Geographical representation

A geographical representation considers the way geoinformation, such as fields and objects, are represented in computers. 

A geographic field can be represented by means of a tessellation, a TIN or a vector representation. The choice between them is determined by the requirements of the application in mind. It is more common to use tessellations, notably rasters, for field representation, but vector representations are in use too.

The representation of geographic objects is most naturally supported with vectors. After all, objects are identified by the parameters of location, shape, size and orientation, and many of these parameters can be expressed in terms of vectors.

Various geographic phenomena have the characteristics of continuous functions in space. Elevation, for instance, can be measured at many locations and each location may give a different value. To represent such a phenomenon in computer memories, we could either:

• try to store as many (location, elevation) observation pairs as possible, or

• try to find a symbolic representation of the elevation field function as a formula in terms of x and y - like (3.0678x2 +20.08x−7.34y) or some such - that can be evaluated to give us the elevation at any given (x, y) location.

Both approaches have their drawbacks. A drawback of the first approach is that it is impossible to store all elevation values for all locations since there are infinitely many pairs. A drawback of the second approach is that it is impossible to know the shape of this function, and it would be extremely difficult to derive such a function.

In GISs, usually a combination of both approaches is taken. We store a finite, but intelligently chosen set of (sample) locations together with their elevations. This gives us the elevations at the locations stored. An interpolation function allows us to infer an acceptable elevation value for locations that are not stored. Interpolation is made possible by a principle called spatial autocorrelation.

Line objects, either by themselves or in their role as region object boundaries, are continuous phenomena that must be finitely represented. In real life, these objects are usually not straight, and can be erratically curved. A famous paradoxical question is whether one can actually measure the length of Great Britain’s coastline, i.e. can one measure around rocks, pebbles or even grains of sand? In a computer, such random, curvilinear features can never be fully represented: they require a degree of generalization.

Phenomena with intrinsic continuous and/or infinite characteristics therefore have to be represented with finite means (computer memory) for computer manipulation, yet any finite representation scheme is open to errors of interpretation. To allow for this, fields are usually implemented with a tessellation approach, and objects with a (topological) vector approach.