Vector Data Model

A vector data model represents geographic features as geometric primitives — points, lines, and polygons — rather than as a grid of cells (the raster model). Each feature is defined by its coordinates and its topological relationships to other features. The vector model is the dominant representation in geographic information systems, mapping platforms, and computer-aided design, where precise boundaries and network topology matter more than continuous field values.

In the vector model, a road is a polyline with vertices at each intersection; a building is a polygon with a boundary; a fire hydrant is a point with a coordinate. The model's power lies in its topology: the vector representation encodes not just where things are, but how they connect. Two roads meet at a shared vertex; a polygon encloses an area; a point lies on a line. These relationships are explicit in the data model, whereas in a raster representation they must be inferred from pixel adjacency.

The Vector-Raster Duality

The vector and raster models are not merely different formats; they are ontological commitments. The vector model assumes that the world is made of discrete objects with sharp boundaries. The raster model assumes that the world is made of continuous fields with values at every location. A city is a collection of buildings and roads in the vector model; it is a population density surface in the raster model.

Neither assumption is universally correct. Coastlines are fractal: the vector model represents them as polylines with finite precision, while the raster model represents them as a boundary between land and sea cells. Both are approximations. The choice between vector and raster is not a technical decision but a philosophical one: do we believe the world is fundamentally discrete or continuous?

The Quadtree and the R-tree are the principal spatial indexes for vector data, each making a different trade-off between query efficiency and update cost. The quadtree subdivides space uniformly; the R-tree groups nearby objects into overlapping bounding boxes. The choice of spatial index is as consequential as the choice of data model, since it determines which queries are fast and which are slow.

Topology vs. Geometry

A vector data model can be purely geometric — a collection of coordinates with no explicit relationships — or topological, with explicit encoding of adjacency, containment, and connectivity. The spaghetti model is purely geometric: each feature is independent, and coincident boundaries are stored twice. The topological data model stores shared boundaries once and records which features use them.

The spaghetti model is simpler to implement but fragile: move a shared boundary in one feature, and the adjacent feature's geometry is silently corrupted. The topological model is more robust but more complex: it requires a graph structure to manage relationships, and updates propagate through the topology. The choice between spaghetti and topology is the same choice that faces every database designer: denormalization for speed, or normalization for integrity.

The vector data model's elegance is its curse. By representing the world as discrete objects with clean boundaries, it imposes a Cartesian clarity on territory that is rarely Cartesian and never clean. The vector model is not a description of reality; it is a tool for imposing order on reality. The distinction matters: GIS analysts who confuse the model with the world make decisions about land, water, and boundaries that treat approximations as truths. The vector model is a powerful fiction, but it is still a fiction.