# Vector Data Structures

## GRASS 6 Vector Architecture

The GRASS vector data model includes the description of topology, where besides the coordinates describing the location of the primitives (points, lines, boundaries and centroids), their spatial relations are also stored. In general, topological GIS require a data structure where the common boundary between two adjacent areas is stored as a single line, simplifying the map maintenance.

The following vector objects are defined:

• point
• line: directed sequence of connected vertices with 2 endpoints called nodes
• boundary: the border line to describe an area
• centroid: a point within a closed boundary
• area: the topological composition of centroid and boundary
• face: a 3D area;
• kernel: a 3D centroid in a volume (not yet implemented)
• volume: a 3D corpus, the topological composition of faces and kernel (not yet implemented)

Note: all lines and boundaries can be polylines (with nodes(vertices) in between)

## ESRI Shapefile

A shapefile stores nontopological geometry and attribute information for the spatial features in a data set. The geometry for a feature is stored as a shape comprising a set of vector coordinates.

The following vector objects are defined:

• Point
• MultiPoint: a set of points
• PolyLine: A PolyLine is an ordered set of vertices that consists of one or more parts. A part is a connected sequence of 2 or more points. Parts may or may not be connected to one another. Parts may or may not intersect one another.
• Polygon: A polygon consists of 1 or more rings. A ring is a connected sequence of 4 or more points that form a closed, non-self-intersecting loop.
• PointM: Point plus a Measure
• PolyLineM: Point plus a Measure
• PolygonM: Point plus a Measure
• MultiPointM: MultiPoint plus a Measure
• PointZ: PointM plus a additional z-coordinate (height)
• PolyLineZ: PolyLineM plus z-coordinates (heights)
• PolygonZ: PolygonM plus z-coordinates (heights)
• MultiPointZ: MultiPointM plus additional z-coordinates (heights)
• MultiPatch: A MultiPatch consists of a number of surface patches. Each surface patch describes a

surface.

## OpenGIS Simple Features

is a nontopological standard implemented by e.g. OGR and PostGIS, etc..

• Point
• LineString
• Polygon
• Multipoint
• Multipolygon
• GeomCollection

## SVG

is a nontopological W3C standard. The following vector objects are defined:

• line
• polyline
• rect: defines a rectangle
• circle
• ellipse
• polygon