Spatial Relationships Overlap & Adjacency: Point to Line to Area

To write intelligent programs that are more than a series of simple commands it is necessary to make commands conditional on data values and relationships between data values. For graphics programming and many spatial modelling tasks, it is necessary to make actions depend on spatial relationships, and to provide tests for them. In this chapter the relationships of overlap and adjacency or neighbourliness between spatial objects are examined. Since spatial objects are often represented by complex data structures, such relationship tests usually have to be implemented as sub-programs. Clearly such programs will depend on the nature of the data structure representing the objects even where the abstract objects, for example polygons, are the same. For this reason the main spatial relationships reflecting the primary differences in the structures involved, are set out in the table given below. The more detailed study of algorithms that follow, are based on the specific data structures commonly used to represent these objects in practice.