NoSQL Geographic Databases: An Overview - Geographical Information Systems: Trends and Technologies - page 78

(1D, 2D, 3D). Finally, we would like to fi nd out the internal data model
used by the analyzed NoSQL system, whether it is based on graph,
document, key-value, or column;
ii. Indexing : indexing techniques are known to speed up query processing.
It has been argued in the literature that traditional indexing techniques,
such as B-Tree, B+-Tree, and hashing, are not suitable for multidimensional
spatial data. Therefore, special indexing techniques for spatial data
have been proposed such as R-tree, R*-tree, quadtree, and gridfi les. It is
important to know how spatial indexing is performed in such NoSQL
spatial systems;
iii. Vector Data types : the Open Geospatial Consortium (OGC) 7 has
proposed a standard for vector data types, known as OpenGIS
Implementation Standard for Geographic Information—Simple
Feature Access for 2D. This standard addresses the data types and the
corresponding spatial functions.
In that OGC standard, the Geometry class has several functions as
presented in Fig. 1, e.g., dimension, equals, and distance. In order to
simplify our comparison, we have separated the spatial functions into
three categories: topological, analysis, and set;
iv. Topological functions: topological functions are invariant concerning
scale, rotation, and zooming. In our reference model we are interested
in the following topological functions:

• equals(theGeom): returns TRUE if the given geometry (theGeom)
represents the same geometry; and FALSE, otherwise;

• disjoint(theGeom): returns TRUE if there is no intersection between the
geometries, i.e., the geometries do not share any common space;

• intersects(theGeom): returns TRUE if the geometries spatially
intersect; and FALSE, otherwise;

• touches(theGeom): returns TRUE if the geometry boundaries intersect,
but their interiors do not intersect; and FALSE, otherwise;

• crosses(theGeom): returns TRUE if the geometry interiors intersect
but are not equal; and FALSE, otherwise;

• within(theGeom): returns TRUE if the geometry theGeom is
completely inside the other geometry; and FALSE, otherwise;

• contains(theGeom): returns TRUE if no points of theGeom lie in the
exterior of the other geometry, and at least one point of the interior
of theGeom lies in the interior of the other geometry; and FALSE,
otherwise;

• overlaps(theGeom): returns TRUE if the geometries share space, are
of the same dimension, but are not completely contained by each
other; and FALSE, otherwise.

OGC, http://www.opengeosatial.org/

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