Geometric Primitives

In many fields of design, including information systems, a “primitive” is the building block from which more complex forms are constructed. Thus, in a geographic information system (GIS), there are a small number of geometric forms that serve as the geometric basis on which a richer system can be constructed. This entry concentrates on the two-dimensional forms that form the basis of the raster and vector GIS software. It also covers some of the primitives developed for surfaces and three-dimensional forms. Arguments over geometric primitives played an important role in the emergence of this technology, and thus history is inseparable from the topic.

Geographic information is distinctive in a number of ways, but the most obvious is that it must represent spatial entities and their relationships. A disciplined approach to data management must begin with the question “What exists?” The concept of a “primitive” seeks a limited set of basic objects from which everything more complex can be constructed. There are a few main approaches to geographic representation [Page 198]that begin from different answers to the fundamental question. Much of the diversity of software design derives as a consequence of these different choices.

In geometry, the concept of a point is clearly a candidate as a primitive. Points have no internal structure, being vanishingly small positions characterized by their geographic coordinates. But can points become the only basic building block? In the established framework of plane geometry, dating back to the ancient Greeks, lines were recognized as composed of many, many points. Later, it became clear that there was an infinite number of points along even the shortest segments of a line. While infinity is a neat mathematical principle, it is totally impractical to represent an infinity of objects in a totally literal way. Here, the primary schools of thought in geographic data design diverge into raster and vector.