Representing geometrical shapes

You learned how to calculate coordinates on the earth's surface. But how can you represent a real object, for example, a river, in a convenient way for a GIS?

There are two main approaches when building a spatial database, modeling vector data or raster data. Vector data uses a set of discrete locations to build basic geometrical shapes, such as points, polylines, and polygons.

Of course real objects are neither a point, nor a polyline or a polygon. In your model you have to decide which basic shape better suits the real object. For example, a town can be represented as a point if you are going to draw a map of the world with the countries' capitals shown. On the other hand, if you are going to publish a counties map, a polygon will enable you to draw the city boundaries to give a more realistic representation.

The simpler geometric object is a point. Points are defined as single coordinate pairs (x,y) when we work in two-dimensional space or coordinate triplets (x,y,z) if you want to take account of the eight coordinates. In the following examples, we use point features to store the location of active volcanoes:

Etna; 37.763; 14.993
Krakatoa; -6.102; 105.423
Aconcagua; -32.653; -70.011
Kilimanjaro; -3.065; 37.358

Did you guess the units and projections used? The coordinates are in decimal degrees and SRS is WGS84 geographic, that is EPSG:4326.

Points are simple to understand but don't give you many details about the spatial extent of an object. If you want to store rivers you need more than a coordinate pair. Indeed, you have to memorize an array of coordinate pairs for each feature in a structure called polyline:

Colorado; (40.472 -105.826, … , 31.901 -114.951)
Nile; (-2.282 29.331, … , 30.167 31.101)
Danube; (48.096 8.155, … ,45.218 29.761)

If you need to model an areal feature such as an island, you can extend the polyline object adding the constraint that it must be closed; that is the first and the last coordinate pairs must be coincident:

Ellis Island; (-74.043 40.699, -74.041 40.700, -74.040 40.700, -74.040 40.701, -74.037 40.699, -74.038 40.699, -74.038 40.698, -74.039 40.698, -74.041 40.700, -74.042 40.699, -74.040 40.698, -74.042 40.696, -74.044 40.698, -74.043 40.699)

Note

The feature model used in GIS is a little bit more complex than what we have discussed. There are some more constraints regarding vertex ordering, line intersections, and areal shapes with holes. Different GIS specified several different set of rules, often in proprietary formats. Open Geospatial Consortium (OGC) defined a standard for simple features, and lately most systems, open source in primis, are compliant with it. If you are curious about it, you can point your browser at http://www.opengeospatial.org/standards/is and look for The OpenGIS® Simple Features Interface Standard.