# Linking Off-Road Points to Routing Networks
## 1 Introduction  
With the growth of the number of new query dimensions that address spatial and temporal properties, business intelligence analysts claim that the buzz-word term Big Data [1] does nowadays put less emphasis on the sheer size of data but focuses more on the \(v\)-terms variety and veracity, which translate to the context of spatial data in the following ways.  
**Variety**: Spatial reference systems encode spatial data by relative location (e.g., coordinates on a local projection) or absolutely (e.g., WGS84 [2] or the Mercator projection [3]) in various formats.
**Veracity**: Every dataset that provides spatial data is incomplete and inaccurate in the open-world assumption, for instance, the dynamic reshaping of infrastructure.  
This can be seen by two facts: On the one hand, in most parts of the world, modern network data are approaching nearly a perfect mapping between digital representation and real-life infrastructure. On the other hand, diverse sources of spatial data emerge due to the vast availability of mobile gadgets that collect location data (e.g., geotagging, -caching, etc.). This phenomenon involves structured geoinformation data sources such as Open Street Map (OSM), as well.  
Nowadays, spatial database systems have already taken the bait to provide useful query access to data with spatial information [4]. They enable fast spatial queries that may involve routing, but they do not provide the easy aggregation of diverse data formats. This comes apparently to light when dealing with routing networks and spatial objects. Common spatial systems map the network locally on a plane such that the Euclidean metric can be used for fast geographic reasoning.  
On the one side, adding, moving or deleting vertices or edges can be naturally interpreted geometrically. On the other side, naive approaches neglect the following problems:  
1. First, the network's graph might not be planar. When projecting a non-planar graph to a plane, the image has intersecting lines that represent two edges. By merely looking at the image, we cannot differentiate whether it is a crossing or whether one street tunnels under the other. A geometrical query, unaware of this fact, might deliver results that do not match real-world expectation. Let us, for instance, consider a long bridge crossing a valley. A query for the nearest access point to the routing network of the valley might suggest this bridge as a result, although it is not directly accessible from the valley.  
2. A second problem arises when very distant points are taken into consideration. For large routing networks, it is not possible to project them on a compact plane that respects both the angles and distances of the Earth. That is because the Earth is not isomorphic to any compact flat model. For instance, let us take a look at the Mercator projection [3]. It gained popularity due to its accuracy of angles and is still used for course information in marine navigation systems [5]. Furthermore, the projection provides a good approximation for nearby spatial reasoning. Unfortunately, the projected shapes of the objects get distorted with respect to angle and length. More precisely, the distortion correlates with the objects' distances to the equator. Hence, the projection exaggerates the distances and sizes of spatial objects near pole regions. This makes spatial objects with large differences in latitude incomparable, and is a main complaint of the Mercator projection. In order to cope with large-distance reasoning, we have to leave the concept of a single chart and move towards a concept that represents a \"truer\" form of the Earth. In other words, distances between distant objects are retrieved by a geodesic line instead of some projection. Having recognized these facts, we want to deal with the following emerging problem.