## 6 Experimental Evaluation  
### Experimental Isopleth Generation  
Using contour lines (also isoline or isopleth) to represent the distribution of data is a common technique when there exists a trade-off between having more information about the data and affording higher costs to collect the additional information [2]. To highlight the potential use of the mapping service, an implementation of isopleth generation is presented. This is a simple implementation, with little regard for efficiency, but nevertheless provides a genuinely useful output for the purposes of visualisation or phenomenon edge delineation. A user makes a request to any node, giving the value of the required isopleth. A threshold figure, \(t\), is also given so that values \(\pm t\) are included. The threshold \(t\) of the isopleth specifies the desired isolines in the isopleth map with the isolevels. The simple algorithm presented here causes this node to then query every other node in the network for their value of the parameter in question. Once all data is collected, the map generation is performed, and every value matching the required isopleth is recorded as being part of that isopleth. An isopleth for a given parameter at a given value can be found by a step-by-step search for the next point in the map at the same level. That is, a single point is used as the start of the isopleth and the next is found by searching the neighbourhood in progressively more detail. The process is repeated until the end of the isopleth moves out of the mapped region or meets the beginning. The highest level of detail that is searched will determine how fine the isopleth is. To implement this algorithm, the Dingo [31] WSNs simulator was used. A section of the Grand Canyon height map [32], is fed into the simulator (see Figure 5). The height map was chosen because using numerous wide-distributed height points has been an important topic in the field of spatial information [33]. Furthermore, the height is a static measure, which makes it suitable for the evaluation  
Figure 4: A Petri-net that models the VCA. of various mapping algorithms. The studied region is \(15,360\)\(m^{2}\), with heights ranging from \(165\)\(m\) to \(284\)\(m\) above sea level. This map was sampled to \(65,536\) points. The sensor nodes were randomly distributed over the height map. The grey value of each pixel denotes the altitude of that point. If the isopleth generation algorithm is applied to this data directly, the result is shown in Figure 6. This contour was generated for a height of \(116\) units and a threshold of \(1\). Figure 7a shows the field generated by the centralised mapping service from \(600\) nodes randomly distributed on the surface of the 2D map in Figure 6a. The result of generating an isopleth on the interpolated field with the same parameters as in Figure 6b, are shown in Figure 7b. Figure 5: Dingo WSN simulator. Figure 6: (**a**) A section of the Grand Canyon height map; (**b**) A contour at 116 units drawn over 2D map in (**a**). Clearly the interpolated terrain is similar to the real surface. Determining exactly how close the similarity is, and what the algorithmic limits to the accuracy of the representation, is a problem we investigated in [20]. Consider, though, that the information used to reconstruct the surface in Figure 7 is just \(600\) points, while the original is recorded as \(65,536\) points. Taking the position of the nodes into account as extra information, the reconstruction is built using less than \(1\%\) of the original data. The cost of mapping using the centralised mapping services is plotted; it is used as base line scheme for comparison with the distributed mapping service. The same improvements intended to decrease the cost of transmission also reduce the cost of computation. The change from global to local area mapping reduces the number of transmissions and makes the task of map generation significantly smaller.