# geos::operation::relate Namespace Reference

Contains classes to implement the computation of the spatial relationships of `Geometry`s. More...

## Classes

class | EdgeEndBuilder
| Computes the geomgraph::EdgeEnd objects which arise from a noded geomgraph::Edge. More...
class | EdgeEndBundle
| A collection of geomgraph::EdgeEnd objects which originate at the same point and have the same direction. More...
class | EdgeEndBundleStar
| An ordered list of EdgeEndBundle objects around a RelateNode. More...
class | RelateComputer
| Computes the topological relationship between two Geometries. More...
class | RelateNode
| Represents a node in the topological graph used to compute spatial relationships. More...
class | RelateNodeFactory
| Used by the geomgraph::NodeMap in a RelateNodeGraph to create RelateNode objects. More...
class | RelateNodeGraph
| Implements the simple graph of Nodes and geomgraph::EdgeEnd which is all that is required to determine topological relationships between Geometries. More...
class | RelateOp
| Implements the SFS `relate()` operation on two geom::Geometry objects. More...

## Detailed Description

Contains classes to implement the computation of the spatial relationships of `Geometry`s.

The `relate` algorithm computes the `IntersectionMatrix` describing the relationship of two `Geometry`s. 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:

- Build topology graphs of the two input geometries. For each geometry all self-intersection nodes are computed and added to the graph.
- Compute nodes for all intersections between edges and nodes of the graphs.
- Compute the labeling for the computed nodes by merging the labels from the input graphs.
- Compute the labeling for isolated components of the graph (see below)
- Compute the `IntersectionMatrix` from the labels on the nodes and edges.

### Labeling isolated components

Isolated components are components (edges or nodes) of an input `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.

## Package Specification

- Java Topology Suite Technical Specifications
- OpenGIS Simple Features Specification for SQL