Geometric query types for data retrieval in relational databases

Olga Sourina, Seng H. Boey
1998 Data & Knowledge Engineering  
This paper describes the application of geometric concepts for data retrieval and proposes a geometric model for accessing and manipulating multidimensional data in relational databases. A geometric query model is proposed for the queries based on locations of geometric objects. In the geometric query model, the data from the database are interpreted geometrically as multidimensional geometric points or geometric objects interpolated on these points, and the query window is a query solid of any
more » ... shape specified by its location. The spatial queries are formulated with geometric objects and operations over them. Descriptions of geometric objects and operations with implicit functions are proposed. This mathematical representation allowed us to develop a compact and easily extensible geometric query model that has been implemented in the geometric query system prototype. data that actually represent some geometric objects and for any numerical data that one wants to display as a geometric object. 3-D visualization techniques are common for the representation of 3-D or higher dimension geometric objects in databases. In addition, there are other possibilities including visualization of the query formulation in databases. Considerable research has been done in the physical implementation of spatial databases [3, 4, 10, 27] . Abstract modelling and querying of spatial data has received relatively less attention [8] . The need for such a study has become increasingly important because of growing interest in the application of modern visualization techniques in database systems. Generally, spatial database queries can be classified into two types: those based on locations of objects, and those based on objects themselves [37] . In the first class, the queries are: • Location queries, i.e. find all objects that contain a point. • Range queries, i.e. find all objects contained in a query window. • Intersection queries, i.e. find all the data objects that overlap with the query window where the query window is an area specified by its location (i.e. coordinates). In the second class of queries, the aim is to retrieve shapes and images independent of their locations. The types of queries are: • Object match queries, i.e. locate a specific object, or objects, in the database. • Similarity match queries, i.e. find all objects that are similar to a given query object. Our aim is to propose a query model that will provide the user of scientific and engineering databases with geometric query tools. As shown above, the user of scientific and engineering databases often needs to visualize and analyze multidimensional data, to interpolate surfaces or solids on points in the database, and to visualize the query formulation. To satisfy these requirements, we propose geometric concepts for accessing and manipulating multidimensional data in the database. The following steps are carried out to define a geometric query model. First, a relational algebra is taken as a basic model for our consideration, and mapping of relational algebra to geometric algebra is described. This idea of the correspondence of constructive solid geometry, (CSG), to relational algebra was first described in [17, 20] . There, the operations used in relational databases were compared with those used in CSG modelling. Martin et al. [20] examines possible ideas from database modelling which may be of use in solid modelling. Our approach contrasts with the Martin et al. approach. We consider the operations over relations as geometric operations over geometric objects that are n-dimensional points and a query solid. Thus, geometric interpretations for both relations and operations of databases are introduced. After that, the geometric algebra is extended with additional geometric objects and operations to satisfy the requirement of scientific and engineering databases. In this model, we consider geometric query types based on locations of the objects. To implement the geometric query model in the most efficient way, it is important to propose an adequate mathematical model for geometric objects and geometric operations. The formal mathematical specification of the geometric query model is proposed with the implicit function representation of geometric objects. We introduce geometric objects as sets of points {x~,x 2 ..... x,} and multidimensional solids defined by the implicit functions f(x" x 2 ..... x)/> 0. Operations over the objects are implemented as a function superposition so that the resulting object is in turn defined implicitly. This uniform representation for the objects and operations provides a very compact and easily extensible geometric query model that is implemented in the geometric query system GEDA. The geometric query system prototype GEDA is implemented as a set of external attachments, treating the kernel relational database management system as a closed system. We use advanced computer graphics algorithms and visualization techniques to implement the geometric query model.
doi:10.1016/s0169-023x(97)00061-x fatcat:k6mgwmzdkvf2jjjj5vfjm7ujwu