The third preference of both the customers are quite special ones, which cannot be incorporated into our model with mere vector analysis tools. One of the requirements is that solar panels can be used on the house efficiently. Of course, there are numerous factors to consider, like the exposure of the roof. However, the simplest feature such a house should have is the aspect of the land it is built on. If we are in the northern hemisphere, the terrain with northern aspect is mostly in shadow. In the southern hemisphere, the land with southern aspect is more shadowy. In reality, there are a lot more factors contributing to the solar energy potential (like latitude, climate, cast shadow, and so on), but for the sake of simplicity, let's just assume for now that the only factor is the aspect of the surface.

For solving surface-related problems, GIS has its most characteristic data type--DEM (Digital Elevation Model). DEMs are representations of a planet's surface (most often Earth). They can be in raster or vector (mesh) format, and can be visualized in 2D, or as a rubber sheet in 3D, which is not 2D, but neither is it true 3D (they are often called 2.5D because of this property). What makes DEMs a very valuable and useful data type is their wide variety of use cases. A lot of terrain-related information can be derived solely from the surface data. The two most basic derivatives are slope and aspect, where slope shows the steepness of the surface, while aspect shows its exposure.

DEMs in a regular grid format (raster) are usually the results of processing raw elevation data in vector format. These raw elevation data can be acquired in multiple ways, such as point clouds from RADAR or LiDAR measurements, digitized elevation contours, or individual GPS measurements. If the resulting vector data is dense enough, a regular grid can be constructed on them, and the individual data points in a cell can be averaged. If not, then spatial interpolation is the usual way of creating DEMs. There are a lot of spatial interpolation techniques, although there is a common concept in them--they take a number of points as input, and create a regular grid by interpolating additional points between existing ones as output (Appendix 1.9). Of course, these irregular elevation points can also form a Triangulated Irregular Network (TIN) if their Delaunay triangulation is calculated.