Issue link: https://read.dmtmag.com/i/75042
Convexity and narrowness indices provide a foothold for objective, unbiased and quantitative measures that assess proposed district compactness. Narrowness can be defined as the "shortest cord passing through a location that connects opposing edges" (see "Author's Note 3"). In practice, narrow- ness is calculated to a specified maximum distance. Locations with cords exceeding this distance are simply identified as "open areas." Less-Partisan Shapes In Figure 3, the narrow locations are shown as a color gradient from the most narrow locations (red = 1 cell length = 30 meters) to minimally narrow (green = 9.9999 * 30 meters = 299.9 meters) to open areas (gray = ≥300 meters). Note the increas- ing number of narrow locations as the map features become increasingly less compact. The NI can be calculated as the ratio of the number of narrow cells to the number of open cells. For the circle in the figure, NI = 152/557 = 0.273, with nearly four times as many open cells as narrow cells. The bug-shape ratio is 0.848, and the spindly Medusa shape with a ratio of 2.232 has more than twice as many narrow cells as open cells. Both CI and NI quantify the degree of irregularity in the configuration of a map feature. However, they provide dramatically different assessments. CI is a nonspatial index, as it summarizes the overall bound- ary configuration as an aggregate ratio focusing on a feature's edge and can be solved through vector or raster processing. NI, however, is a spatial index, as it characterizes the degree and proportion of narrowness throughout a feature's interior and only can be solved through raster processing. Also, the resulting narrowness map indicates where narrow locations occur; that's useful in refining alternative shapes. To date, the analytical power of GIS has been instrumental in gerrymandering congres- sional districts that forge political advantage for whichever political party is in control after a census. In engineering an optimal partisan solution, the compactness criterion often is disregarded. On the other side of the coin, convexity and narrowness indices provide a foothold for objective, Figure 2. Convexity is characterized as the normalized ratio of a feature's perimeter to its area. unbiased and quantitative measures that assess proposed district compactness. Including acceptable CI and NI measures into redistricting criteria would ensure that compactness is addressed. Ladies and gentlemen, start your GIS analytic engines. Author's Notes: 1) The "Beyond Mapping" column on Feature Shape Indices (GeoWorld, September 1991) is posted at www. innovativegis.com/basis/BeyondMapping_I/Topic5/BM_I_T5 .htm#Forest_trees; 2) A PowerPoint on "Gerrymandering and Legislative Efficiency" by John Mackenzie, director of Spatial Analysis Lab, University of Delaware, is posted at www.udel. edu/johnmack/research/gerrymandering.ppt; 3) Narrowness is discussed in the online book, Beyond Mapping III, Topic 25, Calculating Effective Distance and Connectivity, at www. innovativegis.com/basis/MapAnalysis/Topic25/Topic25. htm#Narrowness. Figure 3. Narrowness is characterized as the shortest cord connecting opposing edges. JUL Y 2O12 / WWW . GEOPLA CE . COM 11