Computational Models of Space

Computational models of space are ways in which space is represented to solve spatial problems from given inputs by means of algorithms. The development of computational models of space relates closely to how space is conceptualized: as discrete objects or as continuous fields. Both object- and field-based conceptualizations of space have been represented in various forms to facilitate geographic computation. The nature of a geographic problem determines the suitability and effectiveness of computational models as to how the models represent space, ingest input data, and support algorithm development to derive solutions for the given problem.

Computational models of objects define space by identifiable entities of interest. In traffic analysis, for example, computational space is defined by the transportation network of interest; and trips outside the network are excluded from consideration. Similarly, computational models for power grids may include transmission lines and transformers, and those for census demographics may include areas of enumeration. Object space often is implemented by vector models of points, lines, and polygons with object identifiers, dimensions, coordinates, and attributes. These geometric objects can be further combined to form complex objects to represent geographic entities of complex shape and structure such as rings to represent lakes with islands and aggregates of line segments to represent delivery routes. Computational geometry serves as the foundation for the development of vector algorithms to quantify individual objects and their spatial distributions, topological relationships, and spatial interactions.

A field describes the distribution of a geographic variable for which value is determined by location; that is, value is a function of location such as a temperature field. A field space is said to be planar and spatially exhaustive because every location has one and only one value for a given variable. In field-based computational models, space is partitioned into regular or irregular units, each of which has a fixed location and, therefore, defines a field value. The most commonly used field model is a matrix of squares (i.e., rasters or grids). Remote sensing technologies provide rich sources for raster data. Other possible partitions of space include triangles, hexagons, and[Page 57] irregular polygons. Among all types of spatial partitions, fields of regularly spaced squares are the most computationally efficient because of geometric simplicity and regular tessellation of space. There are two basic approaches to the development of raster algorithms. One is based on cellular automata that consider how a particular cell value (e.g., fire cells) propagates in a raster layer (e.g., to examine how a fire spreads in space). The emerging technique of agent-based modeling takes a similar approach to examine the evolution of spatial patterns aggregated from individual behaviors when discrete cells of a certain value (e.g., individual pedestrians) animate on a raster over time under a specified set of rules and assumptions (e.g., allow moving only to adjacent cells). The other approach is map algebra in which each raster serves as a spatial variable to formulate algebraic expressions. All input and output variables in map algebra are rasters. Computation may be performed on a cell-by-cell basis or on a group of cells.

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