Generalization Operators

Generalization Operators

As suggested by the previous OpenStreetMap example, generalization is a process for dealing with conflict and congestion among map symbols—a strategy for creating a more readable and useful map. Though this is a complex and context-dependent problem, some resources are available to help you determine the appropriate level of detail for your maps. ScaleMaster (Brewer et al. 2007) for example, available at scalemaster.org (Note: As of July 28, 2023, the scalemaster.org site no longer exists), offers advice to mapmakers on which features ought to be included at different scales, and for different mapping purposes.

Figure 8.2.1 An example ScaleMaster diagram (scalemaster.org), as explained by (Roth, Brewer, and Stryker 2011).

Credit: (Roth, Brewer, and Stryker 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

We will not go into the details of ScaleMaster in this lesson, but you are encouraged to read more about this idea through the Cartographic Perspectives article if you are interested. The most important takeaway is that different scales require differing levels of detail, and that the appropriate level of detail is mediated by the map’s context (e.g., topographic vs. zoning maps).

Generalization can be broadly categorized as either selection or symbolization. Selection is simple—it refers to the decision of whether to include (or not include) a feature at a certain scale. Symbolization refers to alteration of the way a feature is designed in order to make its design more appropriate for the scale at hand. For example, when designing a small-scale map, you might choose to not include cities unless they are high population (selection), and to symbolize these cites as labeled points rather than as areas (symbolization). Generalization traditionally refers to reducing detail in a map as much as is necessary to maintain legibility and usefulness at a specified scale. Generalizing multi-scale web maps (which exist at many rather than one scale) is more challenging, but not fundamentally different—we can think of every possible scale step (or zoom level) of a multi-scale web map as its own map for which an appropriate level of detail must be determined.

As generalization is a fundamental topic in cartography, many cartographers have proposed theoretical frameworks for discussing generalization. For simplicity, in this lesson, we will focus on the set of generalization operators recently proposed by Roth et al. (2011), as they were developed based on a comprehensive review of previous literature. As we discuss generalization operators, an important distinction should be made between generalization operators and generalization algorithms. Operator refers to a cartographer’s conceptualization of an intended change (e.g., I want to remove some roads to reduce the visual clutter of this road network), while an algorithm is a system followed for implementing this idea (e.g., I will remove all roads with speed limits below 25mph) (Roth et al. 2011). Like Roth et al., we focus on operators rather than algorithms in this lesson as they are more widely applicable to map-making tasks, and not dependent on the use of specific datasets or GIS software tools.

Roth et al. (2011) classify feature generalization operators into three groups: content, geometry, symbol. Content operators directly alter the content of the map, typically by adding or removing features at particular scales. An example would be deciding not to include local roads or trails in a small-scale map. These operators include: add, eliminate, reorder, and reclassify.

Figure 8.2.2 Content Operator: Add.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.3 Content Operator: Eliminate.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.4 Content Operator: Reorder.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.5 Content Operator: Reclassify.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Geometry operators describe the ways in which different features' geometry can be altered to create a map that is more legible and aesthetically pleasing. Examples include smoothing a line feature and representing a city as a point rather than an area. Geometry operators include: simplify, aggregate, collapse, merge, displace, exaggerate, and smooth.

Figure 8.2.6 Geometry Operator: Simplify.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.7 Geometry Operator: Aggregate.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.8 Geometry Operator: Collapse.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.9 Geometry Operator: Merge.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.10 Geometry Operator: Displace.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.11 Geometry Operator: Exaggerate.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.12 Geometry Operator: Smooth.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Symbol operators alter feature symbology to improve legibility, but do not change the features’ underlying geometry. An example would be simplifying the pattern in an area fill so it still looks good at a smaller scale. Symbol operators include adjust color, enhance, adjust iconicity, adjust pattern, rotate, adjust shape, adjust size, adjust transparency, and typify.

Figure 8.2.13 Symbol Operator: Adjust Color.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.14 Symbol Operator: Enhance.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.15 Symbol Operator: Adjust Iconicity.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.16 Symbol Operator: Adjust Pattern.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.17 Symbol Operator: Rotate.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.18 Symbol Operator: Adjust Shape.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.19 Symbol Operator: Adjust Size.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.20 Symbol Operator: Adjust Transparency.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

Figure 8.2.21 Symbol Operator: Typify.

Credit: Adapted from (Roth et al. 2011) Cartographic Perspectives, (CC BY-NC-ND 3.0).

It is not necessary to memorize the above operators, but you should aim to understand the difference between the three groups of operators (i.e., content, geometry, symbol) and think critically about situations in which each might be useful.