A class that contains the QuadEdges representing a planar subdivision that models a triangulation. The subdivision is constructed using the quadedge algebra defined in the class 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.

Authors:: David Skea; Martin Davis

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 - env the bounding box to surround; tolerance - tolerance the tolerance value for determining if two sites are equal

public static void getTriangleEdges(QuadEdge startQE, QuadEdge[] triEdge)

Gets the edges for the triangle to the left of the given QuadEdge.

Parameters:: startQE - startQE; triEdge - triEdge

Throws:: IllegalArgumentException - IllegalArgumentException if the edges do not form a triangle

public double getTolerance()

Gets the vertex-equality tolerance value used in this subdivision

Returns:: the tolerance value

public Envelope getEnvelope()

Gets the envelope of the Subdivision (including the frame).

Returns:: the envelope

public Collection getEdges()

Gets the collection of base QuadEdges (one for every pair of vertices which is connected).

Returns:: a collection of QuadEdges

public void setLocator(QuadEdgeLocator locator)

Sets the QuadEdgeLocator to use for locating containing triangles in this subdivision.

Parameters:: locator - locator a QuadEdgeLocator

public QuadEdge makeEdge(Vertex o, Vertex d)

Creates a new quadedge, recording it in the edges list.

Parameters:: o - o; d - d

Returns:: a new quadedge

public 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. The quadedge is recorded in the edges list.

Parameters:: a - a; b - b

Returns:: a quadedge

public void delete(QuadEdge e)

Deletes a quadedge from the subdivision. Linked quadedges are updated to reflect the deletion.

Parameters:: e - e the quadedge to delete

public QuadEdge locateFromEdge(Vertex v, QuadEdge startEdge)

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 - v the location to search for; startEdge - startEdge an edge of the subdivision to start searching at

Returns:: a QuadEdge which contains v, or is on the edge of a triangle containing v

Throws:: LocateFailureException - LocateFailureException if the location algorithm fails to converge in a reasonable number of iterations

public QuadEdge locate(Vertex v)

Finds a quadedge of a triangle containing a location specified by a Vertex, if one exists.

Parameters:: v - v the vertex to locate

Returns:: a quadedge on the edge of a triangle which touches or contains the location or null if no such triangle exists

public QuadEdge locate(Coordinate p)

Finds a quadedge of a triangle containing a location specified by a Coordinate, if one exists.

Parameters:: p - p the Coordinate to locate

Returns:: a quadedge on the edge of a triangle which touches or contains the location or null if no such triangle exists

public QuadEdge locate(Coordinate p0, Coordinate p1)

Locates the edge between the given vertices, if it exists in the subdivision.

Parameters:: p0 - p0 a coordinate; p1 - p1 another coordinate

Returns:: the edge joining the coordinates, if present or null if no such edge exists

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 - v the vertex to insert

Returns:: a new quad edge terminating in v

public boolean isFrameEdge(QuadEdge e)

Tests whether a QuadEdge is an edge incident on a frame triangle vertex.

Parameters:: e - e the edge to test

Returns:: true if the edge is connected to the frame triangle

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 - e the edge to test

Returns:: true if the edge is on the border of the frame

public boolean isFrameVertex(Vertex v)

Tests whether a vertex is a vertex of the outer triangle.

Parameters:: v - v the vertex to test

Returns:: true if the vertex is an outer triangle vertex

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 - e a QuadEdge; p - p a point

Returns:: true if the vertex lies on the edge

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 - e; v - v

Returns:: true if the vertex is a endpoint of the edge

public Collection getVertices(boolean includeFrame)

Gets the unique Vertexes in the subdivision, including the frame vertices if desired.

Parameters:: includeFrame - includeFrame true if the frame vertices should be included

See also:: #getVertexUniqueEdges

Returns:: a collection of the subdivision vertices

public List getVertexUniqueEdges(boolean includeFrame)

Gets a collection of QuadEdges 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 getVertices and then locating quadedges attached to them.

Parameters:: includeFrame - includeFrame true if the frame vertices should be included

Returns:: a collection of QuadEdge with the vertices of the subdivision as their origins

public 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 - includeFrame true if the frame edges are to be included

Returns:: a List of QuadEdges

public void visitTriangles(TriangleVisitor triVisitor, boolean includeFrame)

************************************************************************** Visitors **************************************************************************

public 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 - includeFrame true if the frame triangles should be included

Returns:: a List of QuadEdge[3] arrays

public List getTriangleVertices(boolean includeFrame)

Gets a list of the triangles in the subdivision, specified as an array of the triangle Vertexes.

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

Returns:: a List of Vertex[3] arrays

public List getTriangleCoordinates(boolean includeFrame)

Gets the coordinates for each triangle in the subdivision as an array.

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

Returns:: a list of Coordinate[4] representing each triangle

public Geometry getEdges(GeometryFactory geomFact)

Gets the geometry for the edges in the subdivision as a MultiLineString containing 2-point lines.

Parameters:: geomFact - geomFact the GeometryFactory to use

Returns:: a MultiLineString

public Geometry getTriangles(GeometryFactory geomFact)

Gets the geometry for the triangles in a triangulated subdivision as a GeometryCollection of triangular Polygons.

Parameters:: geomFact - geomFact the GeometryFactory to use

Returns:: a GeometryCollection of triangular Polygons

public Geometry getVoronoiDiagram(GeometryFactory geomFact)

Gets the cells in the Voronoi diagram for this triangulation. The cells are returned as a GeometryCollection of Polygons

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

Parameters:: geomFact - geomFact a geometry factory

Returns:: a GeometryCollection of Polygons

public List getVoronoiCellPolygons(GeometryFactory geomFact)

Gets a List of Polygons for the Voronoi cells of this triangulation.

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

Parameters:: geomFact - geomFact a geometry factory

Returns:: a List of Polygons

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 Coordinate of the site. This allows attaching external data associated with the site to this cell polygon.

Parameters:: qe - qe a quadedge originating at the cell site; geomFact - geomFact a factory for building the polygon

Returns:: a polygon indicating the cell extent