Vector Data Representation

Vector Data Representation
Reading: Changs Chapter 3
Geometric Objects
The vector data model uses x, y-
coordinates and simple geometric
objects:
points, line and areas
to represent spatial features.
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A point (node, vertex or 0-cell) has 0

dimension and has only the property of
dimension.
A line (edge, link, chain, 1-cell) has 1
dimension and has the property of length.
An area (polygon, face, zone, 2-cells) has
2 dimension and has the property of area
and boundary.
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The basic units of vector data model

are points and their coordinates.
A line feature is made of points.
See Figure 3.2
An area feature is defined by lines.
See Figure 3.3
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Topology
Explains the arrangement of geometric
objects and the relationships between
objects.
In vector data model topology is explained
by digraph (directed graph) which include
points and directed lines (arcs).
Adjacency and incidence are two relationships
that can be established between the point and
line objects in digraphs. See Figure 3.4.
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Adjacency and Incidence

If a line joins two points, the points are said to
be adjacent and incident with the line.
Adjacency and incidence relationships can be
expressed as matrices.
See Figure 3.4
In the adjacency matrix, the rows and column
numbers are the node numbers, and the values
in the cells are number of arcs joining the
corresponding nodes.
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The direction of the arc determines if 1 or 0

should be assigned.
Ex: 1 in (11,12) and 0 in (12,11)
The row numbers of the incidence matrix
correspond to the node numbers in Figure 3.4,
the column number correspond to the arc
numbers.
The number 1 in the matrix means an arc is incident
from a node, -1 means an arc is incident to a node,
and 0 means an arc is not incident from or to a node.
Ex: Arc 1 and 13 in Figure 3.4
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In ArcInfo, a coverage support 3

basic types of topology:
Connectivity: Arcs connect to each
other at nodes.
Area definition: An area is defined by a
series of connected arcs.
Contiguity: Arcs have directions and
left and right polygons.
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Topological Data Structures
Point features are simple and coded

with pairs of coordinates.
Topology does not apply to points
because points are separated from
one another.
See Figure 3.6
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Line features have topology.

In ArcInfo, a line segment is called
an arc which is connected to nodes
(two end points).
The starting point is called from-
node.
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The ending point is called to-node.

The arc-node list sorts out the arc-
node relationship.
The arc-coordinate list shows the
x,y-coordinates that make up each
arc.
See Figure 3.7
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Area data structure has polygon/arc

list, and left/light list.
The polygon/arc list shows the
relationship between polygons and
arcs.
See Figure 3.8.
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The left/right list shows the

relationship between arcs and their
left right polygons.
The topology-based data structure
facilitates the organization of data
files and reduces data redundancy.
The share boundary between
polygon is listed once not twice.
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Non-Topological Vector Data
The main advantage of non-

topological (NTP) vector data is that
they display more rapidly on the
monitor, and can be used directly in
different GIS software packages.
The standard NTP format used in
ArcView is shapefile.
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Shapefile saves a point as a pair of x, y-

coordinates, a line as a series of points,
and a polygon as a series of lines.
No files describe the spatial relationship
among geometric objects.
Two basic files in shapefile:
.shp file stores the feature geometry
.shx file maintains the index of feature
geometry
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Shapefiles can be converted to coverages

and vice versa.
Conversion from shapefile to coverage
require building topological relationships
and removal of duplicate arcs.
Conversion of coverages to shapefiles is
simpler but need error-free coverage
otherwise some features are missing in
shapefiles (see Figure 3.9a, 3.9b).
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Higher-level Objects
TIN (triangulated irregular network)

A vector data for terrain mapping
and analysis.
A TIN approximates the surface with
a set of non-overlapping triangle.
Each triangle in the TIN is assumed
to have a constant gradient.
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These triangles are constructed using
Delaunay triangulation, by iterative
process of connecting points with their
two nearest neighbors to form triangles
as equi-angular as possible. (See Figure
3.10)
Components of TIN
Elevation points with x, y, z values
Edges (lines) that connect these points to
form triangles
Slope and aspect of each triangle can be
calculated from x,y,z and edges.
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Regions
Built from lines and areas
Consists of region layers and regions
(see Figure 3.11)
A region layer is made of regions of the
same attribute.
Characteristics of region data model:
Region layers may overlap with another
region layer
A region may have disconnected or disjoint
components.
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Region data structure

Region-polygon list
Region-arc list
See Figure 3.12
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Dynamic Segmentation
Combines a line coverage and a linear
measurement such as milepost system to
form a higher level object.
ArcInfo uses 3 basic elements for the
model:
Sections
Routes
Events
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Sections
Arcs of a line coverage and positions
along arcs.
Routes
Collections of sections that represent
linear phenomena such as roads, streams.
Events
Attribute data associated with routes.
See Figure 3.13
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Vector Data Representation

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Vector Data Representation

Reading: Changs Chapter 3

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