# A: Spatial data analysis

From the point of view of the database systems on which the geo-information systems are based, analysis functions can generally be divided into standard and non-standard analyses. Standard analysis methods are those methods that can be implemented using queries available in relational database systems and derived from relational algebra. These operations include, for example, the selection of values that fulfill certain conditions (`SELECT * FROM TABLE WHERE ..`), logical links using Boolean algebra (`AND, OR, NOT`), sorting or grouping of data series (`SORT, GROUP BY`), or the derivation of simple statistical (`AVERAGE, MAXIMUM ..`) parameters that can usually already be formulated on relational databases using the query language SQL (Structured Query Language). Queries and analyses, on the other hand, that require special geometric, topological or temporal operations are non-standard analyses and require corresponding systems such as GIS. As previously described, selected geometric-topological functions may be already contained in object-relational databases, provided that these are extended by spatial data types and operators, e.g. in Microsoft SQL Server, Oracle Spatial, MySQL or PostgreSQL (PostGIS). PostGIS as a spatial extension for PostgreSQL offers spatial data types such as polygons, polylines and points, spatial operators for comparing geometries regarding overlapping and spatial functions such as area and distance calculations, area intersections, buffer formation or coordinate transformations.

Data analysis is the heart of a GIS. This includes functions such as polygon overlay, network analysis, digital terrain analysis, report generation, statistical analysis and many special functions derived from the application requirements, which are increasingly provided. For example, the information can be provided to guide vehicle drivers from a starting point to a destination using the shortest route calculation via the car navigation systems on board.

Analysis methods can be roughly divided into 6 groups (for functionalities and methods see Bill, 2016, chapter 7 resp. de Smith et. al. 2018):

1. Geometric methods are essentially based on the mathematical foundations of geometry. They are characterized by calculating with coordinates. Important functions are the distance and area calculation (e.g. for parcels of a municipality), the zone or buffer generation (e.g. around a planned route), the point in polygon check - explained in the video (e.g. measuring points in a district), the polygon overlay (e.g. parcels versus real land use, see video) and the triangular intermeshing (e.g. digital terrain models).

2. Topological methods are based on neighbourhood relations; they essentially use graph theory as a mathematical basis. They can be used to express neighborhood relations (two parcels bordering each other) without using coordinates. A well-known function is the calculation of the shortest paths in a network (e.g. a pipeline network).