Summary

Space can be considered from different points of view. Space is defined as the relations between the spatial objects. Distance relations are the basis of the concept of accessibility. Distances on the other hand depend on three conditions: a) the metric space, b) the discretization of space (vector data model or raster data model) and c) the spatial constraints. There is more than the metric space defining distance concepts. Distances can also be expressed by costs or time. In this lesson, the focus is mainly on unrestrained distance relations respectively on the accessibility of objects (there is assumed to be no objects constraining the way between location A and location B.

Different forms of distance calculations are related to the three geometric primitives in the 2D case: Points, lines and polygons. There are several options to calculate the distances between these primitives. It has been shown, that there is no clear solution for the distance calculation between two lines. The construction of distance zone is an extension of the distance calculation. This function allocates distance values, according to the distance to the next associated object. In raster data models, such functions are called distance transformation, in vector data models, they are called distance buffers. In the proximity analysis, Thiessen polygons are used. Within such polygons, all the locations are nearer to the associated center than to any other point. The edges of the polygons are the perpendicular bisectors on the connecting line between two centers. The intersections of these bisectors build the vertices of the Thiessen polygons.