Abstract
This chapter describes the various ways of modeling and representing geometric and topological information in geographic information systems (GIS). Geographic object has two components such as a description, and a spatial component that is also referred to as spatial object or spatial extent, which corresponds to the shape and location of the object in the embedding space. This view of geographic information gathers within spatial object points of the embedding space sharing several common properties. In order to distinguish an object from others, an explicit identity is assigned to it. This entire set containing identity, spatial object, and common description, constitutes a geographic object, which is also known as an entity or feature. In a field-based or space-based approach, with each point in space is associated one or several attribute values, defined as continuous functions in x and y. The measures for several phenomena can be collected as attribute values varying with the location in the plane. This view of space as a continuous field is in contrast with the entity-based model, which identifies a set of points as an entity or object. The concept of object is not relevant in the field-based approach. The chapter describes these models and presents three representation modes commonly used to support these models. They are namely the tessellation modes, the vector mode, and a half-plane representation. These modes are explained with a focus on the representation of single objects in the plane. The chapter also discusses the methods of representation of collections of spatial objects, including their interrelationships, and provides an illustration of the basic concepts through the description of spatial data exchange formats.
Published Version
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