JTS Topology Suite version 1.12

```java.lang.Object
```

`public class QuadEdgeSubdivisionextends java.lang.Object`

A class that contains the `QuadEdge`s representing a planar subdivision that models a triangulation. The subdivision is constructed using the quadedge algebra defined in the classs `QuadEdge`. All metric calculations are done in the `Vertex` class. In addition to a triangulation, subdivisions support extraction of Voronoi diagrams. This is easily accomplished, since the Voronoi diagram is the dual of the Delaunay triangulation.

Subdivisions can be provided with a tolerance value. Inserted vertices which are closer than this value to vertices already in the subdivision will be ignored. Using a suitable tolerance value can prevent robustness failures from happening during Delaunay triangulation.

Subdivisions maintain a frame triangle around the client-created edges. The frame is used to provide a bounded "container" for all edges within a TIN. Normally the frame edges, frame connecting edges, and frame triangles are not included in client processing.

Author:
David Skea, Martin Davis

Constructor Summary
```QuadEdgeSubdivision(Envelope env, double tolerance)```
Creates a new instance of a quad-edge subdivision based on a frame triangle that encloses a supplied bounding box.

Method Summary
` QuadEdge` ```connect(QuadEdge a, QuadEdge b)```
Creates a new QuadEdge connecting the destination of a to the origin of b, in such a way that all three have the same left face after the connection is complete.
` void` `delete(QuadEdge e)`
Deletes a quadedge from the subdivision.
` java.util.Collection` `getEdges()`
Gets the collection of base `QuadEdge`s (one for every pair of vertices which is connected).
` Geometry` `getEdges(GeometryFactory geomFact)`
Gets the geometry for the edges in the subdivision as a `MultiLineString` containing 2-point lines.
` Envelope` `getEnvelope()`
Gets the envelope of the Subdivision (including the frame).
` java.util.List` `getPrimaryEdges(boolean includeFrame)`
Gets all primary quadedges in the subdivision.
` double` `getTolerance()`
Gets the vertex-equality tolerance value used in this subdivision
` java.util.List` `getTriangleCoordinates(boolean includeFrame)`
Gets the coordinates for each triangle in the subdivision as an array.
` java.util.List` `getTriangleEdges(boolean includeFrame)`
Gets a list of the triangles in the subdivision, specified as an array of the primary quadedges around the triangle.
`static void` ```getTriangleEdges(QuadEdge startQE, QuadEdge[] triEdge)```
Gets the edges for the triangle to the left of the given `QuadEdge`.
` Geometry` `getTriangles(GeometryFactory geomFact)`
Gets the geometry for the triangles in a triangulated subdivision as a `GeometryCollection` of triangular `Polygon`s.
` java.util.List` `getTriangleVertices(boolean includeFrame)`
Gets a list of the triangles in the subdivision, specified as an array of the triangle `Vertex`es.
` java.util.List` `getVertexUniqueEdges(boolean includeFrame)`
Gets a collection of `QuadEdge`s whose origin vertices are a unique set which includes all vertices in the subdivision.
` java.util.Collection` `getVertices(boolean includeFrame)`
Gets the unique `Vertex`es in the subdivision, including the frame vertices if desired.
` Polygon` ```getVoronoiCellPolygon(QuadEdge qe, GeometryFactory geomFact)```
Gets the Voronoi cell around a site specified by the origin of a QuadEdge.
` java.util.List` `getVoronoiCellPolygons(GeometryFactory geomFact)`
Gets a List of `Polygon`s for the Voronoi cells of this triangulation.
` Geometry` `getVoronoiDiagram(GeometryFactory geomFact)`
Gets the cells in the Voronoi diagram for this triangulation.
` QuadEdge` `insertSite(Vertex v)`
Inserts a new site into the Subdivision, connecting it to the vertices of the containing triangle (or quadrilateral, if the split point falls on an existing edge).
` boolean` `isFrameBorderEdge(QuadEdge e)`
Tests whether a QuadEdge is an edge on the border of the frame facets and the internal facets.
` boolean` `isFrameEdge(QuadEdge e)`
Tests whether a QuadEdge is an edge incident on a frame triangle vertex.
` boolean` `isFrameVertex(Vertex v)`
Tests whether a vertex is a vertex of the outer triangle.
` boolean` ```isOnEdge(QuadEdge e, Coordinate p)```
Tests whether a `Coordinate` lies on a `QuadEdge`, up to a tolerance determined by the subdivision tolerance.
` boolean` ```isVertexOfEdge(QuadEdge e, Vertex v)```
Tests whether a `Vertex` is the start or end vertex of a `QuadEdge`, up to the subdivision tolerance distance.
` QuadEdge` `locate(Coordinate p)`
Finds a quadedge of a triangle containing a location specified by a `Coordinate`, if one exists.
` QuadEdge` ```locate(Coordinate p0, Coordinate p1)```
Locates the edge between the given vertices, if it exists in the subdivision.
` QuadEdge` `locate(Vertex v)`
Finds a quadedge of a triangle containing a location specified by a `Vertex`, if one exists.
` QuadEdge` ```locateFromEdge(Vertex v, QuadEdge startEdge)```
Locates an edge of a triangle which contains a location specified by a Vertex v.
` QuadEdge` ```makeEdge(Vertex o, Vertex d)```
Creates a new quadedge, recording it in the edges list.
` void` `setLocator(QuadEdgeLocator locator)`
Sets the `QuadEdgeLocator` to use for locating containing triangles in this subdivision.
` void` ```visitTriangles(TriangleVisitor triVisitor, boolean includeFrame)```
Visitors

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

```public QuadEdgeSubdivision(Envelope env,
double tolerance)```
Creates a new instance of a quad-edge subdivision based on a frame triangle that encloses a supplied bounding box. A new super-bounding box that contains the triangle is computed and stored.

Parameters:
`env` - the bouding box to surround
`tolerance` - the tolerance value for determining if two sites are equal
Method Detail

### getTriangleEdges

```public static void getTriangleEdges(QuadEdge startQE,
Gets the edges for the triangle to the left of the given `QuadEdge`.

Parameters:
`startQE` -
`triEdge` -
Throws:
`java.lang.IllegalArgumentException` - if the edges do not form a triangle

### getTolerance

`public double getTolerance()`
Gets the vertex-equality tolerance value used in this subdivision

Returns:
the tolerance value

### getEnvelope

`public Envelope getEnvelope()`
Gets the envelope of the Subdivision (including the frame).

Returns:
the envelope

### getEdges

`public java.util.Collection getEdges()`
Gets the collection of base `QuadEdge`s (one for every pair of vertices which is connected).

Returns:

### setLocator

`public void setLocator(QuadEdgeLocator locator)`
Sets the `QuadEdgeLocator` to use for locating containing triangles in this subdivision.

Parameters:
`locator` - a QuadEdgeLocator

### makeEdge

```public QuadEdge makeEdge(Vertex o,
Vertex d)```
Creates a new quadedge, recording it in the edges list.

Parameters:
`o` -
`d` -
Returns:

### connect

```public QuadEdge connect(QuadEdge a,
Creates a new QuadEdge connecting the destination of a to the origin of b, in such a way that all three have the same left face after the connection is complete. The quadedge is recorded in the edges list.

Parameters:
`a` -
`b` -
Returns:

### delete

`public void delete(QuadEdge e)`

Parameters:
`e` - the quadedge to delete

### locateFromEdge

```public QuadEdge locateFromEdge(Vertex v,
Locates an edge of a triangle which contains a location specified by a Vertex v. The edge returned has the property that either v is on e, or e is an edge of a triangle containing v. The search starts from startEdge amd proceeds on the general direction of v.

This locate algorithm relies on the subdivision being Delaunay. For non-Delaunay subdivisions, this may loop for ever.

Parameters:
`v` - the location to search for
`startEdge` - an edge of the subdivision to start searching at
Throws:
`LocateFailureException` - if the location algorithm fails to converge in a reasonable number of iterations

### locate

`public QuadEdge locate(Vertex v)`
Finds a quadedge of a triangle containing a location specified by a `Vertex`, if one exists.

Parameters:
`x` - the vertex to locate
Returns:
a quadedge on the edge of a triangle which touches or contains the location

### locate

`public QuadEdge locate(Coordinate p)`
Finds a quadedge of a triangle containing a location specified by a `Coordinate`, if one exists.

Parameters:
`p` - the Coordinate to locate
Returns:
a quadedge on the edge of a triangle which touches or contains the location

### locate

```public QuadEdge locate(Coordinate p0,
Coordinate p1)```
Locates the edge between the given vertices, if it exists in the subdivision.

Parameters:
`p0` - a coordinate
`p1` - another coordinate
Returns:
the edge joining the coordinates, if present

### insertSite

`public QuadEdge insertSite(Vertex v)`
Inserts a new site into the Subdivision, connecting it to the vertices of the containing triangle (or quadrilateral, if the split point falls on an existing edge).

This method does NOT maintain the Delaunay condition. If desired, this must be checked and enforced by the caller.

This method does NOT check if the inserted vertex falls on an edge. This must be checked by the caller, since this situation may cause erroneous triangulation

Parameters:
`v` - the vertex to insert
Returns:
a new quad edge terminating in v

### isFrameEdge

`public boolean isFrameEdge(QuadEdge e)`
Tests whether a QuadEdge is an edge incident on a frame triangle vertex.

Parameters:
`e` - the edge to test
Returns:
true if the edge is connected to the frame triangle

### isFrameBorderEdge

`public boolean isFrameBorderEdge(QuadEdge e)`
Tests whether a QuadEdge is an edge on the border of the frame facets and the internal facets. E.g. an edge which does not itself touch a frame vertex, but which touches an edge which does.

Parameters:
`e` - the edge to test
Returns:
true if the edge is on the border of the frame

### isFrameVertex

`public boolean isFrameVertex(Vertex v)`
Tests whether a vertex is a vertex of the outer triangle.

Parameters:
`v` - the vertex to test
Returns:
true if the vertex is an outer triangle vertex

### isOnEdge

```public boolean isOnEdge(QuadEdge e,
Coordinate p)```
Tests whether a `Coordinate` lies on a `QuadEdge`, up to a tolerance determined by the subdivision tolerance.

Parameters:
`e` - a QuadEdge
`p` - a point
Returns:
true if the vertex lies on the edge

### isVertexOfEdge

```public boolean isVertexOfEdge(QuadEdge e,
Vertex v)```
Tests whether a `Vertex` is the start or end vertex of a `QuadEdge`, up to the subdivision tolerance distance.

Parameters:
`e` -
`v` -
Returns:
true if the vertex is a endpoint of the edge

### getVertices

`public java.util.Collection getVertices(boolean includeFrame)`
Gets the unique `Vertex`es in the subdivision, including the frame vertices if desired.

Parameters:
`includeFrame` - true if the frame vertices should be included
Returns:
a collection of the subdivision vertices
`getVertexUniqueEdges(boolean)`

### getVertexUniqueEdges

`public java.util.List getVertexUniqueEdges(boolean includeFrame)`
Gets a collection of `QuadEdge`s whose origin vertices are a unique set which includes all vertices in the subdivision. The frame vertices can be included if required.

This is useful for algorithms which require traversing the subdivision starting at all vertices. Returning a quadedge for each vertex is more efficient than the alternative of finding the actual vertices using {@link #getVertices) and then locating quadedges attached to them.

Parameters:
`includeFrame` - true if the frame vertices should be included
Returns:
a collection of QuadEdge with the vertices of the subdivision as their origins

### getPrimaryEdges

`public java.util.List getPrimaryEdges(boolean includeFrame)`
Gets all primary quadedges in the subdivision. A primary edge is a `QuadEdge` which occupies the 0'th position in its array of associated quadedges. These provide the unique geometric edges of the triangulation.

Parameters:
`includeFrame` - true if the frame edges are to be included
Returns:

### visitTriangles

```public void visitTriangles(TriangleVisitor triVisitor,
boolean includeFrame)```
Visitors

### getTriangleEdges

`public java.util.List getTriangleEdges(boolean includeFrame)`
Gets a list of the triangles in the subdivision, specified as an array of the primary quadedges around the triangle.

Parameters:
`includeFrame` - true if the frame triangles should be included
Returns:

### getTriangleVertices

`public java.util.List getTriangleVertices(boolean includeFrame)`
Gets a list of the triangles in the subdivision, specified as an array of the triangle `Vertex`es.

Parameters:
`includeFrame` - true if the frame triangles should be included
Returns:
a List of Vertex[3] arrays

### getTriangleCoordinates

`public java.util.List getTriangleCoordinates(boolean includeFrame)`
Gets the coordinates for each triangle in the subdivision as an array.

Parameters:
`includeFrame` - true if the frame triangles should be included
Returns:
a list of Coordinate[4] representing each triangle

### getEdges

`public Geometry getEdges(GeometryFactory geomFact)`
Gets the geometry for the edges in the subdivision as a `MultiLineString` containing 2-point lines.

Parameters:
`geomFact` - the GeometryFactory to use
Returns:
a MultiLineString

### getTriangles

`public Geometry getTriangles(GeometryFactory geomFact)`
Gets the geometry for the triangles in a triangulated subdivision as a `GeometryCollection` of triangular `Polygon`s.

Parameters:
`geomFact` - the GeometryFactory to use
Returns:
a GeometryCollection of triangular Polygons

### getVoronoiDiagram

`public Geometry getVoronoiDiagram(GeometryFactory geomFact)`
Gets the cells in the Voronoi diagram for this triangulation. The cells are returned as a `GeometryCollection` of `Polygon`s

The userData of each polygon is set to be the {@link Coordinate) of the cell site. This allows easily associating external data associated with the sites to the cells.

Parameters:
`geomFact` - a geometry factory
Returns:
a GeometryCollection of Polygons

### getVoronoiCellPolygons

`public java.util.List getVoronoiCellPolygons(GeometryFactory geomFact)`
Gets a List of `Polygon`s for the Voronoi cells of this triangulation.

The userData of each polygon is set to be the {@link Coordinate) of the cell site. This allows easily associating external data associated with the sites to the cells.

Parameters:
`geomFact` - a geometry factory
Returns:
a List of Polygons

### getVoronoiCellPolygon

```public Polygon getVoronoiCellPolygon(QuadEdge qe,
GeometryFactory geomFact)```
Gets the Voronoi cell around a site specified by the origin of a QuadEdge.

The userData of the polygon is set to be the {@link Coordinate) of the site. This allows attaching external data associated with the site to this cell polygon.

Parameters:
`qe` - a quadedge originating at the cell site
`geomFact` - a factory for building the polygon
Returns:
a polygon indicating the cell extent

JTS Topology Suite version 1.12