Geometrys.
The relate algorithm computes the IntersectionMatrix describing the
relationship of two Geometrys. The algorithm for computing relate
uses the intersection operations supported by topology graphs. Although the relate
result depends on the resultant graph formed by the computed intersections, there is
no need to explicitly compute the entire graph.
It is sufficient to compute the local structure of the graph
at each intersection node.
The algorithm to compute relate has the following steps:
IntersectionMatrix from the labels on the nodes and edges.
Geometry which
do not contain any intersections with the other input Geometry. The
topological relationship of these components to the other input Geometry
must be computed in order to determine the complete labeling of the component. This can
be done by testing whether the component lies in the interior or exterior of the other
Geometry. If the other Geometry is 1-dimensional, the isolated
component must lie in the exterior (since otherwise it would have an intersection with an
edge of the Geometry). If the other Geometry is 2-dimensional,
a Point-In-Polygon test can be used to determine whether the isolated component is in the
interior or exterior.