Perform "Polygon in Polygon" Operations

This topic comes from the case files of Manifold Technical Support. A customer is using Manifold System Release 4.50.

The customer has a map of areas in one layer. Each area has a value, such as population, for that area. Let's say this first layer shows counties in a particular region with the population for each county. The map also includes a second layer that shows different areas. Let's say this second layer shows school districts that are participating in a particular pilot project. The task is to automatically take the population values from the county areas and to assign that pro-rata share of population to any school district that overlays a particular county.

This is a typical "polygon in polygon" operation. Although Manifold Release 4.50 does not include a polygon in polygon operation, the Spatial Overlays tool may be used to estimate this using "point in polygon" operations. The trick is to first create a regular grid of points and to transfer pro-rata values from the "source" areas to those points using the Spatial Overlays dialog. One can then transfer an aggregated sum of pro-rata values from those points to the "target" areas using the Spatial Overlays dialog as well. Using few points in the grid will result in coarse approximations. Using many points in the grid will result in better approximations.

We illustrate the procedure using a simple map that was created "free hand" in abstract coordinates. The task has been simplified for clarity. We wish to transfer the pro-rata share of a given value from a source area to a target area that partially overlaps the source area. The amount of the value transferred is to be in proportion to the amount of overlap. The map has three layers called area, points and new area. The new area layer has default layer formatting in a "transparent" area style.

	Create a dense grid of points using the Insert Shape - Grid tool set to create points only. Draw the two areas free-hand in the two different layers. Open Table View and add a field called value that's a floating point number and enter the value 100 for the first area created in the layer area. The illustration shows Table View. Note that there are no values (as yet) in the value field for the points or for the second area in the new area layer.
	Launch Tools - Spatial Overlays and run the dialog with the parameters shown. We are taking the value of the field value and distributing it among all the points that are found in the area.
	Here is what Table View looks like after the Spatial Overlay operation. Table View has been scrolled to show that those points inside the area have acquired values while those points outside the area have not.
	We now need to take all the points that fall within the new area layer's area and sum up their values and place it in that new area. We run the Spatial Overlay dialog one more time, this time using "transfer sum of point values to area" from points to new area to do so.
	Note that now Table View has a value of 26.6666... for the value field for the area in the new area layer. That's the sum of the points values that occur within that new area. Isn't Manifold wonderful?

This simple example used only one source area and one target area so that what's happening could be clearly seen in Table View. Spatial Overlays works just as well with many source areas and many target areas. This same procedure could be used on a map of 80 counties overlapped by 18 school districts. Note that the "pro-rata" transfer of the value works even if a school district overlaps two different counties... it "inherits" that share of points from each county that it overlaps.

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