# Overlapping polygons in a coverage: Regions

This topic applies to ArcInfo only.

## Overview of regions

Regions support the modeling of complex relationships between geographic features, represented as polygons. In a coverage, the building block of a polygon is the arc, and the building block of a region is the polygon. Therefore, a region is represented as a set of polygons.

There are two basic premises of representing geographic objects as polygons: the polygons do not overlap, and they completely cover the area being represented (that is, they don't contain any void areas). These constraints are eliminated for regions. In a region, the polygons representing geographic features can be freestanding, they can overlap, and they need not exhaust the total area. For example, in a region of forest fire, damage can be represented by polygons indicating the area and time of damage.

Another premise of polygons is that each geographic feature is represented by one polygon. This is extended for regions so that a single geographic feature can be represented by several polygons. For example, the islands composing the state of Hawaii are a region made up of several polygons.

As with points, lines, and polygons, each region is given a unique identifier. As with polygons, area and perimeter are maintained for each region.

Constructing regions with polygons is similar to constructing polygons from arcs. Just as a polygon is a list of arcs, a region is simply a list of polygons. One important distinction exists: the order of the polygons is not significant.

Constructing overlapping regions is similar to constructing polygons. However, polygons share an arc where they meet, and regions share a polygon where they overlap.

Regions substantially improve data management because they integrate many different kinds of geographic features into a single view while retaining the characteristics of the original geographic features. Managing relationships between geographic features within the data model is particularly valuable when performing complex analyses.

## Region data structure

### Composite features

The region data structure resembles that of dynamic segmentation, where nonplanar lines are achieved by the route and section of a system that "lies above" the arc topology. Routes may overlap because they share base geometry. Regions, likewise, lie above the polygon topology; use shared geometry; and may, therefore, overlap.

The diagram below shows the relationships between feature classes in a coverage dataset. Composite feature classes are built on elementary feature classes, routes and sections are built on arcs, and regions are built on arcs and polygons. This data structure allows you to combine the elementary feature types into integrated coverages.

### Relationship of regions to arcs

Regions consist of one or more nonoverlapping outer rings, or sets of arcs, and zero or more nonoverlapping inner rings.

The figure below shows how region boundaries are defined by the outer and inner rings of arcs. Region 1 comprises two outer rings, and region 2 comprises one outer ring and two inner rings.

Even though many regions use the same arcs, the topology for the arc is stored only once. Thus, one arc may be assigned to many regions with no duplication of topology.

### Relationship of regions to polygons

Polygons are composed of one or more arcs, and polygons may share the same arc (that is, a common boundary). Similarly, regions are composed of one or more polygons, and several regions may share the same polygon.

One polygon may be assigned to many regions without topology being duplicated. Topology is stored for the polygons only.

Regions share the same geometry as the base polygons (although the universe polygon may not belong to a region). With the shared geometry approach, regions do not exist independently but are composites of one or more base polygons.

The figure below demonstrates how two regions can lie above the polygon topology. Region 1 is made up of polygons 2 and 3, and region 2 is made up of polygons 3 and 4. Polygon 3 belongs to both regions.

### Region topology

A fully constructed region has both the region–arc relationship and the region–polygon relationship. A preliminary region has the region–arc relationship but not the region–polygon relationship. In other words, preliminary regions have no polygon topology.