A conservation law for map space in portrayal and generalisation

The paper describes new approaches in computational cartography to assist online map portrayal e.g., in web map and location-based services. Such services demand increasing levels of flexibility to support portrayal operations such as the on-the-fly combination (conflation) of data from different sources in response to ad hoc database queries and dynamic generalisation of information in response to different device profiles, user preferences and interaction. The research described in the paper takes the position of a conservation law for mapping to build models of representation that can assist in portrayal tasks, specifically cartographic generalisation and data conflation (to support online information retrieval services). It uses a grid mesh that is fitted to the map objects, such that the grid shares the same ‘topology’ as the features. That is, a feature’s geometry lies on a grid vertex (if it is a point object), follows a grid edge or crosses a grid face diagonally (if it is a linear object). This grid is then used as a parameter space to compute coordinate transformations that model the deformations that occur when features are symbolised. By adding structural constraints to the grid it is then shown how these transformations can be used to perform conflation and generalisation operations. Two cartographic activities where this issue is encountered are conflation and cartographic generalisation. Here, conflation refers to the task of portraying and combining data from ad hoc queries on geo-referenced databases with a topographic base map. This task is performed frequently in online mapping systems, for example weband location based services. Cartographic generalisation is a portrayal task that seeks to balance requirements for good map legibility with accuracy and optimal information content. It does so by abstracting both the spatial relationships and semantics of the map information and reorganising features accordingly. Introduction Maps are an analogue representational media (Palmer, 1978) that communicate information in two ways; symbolically and spatially (Berendt et al, 1998). Symbolic information is represented explicitly by presenting attribute information of features pictographically. Spatial information is represented implicitly by using the spatial characteristics that constrain the map medium as analogous to those constraining geographic space (Sloman, 1985). Hence spatial relationships in geographic space can be said to be represented more or less “faithfully” in the map space. These two dichotomous forms of information description do not generally sit happily together. Symbolising features on a map, beyond their real world footprint, necessarily impacts on the ability of the map to represent spatial relationships. Two inter-related mapping activities can be distinguished affecting this relationship: portrayal and scale selection. ?? Portrayal relates to the selection and application of a set of signs that will be used to communicate information symbolically. Different forms of portrayal will have different effects on the ability to describe spatial relations. ?? The scale selection affects the way in which the dimensions of the symbol scale relative to how properties of space scale. Figure 1 illustrates this for a circular point symbol, shown in the inset for different scales. 0 50 100 150 200 250 300 0 500