1 Enviromatics Spatial database systems Spatial database systems Вонр. проф. д-р Александар Маркоски Технички факултет – Битола 2008 год.

2 Enviromatics Spatial database systems Introduction Spatial database systems represent an attempt to provide suitable data management tools to developers and users in application areas that deal with spatial data. The data management requirements of spatial applications differ substantially from those of business applications. These applications tend to have simply structured data records. There are only a small number of relationships between data items. Relational database systems meet this requirement very well. In opposite of that, spatial databases contain multidimensional data with explicit knowledge on data objects, their extent, and their position in space. The objects are usually represented in some vector-based format. Their relative position may be given explicit or implicit.

3 Enviromatics Spatial database systems Introduction (2) Spatial data objects have a complex structure. A spatial data object may be composed of a single point or several polygons distributed across space. Spatial data objects are dynamic structures. Insertions and deletions are interleaved with updates. Data structures have to support this dynamic behaviour without deteriorating over time. Spatial databases tend to be large. Geographic maps occupy a high number of memory places. There is no standard algebra defined on spatial data. This means in particular that there is no standardised set of base operators. This set depends on the given application domain.

4 Enviromatics Spatial database systems Spatial data types Traditional database systems do not provide any spatial data types. In addition to the classical data types integer, real, character, string they offer sometimes non-standard types of data such as date and time. An object in a spatial database is defined by several non-spatial attributes and one attribute of some spatial data type. This spatial attribute describes the spatial extent (geometry, shape) of the object. Spatial data management suffers from an impedance mismatch between its theoretical requirements for infinite accuracy and the limited accuracy provided by computers. The fact that computers can not represent real numbers with arbitrary accuracy leads to the implicit implementation of a grid-based data model. A realm is a finite set of points and lines over a discrete grid that fulfils certain conditions. Each realm point has to be a grid point. Each realm line has to be the direct connection between two realm points. Realm lines are not allowed to intersect.

5 Enviromatics Spatial database systems Spatial operators Operators are grouped into different classes, depending on their input-output behaviour. At least one of the operators has to be of a spatial data type. The input behaviour refers to a unary, binary or n-ary operator and the type of its operand. The output behaviour refers to the type of result. 1.Unary operators with a Boolean result. 2.Unary operators with a scalar result. These operators map a spatial object into a real or an integer number. 3.Unary operators with a spatial result. The most important operators are the similarity operators that map a spatial object into a similar object by translation, rotation or scaling. Similarity operators are a subset of the class of topological transformations where the dimension of the input object is always retained.

6 Enviromatics Spatial database systems Spatial operators (2) 4.Other unary operators map a d-dimensional spatial object into an object of lower or higher dimension. The boundary operator maps a d dimensional spatial object into a (d-1)- dimensional object. In opposite of that, an interior operator maps a d-dimensional object into a (d+1)- dimensional object. 5.Binary operators with a Boolean result. These operators are known as spatial predicates or spatial relationships. They use two spatial objects as input and produce a Boolean as output. They will be classified by topological relationships, direct relationships and metric relationships.

7 Enviromatics Spatial database systems Cont… Topological relationships are invariant with respect to topological transformations (translation, rotation, scaling). Examples are intersects, contains, adjacents. These operators are known as spatial predicates or spatial relationships. They use two spatial objects as input and produce a Boolean as output. They will be classified by topological relationships, direct relationships and metric relationships or is-enclosed-by. Direct relationships refer to the current location of spatial objects. They are sensitive to rotations. Examples: Northwest of, above, under, near to. Metric relationships are sensitive to topological transformations. Example: Distance < 100 m.

8 Enviromatics Spatial database systems Spatial operators (3) 6.Binary operators with a scalar result. Example: Distance operator. 7.Binary operators with a spatial result. These types of operators cover set operators and search operators. 8.The class of set operators comprises the unification, difference and intersection of two spatial objects. 9.The class of search operators concerns spatial search in a large area of spatial objects.

9 Enviromatics Spatial database systems Computer implementation of spatial operators An efficient computation of spatial operators requires special implementations of spatial data types. Sometimes it is useful to represent the same spatial object in more than one way in order to express a broad variety of spatial operators. Examples: 1.A polygon may be represented by a vertex list containing all the polygon’s vertices (e. g. coordinates of triangle). The vertex list supports similarity operators. 2.A scaling corresponds to a scalar multiplication (B = r ⋅ C). 3.A rotation corresponds to a matrix multiplication.

10 Enviromatics Spatial database systems Computer implementation of spatial operators (2) Also, a spatial query language has to be used. 1.Standard SQL (structured query language) is used for querying and retrieval of non-spatial data. 2.Certain extensions to SQL are used for querying and retrieval of spatial data. 3.Graphical aspects are handled by a special graphical presentation language GPL. 4.Interaction of spatial SQL and GPL offers a wide variety of choices for the graphical rendering of a query result.

11 Enviromatics Spatial database systems Computer implementation of spatial operators (3) Problems of computer implementation come out by the fact that this representation of spatial data is not unique. No DBMS covers all needs. In order to appeal to a broad range of users, DBMS have to be designed independently of any application. With abstract data types the system needs to offer only a small number of basic data types and operators directly. A user may perceive only those basic data types plus the abstract data types that have been declared specifically for a given application. This approach simplifies the use of a database system for inexperienced users and helps to reduce training time.

12 Enviromatics Spatial database systems Questions?