# Dimension

The Dimension of an object (whether in the real world or a digital representation) is an ordinal measure of its spatial extent. Geographic features, and the representations thereof in GIS and maps, are commonly classified by dimension as points, lines, regions, and volumes. In mathematics, it is defined as the number of coordinates necessary to specify a location within its extent. Thus, a single point has 0 dimensions (since there are not multiple points within its extent); a line is one dimensional (one can only measure a distance along it); a region is two dimensional (needing two cartesian coordinates to identify a constituent point); and a volume is three dimensional. When working with Geographic information in GIS and maps, it is important to recognize the dimension of both the real-world phenomena being represented, and the dimension of the digital representations thereof, as these are not necessarily the same..

## Vector Data

The most common mention of dimension within GIS is in regards to vector data, as the data organization of a vector shape depends entirely on its dimension:

• Points (zero-dimensional) are represented by a single coordinate (a pair of distance measurements within a coordinate system). Houses, buildings, and fire hydrants are commonly represented as point features. Other larger elements like cities can also be represented by points when the map scale is appropriate.
• Lines (one-dimensional) are represented by a sequence or point coordinates, connected by lines when drawn or analyzed. Features that have a form of one-dimensional meaning or use (i.e., things happen "along" the feature) are commonly represented as lines, such as rivers, roads and political boundaries.
• Regions (two-dimensional) are represented by polygons, lines in which the two ends close, representing the boundary of the feature; the software is expected to be able to interpolate all constituent points inside the boundary. Vegetation types, lakes and land use patterns are examples of features commonly represented as regions.
• Volumes (three-dimensional) are represented by a number of techniques adopted from computer graphics technology, such as connected shells of 2-d polygon faces, as in a Triangulated irregular network. This dimension can be clearly appreciated in a topographic map where it is represented as a value or quantity, in this specific case the elevation of the land.

## Raster Data

A raster grid is a two-dimensional representation of a geographic phenomenon. The meaning of each cell can vary, though. In a lattice, each value represents a point sample; in a grid, each value represents a two-dimensional (usually square) area. The raster model can be extended to three dimensions by making each cell a cube, or voxel.