchases back in the box when you need to return them.

ADDENDUM

Your packing could be further complicated, since you have assumed a circular packing perhaps reflecting safety or some other issues.  The size is pretty concise for some reason and it is circular.  What are the reasons that the area is specified this way? blade rotation, I presume is vertical and hence would imply that the minimum separation would/could be less along one axis than along the blade axis.  Is this due to air flow issues? or some other reason? The answer and shape and size of the containment area will be affected by this, since you might be packing rectangles rather than circles, which is more efficient

[CraigRattigan]

Hi, Dan

The circular packing has been chosen due to regulations by the UK government declaring that turbines have to be situated at least 3 radius along the blade rotation axis away from each other.

Would it be more appropriate to buffer the polygons to this radial distance and take the measurements inside the polygons from the points? As if I identify that the buffer zones must be contained within the boundary the buffer point should be in the same location as compared to if I allowed the buffers to overflow from the polygon, therefore the same number of buffered points can be calculated.

I understand airflow issues affect the distance between turbines greatly but this is not the aim for this project only the potential for low carbon technologies as an alternative to a proposed nuclear development, so only simple distances will be considered.

[DanPatterson_Retired]

I would do the packing first, then overlay the bounding area on top of it, rather than try to fit the packing inside the bounds.  It may optimize the number possible.

Determine the minimum area bounding rectangle and get the orientation axis

http://www.arcgis.com/home/item.html?id=564e2949763943e3b9fb4240bab0ca2f

Use it to produce a hexagonal packing with the minimum axis greater than your smallest required radius

Numpy Snippets # 3 ... Phish_Nyet ... creating sampling grids using numpy and arcpy

Then fiddle as necessary