A conforming Delaunay triangulation is a true Delaunay triangulation. In it each constraint segment is present as a union of one or more triangulation edges. Constraint segments may be subdivided into two or more triangulation edges by the insertion of additional sites. The additional sites are called Steiner points, and are necessary to allow the segments to be faithfully reflected in the triangulation while maintaining the Delaunay property. Another way of stating this is that in a conforming Delaunay triangulation every constraint segment will be the union of a subset of the triangulation edges (up to tolerance).

A Conforming Delaunay triangulation is distinct from a Constrained Delaunay triangulation. A Constrained Delaunay triangulation is not necessarily fully Delaunay, and it contains the constraint segments exactly as edges of the triangulation.

A typical usage pattern for the triangulator is:

  	 ConformingDelaunayTriangulator cdt = new ConformingDelaunayTriangulator(sites, tolerance);

    // optional
    cdt.setSplitPointFinder(splitPointFinder);
    cdt.setVertexFactory(vertexFactory);

 	 cdt.setConstraints(segments, new ArrayList(vertexMap.values()));
 	 cdt.formInitialDelaunay();
 	 cdt.enforceConstraints();
 	 subdiv = cdt.getSubdivision();

Authors:: David Skea; Martin Davis

public ConformingDelaunayTriangulator(Collection initialVertices, double tolerance)

Creates a Conforming Delaunay Triangulation based on the given unconstrained initial vertices. The initial vertex set should not contain any vertices which appear in the constraint set.

Parameters:: initialVertices - initialVertices a collection of ConstraintVertex; tolerance - tolerance the distance tolerance below which points are considered identical

public void setConstraints(List segments, List segVertices)

Sets the constraints to be conformed to by the computed triangulation. The constraints must not contain duplicate segments (up to orientation). The unique set of vertices (as ConstraintVertexes) forming the constraints must also be supplied. Supplying it explicitly allows the ConstraintVertexes to be initialized appropriately (e.g. with external data), and avoids re-computing the unique set if it is already available.

Parameters:: segments - segments a list of the constraint Segments; segVertices - segVertices the set of unique ConstraintVertexes referenced by the segments

public void setSplitPointFinder(ConstraintSplitPointFinder splitFinder)

Sets the ConstraintSplitPointFinder to be used during constraint enforcement. Different splitting strategies may be appropriate for special situations.

Parameters:: splitFinder - splitFinder the ConstraintSplitPointFinder to be used

public double getTolerance()

Gets the tolerance value used to construct the triangulation.

Returns:: a tolerance value

public ConstraintVertexFactory getVertexFactory()

Gets the ConstraintVertexFactory used to create new constraint vertices at split points.

Returns:: a new constraint vertex

public void setVertexFactory(ConstraintVertexFactory vertexFactory)

Sets a custom ConstraintVertexFactory to be used to allow vertices carrying extra information to be created.

Parameters:: vertexFactory - vertexFactory the ConstraintVertexFactory to be used

public QuadEdgeSubdivision getSubdivision()

Gets the QuadEdgeSubdivision which represents the triangulation.

Returns:: a subdivision

public KdTree getKDT()

Gets the KdTree which contains the vertices of the triangulation.

Returns:: a KdTree

public List getInitialVertices()

Gets the sites (vertices) used to initialize the triangulation.

Returns:: a List of Vertex

public Collection getConstraintSegments()

Gets the Segments which represent the constraints.

Returns:: a collection of Segments

public Geometry getConvexHull()

Gets the convex hull of all the sites in the triangulation, including constraint vertices. Only valid after the constraints have been enforced.

Returns:: the convex hull of the sites

public void insertSite(Coordinate p)

Inserts a site into the triangulation, maintaining the conformal Delaunay property. This can be used to further refine the triangulation if required (e.g. to approximate the medial axis of the constraints, or to improve the grading of the triangulation).

Parameters:: p - p the location of the site to insert

public void formInitialDelaunay()

Computes the Delaunay triangulation of the initial sites.

public void enforceConstraints()

Enforces the supplied constraints into the triangulation.

Throws:: ConstraintEnforcementException - ConstraintEnforcementException if the constraints cannot be enforced