Definition of Topological Functions

OGC 11-017 Copyright © 2007-2011 Open Geospatial Consortium 17

8.1 Definition of Topological Functions

All functions defined in this section SHALL take two arguments of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and return a value of data type “http:www.w3.org2001XMLSchemaboolean”. In the following definitions, a geometry is treated as a representation of a possibly infinite set of points. The representations obviously are not infinite, but use a variety of interpolation algorithms. Containsg1:Geometry, g2:Geometry : Boolean This function SHALL return a TRUE value if and only if the geometry g2 lies in the closure boundary union interior of geometry g1 – the inverse of Withing1: Geometry, g2: Geometry. Crossesg1:Geometry, g2:Geometry : Boolean This function SHALL return a TRUE value if and only if the geometries g1 and g2 share some but neither is contained in the other, and the dimension of the intersection is less than that of both of the geometries. Disjointg1:Geometry, g2:Geometry : Boolean This function SHALL return a TRUE value if and only if the geometries g1 and g2 have no point in common. Equalsg1:Geometry, g2:Geometry : Boolean This function SHALL return a TRUE value if and only if the geometries g1 and g2 are equal geometrically contain exactly the same points. Intersectsg1:Geometry, g2:Geometry : Boolean This function SHALL return a TRUE value if and only if the geometries g1 and g2 have at least one point in common the inverse of Disjoint. Overlapsg1:Geometry, g2:Geometry : Boolean This function SHALL return a TRUE value if and only if the geometries g1 and g2 share some but not all points in common, and the intersection has the same dimension as the geometries themselves. Touchesg1:Geometry, g2:Geometry : Boolean This function SHALL return a TRUE value if and only if the geometries g1 and g2 have at least one boundary point in common, but no interior points. Withing1:Geometry, g2:Geometry : Boolean This function SHALL return a TRUE value if and only if the geometry g1 is spatially within geometry g2; that is if every point on g1 is also on g2. OGC 11-017 18 Copyright © 2007-2011 Open Geospatial Consortium

8.2 Definition of Geometric Functions