Creation of Unclassed Choropleth Maps with Postscript. Cartographic Perspectives, No. 12, 1992, pp. 4-6.
Michael P. Peterson
Department of Geography / Geology
University of Nebraska at Omaha
Omaha, NE 68182
First introduced in 1973 by Tobler, unclassed choropleth mapping has a tortuous history in cartography. Although the technique of assigning shadings proportional to the data values made it possible to create choropleth maps without classifying the data, the method of mapping has not been widely accepted. The basic objection to the technique is that the cartographer loses the ability to direct the message of communication (Dent 1990, p. 167).
A more practical reason, however, that the unclassed method is not more widely used is the difficulty in creating a continuum of shadings. Tobler used a coordinate plotter to create a continuum of crossed-line shadings. The introduction of the laser printer and a software interface called Postscript has made it possible to create a white to black continuum of dot shadings. The procedure is described here for creating unclassed choropleth maps with Postscript.
I. The Shadings
Figure 1 depicts a series of shadings that were created with Adobe Illustrator. A percentage ink value was assigned to each rectangle with the 'Style' command. The shadings have been perceptually adjusted using the formula by Williamson (1982):
W = P (raised to the power of .8333) / 0.464;
where, W is the gray tone in percentage of area white and P is the desired perceived value. A desired value of 50 (P) equals a 56.14 percent white or 43.86 percent ink.
Illustrator files are in Postscript text format and can be edited with a text processor. Figure 2 is a listing of part of the file created above. The x, y coordinates that outline the middle rectangle are listed below the .5614 g command that defines its shading. The value was entered in Illustrator as a percentage black, but was converted to a percentage white in a decimal format (i.e., 1.0 = white; .0 = black) in the saved document. The decimal value associated with the Postscript "g" command can have as many as four places. Thus, gray shadings can be defined between .0001 and .9999, making the definition of 9,999 separate shadings between white and black possible. (Whether 9,999 distinct shadings are actually produced depends upon the resolution of the printer or imagesetter.)
0.5614 g ! =43.86 % ink 254 335.5 m ! point to move to 254 353.5 L ! points to draw to 223 353.5 L 223 335.5 L 254 335.5 L b ! end of polygon
Figure 2. Postscript commands that define a shaded rectangle.
II. The Base Map
Postscript files containing polygon outlines appropriate for the creation of choropleth maps can be created with Illustrator or FreeHand. Tools are available in both programs for the conversion of a scanned map to a series of polygon objects, but the process is tedious. The MapArt collection from MicroMaps includes numerous polygon-based files in a Postscript format that can be used with Illustrator or Freehand. A portion of the MapArt file for the state of Nebraska by county is shown in Figure 3.
%%Note:31077,Greeley,NE ! id of county 367.9533 385.0322 m ! move to point 403.29 385.631 l ! line to point 403.29 358.0805 l 403.29 348.4977 l 368.5523 348.4977 l 367.9533 385.0322 l s ! end
Figure 3. Greeley county, Nebraska in Postscript
The "Note" statement includes a combination of the state (31) and county (077) FIPS codes and the name of the county. The following six coordinates outline Greeley county (m indicates a move; l is for a line).
III. The Data
Computing the shading value for a polygon is simply a matter of re-scaling the data on a 0 to 100 scale:
P = (z [i] - zMin) * (100. / zRange);
where, P is the perceived value to be used in the perceptual adjustment formula, z[i] is the data value, zMin is the minimum data value and zRange is the difference between the maximum and minimum data values.
Assigning a shading value to a polygon is possible within Illustrator or FreeHand by selecting a polygon and specifying a shading value as a percentage ink. However, shadings can be assigned more quickly with a text processor. This is done by simply inserting the "g" command along with the corresponding shading value expressed as percentage white (as computed with the perceptual adjustment formula) following the 'Note' statement. The "s" at the end of the polygon in the unshaded file must also be changed to a "b" (last line) to have the shading take effect. The listing in Figure 4 depicts the addition of a shading value for Greeley county, Nebraska.
0.6543 g !the shading value
280.1552 53.6423 m
312.1679 54.1848 l
312.1679 29.2257 l
312.1679 20.5443 l
280.6977 20.5443 l
280.1552 53.6423 l
Figure 4. Greeley country with shadings value
IV. The Map
Figure 5 is an unclassed choropleth map of Nebraska depicting median housing value. The shadings were assigned using a text processor - MacWrite II - and the file saved in a text format. Illustrator was used to add the text, legend and neat line and for the printing of the map.
V. The Program
A utility program that assigns shadings to polygons for the creation of unclassed choropleth maps is available from the author. The program, called PostShade, incorporates a spreadsheet for data entry, a graphics window for the display of the map and an editor window to view the Postscript text files (Figure 6). The program works with base maps in a Postscript polygon format that include a "Note" statement for each polygon. Once the Postscript file is opened, the area names are displayed in the first column and up to 50 columns of data may then be entered and saved as a file. A "data" palette menu incorporates a number of spreadsheet functions (see menu palette in Figure 7): 1) the display of the spreadsheet; 2) the addition of descriptive text for each column of data; 3) modifying a column of data through division, multiplication subtraction or addition by another variable or; 4) a constant; 5) the setting of upper and lower thresholds in the data; 6) a logarithmic or square root transformation of a column of data; 7) moving a column of data; 8) deleting a column of data and; 9) the display of the numeric identifications (i.e., 31077) or; 10) the character identifications (i.e., Greeley) for each separate statistical area. The unclassed choropleth map is created by selecting a column of data and the Postscript map file. The program then creates another Postscript map file that defines the shadings for each polygon and includes a legend. The addition of text as well as the printing of the map is left to programs such as Illustrator or FreeHand.
The Postscript page description language provides a method for defining a continuum of dot shadings between white and black for the creation of unclassed choropleth maps. The procedure outlined here involves the insertion of a Postscript statement that defines the gray value, as percentage white, for a polygon. Modification of the Postscript file in this way can be done with a text processor, although adding the legend and text elements would require a program such as Illustrator or FreeHand. A utility program is available to automate the computation of shadings, their assignment to polygons and the creation of the legend.
Dent, Borden D. Cartography: Thematic Map Design, 2nd Ed. Dubuque, IA.: Wm. C. Brown, 1990.
MapArt, a collection of maps in Postscript format. MicroMaps Software (1992).
Williamson, Glen R., "The Equal Contrast Gray Scale," The American Cartographer 9 (1982): 131-139.
Tobler, W. "Choropleth Maps Without Class Intervals?." Geographical Analysis 3 (1973): 262-265.
Figure 1. A Ten Shading Continuum defined with Postscript
Figure 6. PostShade program with map and spreadsheet windows
Figure 7. Data menu palette from PostShade program