Pitney Bowes MapInfo Vertical Mapper - Manual (Page 170)

Polygon Overlay
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Vertical Mapper 3.7
The second step is to calculate the value for each cell in the new grid. The calculation involves
knowing how many cells each region contains, and then dividing the region’s value by that number.
In this way, the region’s total value is spread among the grid cells contained inside it. A grid cell is
considered to be inside the polygon when the centre of the grid cell (the grid node) is located within
the polygon.
The third and final step is to transfer the gridded information to the region file to be updated. A new
field is created in the database, and each region in the file is examined against the grid. The sum of
the grid values that are contained within each region is then calculated and transferred to the new
field in the database.
A proportional sum analysis begins generally with demographic information. A grid is
then spatially overlaid and grid cells are attributed with a proportional value from the
region they fall inside of.
In the second illustration above, the region labeled with a value of 794 has four grid cells that fall
inside it where each cell would be attributed with a value of 198.5. In the regions labeled with the
values 1256 and 897 there is a single cell contained in the region, and therefore each cell will be
attributed with the full value of the region. Once the grid has been processed the cell values are
applied to another region file by simply adding the cell values that fall in each region.
In the third figure, the value given to the central circular area will be the sum of the three cells that fall
inside. In this case the value will be 2341.5.
The polygon overlay tool makes the assumption that the attribute value of a region is representative
of the whole geographic area the region covers and not of a smaller location within the region. When
this is assumed, then it is logical to assume that a region’s value can be divided and spread equally
over the region area. In other words, if you have an area 10 km square with a population of 100
people, it is logical assume that there is one person for every square kilometer of the region. It is
important to note that, although this almost never occurs in reality, there is no way of knowing where
the population is distributed within the region because of the way the data was collected. Therefore,
the best guess is to spread the population evenly throughout the region.
One concern when approaching a proportional sum analysis using a grid-based solution is retaining
information from very small polygons when performing the vector to grid conversion step. This
becomes an issue when there are no cells in the grid that are contained within the polygon. This is
illustrated in the next figure, where the highlighted polygon does not contain a grid cell. In a normal
Region to Grid operation, the value associated with this polygon would be lost. However, the
Polygon Overlay tool attributes this information to the nearest grid node. For example, in the next
figure, the nearest node is to the upper-right of the polygon in question. This does lead to a varying
degree of geographic displacement of the information. This displacement will be as large as the cell
size used.