Hexagonal Sampling Polygons – Benefits of Hexagonal Sampling Polygons

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I am always on the lookout for useful methods to sample or partition study areas (usually in the form of raster datasets) into smaller units. Recently, I read an ESRI blog post about a new tool for creating sampling hexagons. Although the hexagons are an eye catcher, my first thought is that they are more complicated and contain more vertices than, for example, a fishnet grid which could accomplish the same goals. What are the benefits of working with hexagonal grids over rectangular grids for study area sampling or partitioning raster datasets?

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Best Answer

The idea with hexagons is to reduce sampling bias from edge effects of the grid shape, which is related to high perimeter:area ratios. A circle is the lowest ratio, but cannot form a continuous grid, and hexagons are the closest shape to a circle that can still form a grid.
Also, if you are working over a larger area, a square grid will suffer more from distortion due to curvature than shapes like hexagons.

There are a number of tools and extensions for creating and using hex grids for ecological/landscape analysis, Patch analyst (Rempel et al., 2003) being a good example, that also provides a large volume of landscape metric measurement capacity. The former Hawth's Tools, now redesigned as the Geospatial Modeling Environment has a wide array of tools that were developed to fill in gaps in arcgis functionality, including repeating grids. A number of third-party extensions have been made for this sort of thing, usually by the researchers who need them, so they frequently don't have the resources to rebuild their products after every new GIS version is released, so it often seems like there is nothing available

This paper (Birch, 2007) also presents a thorough comparison of rectangular and hexagonal grids for ecological applications, showing how hexagonal grids are preferable when issues of connectivity, nearest neighbourhood or movement paths are crucial aspects to be considered in the analysis.

Related Solutions

[GIS] What sampling tools are available in QGIS

fTools is still there under the Vector menu. The sampling tool you need is Vector|Research Tools|Random Points.

You need to create a new attribute (like 'points') for your polygon layer; for each stratum, you enter the number of points you need to be generated for that stratum. In the dialog you select that new attribute in the 'value from input field' dropdown.

Update: This only seems to be working in QGIS 1.9, not 1.7.4.

Update 2: If you're using 1.7, this is a known bug but there is a workaround:

Make sure you have another polygon layer loaded;
Open the Random Points tool again, and first select a different layer to the one you want to use as the strata boundaries;
Select the strata boundaries layer, and then you can select the proper field name.

[GIS] How to computational efficiently check if there are any overlapping polygons in a group of polygons

There are 105 combinations for testing the intersections of pairs of fifteen polygons, or mathematically (using combinations) expressed as 15 choose 2, or symbolically (15 over 2).

To borrow some similar logic with Shapely, you can do this:

from itertools import combinations

# gather the 15 Shapely polygons in something iterable, like a list
shapes = [poly1, poly2, ..., poly15]

# test the intersection on the combinations of pairs
intersections = [pair[0].intersects(pair[1]) for pair in combinations(shapes, 2)]
# intersections is a list with 105 elements of True or False

if any(intersections):
    print("yes, %d of %d combinations intersect" % (sum(intersections), len(intersections)))
else:
    print("no intersections")

Best Answer

Related Solutions

[GIS] What sampling tools are available in QGIS

[GIS] How to computational efficiently check if there are any overlapping polygons in a group of polygons

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