Distance zones: Distance buffer and distance transformation

Besides the calculation of the shortest path between two objects, there is another important application performed in a GIS: The determination of distance zones. This function can be used to assign for all the objects in space the corresponding distance between it and the nearest object. The calculation of the distance zones is different for vector data models and raster data models.

Vector data model

Vector data models are often used to model exact phenomena. Distance zones are again exact entities. Therefore, distance zones are called distance buffer. The calculation of a buffer always results in a polygon, independent of the original geometric primitive (point, line, and polygon). The boundary line of those polygons is of interest. They surround the objects in a certain distance (cf. animation below). The calculation of distance buffers is based on the Euclidean distance. Further methods, e.g. those which can be easily implemented in raster data models, are complex and need a lot of effort to be realized in vector data models. Distance zones (e.g. 0-500m, 501-1000m, 1001-2000m) which are nested inside each other, can only be realized by repeated calculation and subsequent application of polygon overlay. The possibilities of buffering in the vector data model are more limited than those in the raster data model. Nevertheless, there are a few possibilities to vary the distance buffer (cf. animation below):

• The shape of a buffer can be varied. A line buffer's end can be rounded or flat.
• Buffering distances can be calculated depending on the attribute value of the object. E.g.: The transmission power of a mobile phone antenna determines its range.
• Buffer can also be formed on one side only, e.g. a building ban zone around a lake.

Raster data model

Also single grid cells in raster data models can be buffered. In raster data models distance zones assign a distance value to each grid cell according to their distance to the nearest source cell. This results in a quasi continuous result. Since space is transformed according to the distance to a certain object, we can speak about distance transformation. In raster data models an appropriate metric space can be chosen for the distance transformation: Euclidean metric, Manhattan metric or other metrics what include in addition also the diagonal neighbors. In addition, path costs and travel time are included are considered, e.g. as cost surfaces. Cost surfaces contain information about the effort needed to overcome a distance per cell. A quasi continuous raster distance transformation can be converted elegantly into a simple classification of distance zones (e.g. distance zone up to 250m, up to 550m etc.). The accuracy of the results depends on the raster resolution (cell size).

	Vector data model	Raster data model
Denomination	Distance buffer	Distance transformation
Metric space	Euclidean distance	different metric spaces possible
Modeling	Clear defined phenomena	Phenomena that vary continuously over space
Distance zones	Intersection of the distance buffer using polygon overlay. Additional possibilities: unilateral buffer, weighted buffer (depending on the attribute value of the object), form of the buffer (rounded or flat end)	reclassification of the distance transformation
Variable costs	impossible	Inclusion of cost surfaces as effort for distance overcoming
Accuracy	Depending on the data accuracy and precision of the calculation	Depending on the raster resolution