# Map foundations: topology and geometry

The most fundamental component of a digital road map is the topology representing a road network.

The basic Road Model uses a simple logical topology consisting of roads (called "links") forming linear connections between intersections (called "nodes") where three or more roads join. The nodes are accurately geolocated in 2D space. Links — which start, end, and meet at nodes — are straight lines that do not follow the curves of actual roads.

The Road Model also uses a special type of node, called a "bivalent node," which can be placed between intersections to support changes of attributes, such as a change of Speed Limit between intersections. A bivalent node connects exactly two links. Similarly, by using geolocated "shape points" along links, the geometry of road curves can be approximated by a series of connected line segments called a "polyline." These bivalent nodes and shape points affect the geometry of a road, but they are not part of the logical topology.

The first figure below represents a real road. In the second figure below, the squares are nodes at intersections; the circles are shape points between intersections; and the line segments connecting the nodes are links represeting roads.

In more advanced road models such as the Lane Model, the 3D curves of actual roads (including changes in elevation) are more accurately represented by NURBS (Non-Uniform Rational B-Splines), which are mathematical splines in 3D space. Surface paths using NURBS are typically placed along the centerline of road surfaces and along lane paths. In published maps, internal road and lane data using NURBS are typically tessellated into nodes and topology segments, with shape points, for backward compatibility with basic road models and the navigational apps based on them.

Road maps can be further enriched by the inclusion of attributes on links, such as speed limits and direction of travel, and geo-located objects like street signs and barriers associated with roads for localization. Because advanced road and lane models support parametric attributes, which can be applied along subsections of each segment, these models don't use bivalent nodes.

Cartographic features such as lakes, buildings, railways, rivers, and administrative boundaries can be represented by non-navigable segments. Specifically, cartographic surfaces such as land use (e.g. parks) are represented by segments forming closed polygons.

In summary, HERE uses three primary map models to represent road and lane topology, as well as attributes and objects associated with roads: the Road Model, the Lane Model, and the Localization Model. HERE HD Live Map is an example of a map product that integrates all three models. For details on these map models, see the Map models chapter in this document.