Definition of Constructive Geometric Functions

OGC 11-017 18 Copyright © 2007-2011 Open Geospatial Consortium

8.2 Definition of Geometric Functions

8.2.1 Definition of Constructive Geometric Functions

Bufferg:Geometry, d:Double : Bag This function SHALL take two arguments of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and “http:www.w3.org2001XMLSchemadouble. This function SHALL return a bag of geometry values representing the buffer of geometry g at distance d. The buffer of a geometry at distance d is the Polygon or MultiPolygon which contains all points within a distance d of the geometry. The unit of measure for the argument d SHALL be metre. Boundaryg:Geometry : Bag This function SHALL take one argument of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and return a Bag of geometries. This function SHALL return a bag of geometry values representing the combinatorial boundary of geometry g. ConvexHullg:Geometry : Geometry This function SHALL take one argument of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and return a value of the same data type. This function SHALL return a geometric object that represents the convex hull of geometry g. The convex hull is the smallest convex polygon that contains all points of the geometry. The convex Hull for a geometry of encoding data type Point is the point itself. Centroidg:Geometry : Geometry This function SHALL take one argument of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and return a value of the same data type. This function SHALL return the point that is the geometric centre of gravity of the geometry g. Differenceg1:Geometry, g2:Geometry : Bag This function SHALL take two arguments of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and return a Bag of geometries. This function SHALL return a bag of geometry values representing the closure of the set difference between the two geometries g1 and g2. The difference is the set of all points which lie on g1 but not on g2. SymDifferenceg1:Geometry, g2:Geometry : Bag This function SHALL take two arguments of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and return a Bag of geometries. OGC 11-017 Copyright © 2007-2011 Open Geospatial Consortium 19 This function SHALL return a bag of geometry values representing the closure of the symmetric difference of two Geometries. The symmetric difference is the set of points which lie on either g1 or g2 but not in both. Intersectiong1:Geometry, g2:Geometry : Bag This function SHALL take two arguments of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and return a Bag of geometries. This function SHALL return a bag of geometry values representing the Point set intersection of geometry g1 and geometry g2. Uniong1:Geometry, g2:Geometry : Bag This function SHALL take two arguments of data type “urn:ogc:def:dataType:geoxacml:1.0:geometry” and return a Bag of geometries. This function SHALL return a bag of geometry values representing a Point set union of geometry g1 with geometry g2.

8.2.2 Definition of Scalar Geometric Functions