4.3 Manipulating and measuring spatial data Most GIS software packages come with a suite of options that allow the user to manipulate spatial data. One of the most basic of these is simply to change the projection system used. This can significantly alter the appearance of maps, particularly maps of the world, and can also make it possible to integrate data from layers that use different projection systems. In Britain, this could be used to take a variety of early maps on different projections and re-project them onto the National Grid. This would allow comparisons between different early maps, as well as with modern ones. Putting adjacent map sheets onto the same projection allows their digital representations to be joined to form a single layer. Where there are distortions to the sheets the maps will have to be rubber-sheeted (or edge-matched) to ensure that the edges of the two sheets make a perfect join. This involves telling the software where certain key points are on the layer and where they actually should be. The entire layer will then be distorted using these references. Figure 4.1 shows an example of this. 
Figure 4.1: Rubber sheeting to join two layers together
A user wants to join the two input line layers together, but due to inaccuracy in one or both of the layers the lines do not match exactly. As part of the joining process the lines on the right-hand layer are systematically distorted to allow them to join to the corresponding line on the left. This distortion is at its maximum at the end points of the line and reduces as we move away from the join. The layers can then be seamlessly joined. Most GIS software packages will also calculate basic statistics about their spatial features. Typical examples include calculating the length of lines, the area and perimeter of polygons, and the distances between points. There are many examples of why these basic measures can be useful. These include measuring distances along a transport network, the use of areas to calculate population densities, and calculating the distances between settlements. | 
