Academic journal article Cartography and Geographic Information Science

Scale, Sinuosity, and Point Selection in Digital Line Generalization

Academic journal article Cartography and Geographic Information Science

Scale, Sinuosity, and Point Selection in Digital Line Generalization

Article excerpt


On paper maps, lines usually have beginnings, ends, widths and flow from place to place as continua, turning occasional corners. In digital maps, lines have beginnings and ends but not widths, and are sequences of dimensionless points, each of which has little intrinsic importance, possibly representing nothing in particular. Digital cartography has, however, instilled in its practitioners a sense that such points really do exist, and that their importance can be quantified and classified. Perhaps that is why--seen from other perspectives--the literature on map generalization often seems to make much ado about nothing, or almost nothing. This paper attempts to sort through some assumptions found in the literature on line generalization, and then to empirically test them to see how useful they are.

We begin with some observations regarding the primary impetus for generalization, changing map scale. Given the pervasiveness of this activity there is surprisingly little reference to scale in the automated generalization literature. Most of what is found derives from a misinterpretation of Topfer's (1974) work, still the standard in the field. We then examine the concept of characteristic points, seen in the literature as describing major inflections along a feature that contribute more overall shape information than most locations do. The notion comes to cartography from the work of psychologist Attneave via Douglas, Poiker, Buttenfield and others, including computer vision researchers. This line of thought makes the assumption that the identities of the points are knowable only after analyzing an entire feature as a whole. Furthermore it has been assumed--based on relatively slim evidence--that having identified the most significant points on a feature, they should be preferred to other points in the process of simplifying its shape for generalization purposes.

To test these notions, we present evidence that selecting characteristic points chosen for their global importance may produce less than optimal results in simplifying map features, compared to other point selection strategies. We then show how adding local intelligence to cartographic data and processing it using local, contextual generalization methods can be helpful. While such techniques impose added burdens of complexity for computation and control, this price is probably inevitable if automated generalization is to become truly feasible for interactive and hardcopy mapping.

Map Generalization and Map Scale

Generalization is not simply making little things look like big things. Children are proportioned differently than adults, and map features at small scales should not slavishly mimic their shapes at large scales. In addition, contextual factors may also influence shape representation, such that simplifying features can require more than merely removing vertices; sometimes entire shapes (such as a meander or a switch back) should be deleted at a certain scale (Plazanet et al. 1995; Wang and Muller 1998). In other instances, entire features (points, polylines, polygons or sets of them) will need to be transformed or eliminated. But long before it vanishes, a feature will tend to lose much of its character as a consequence of being reduced. This needs to occur in a sensible way; as the following sections describe, commonly used numerical criteria for evaluating solutions do not necessarily provide useful guidance, in part because they do not reflect the imperatives of map scale, in part because they are too global, and because the geometric properties they preserve may be undesirable.

Articles describing techniques for map generalization frequently observe that their application should always be tempered by the scale and purpose of the map being produced (McMaster and Shea 1992). To these considerations some authors also add constraints based on the display medium and its resolution (McMaster 1987). …

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