Shared geometry

Shared geometry occurs when map features share common boundaries. Many vector datasets contain features that share geometry. Features can share edges, such as line segments — or nodes, the points at the ends of segments. For example, watershed polygons might have common edges along ridgelines, and lake polygons might share their shoreline edges with land-cover polygons. Three watersheds might share a single node at a mountain peak, and three river-reach features might share a node at a confluence.

Consider a map of the United States. Adjoining states such as California and Oregon share a common border. This particular border is represented on maps as a straight line, and this line represents a shared feature of the two polygons; it is a feature that belongs to both of the two-dimensional geometric shapes that define these states.

Now consider the states of Arizona, New Mexico, Utah and Colorado. The borders of these states are called polylines in that they are not straight lines, but include either curved sections or corners. The polyline that defines the border of Colorado has four vertices. The point at which these four states meet is commonly referred to as "Four Corners."

The northeast corner of Arizona is a vertex along the line that defines the boundary between Arizona and its adjoining states, as is the northwest corner of New Mexico, the southwest corner of Colorado, and the southeast corner of Utah. Thus Four Corners may be considered to be a "shared vertex," i.e., it is a common feature of the geometries of all four states.