Represents a directed component of an edge in an EdgeGraph. HalfEdges link vertices whose locations are defined by Coordinates. HalfEdges start at an origin vertex, and terminate at a destination vertex. HalfEdges always occur in symmetric pairs, with the sym() method giving access to the oppositely-oriented component. HalfEdges and the methods on them form an edge algebra, which can be used to traverse and query the topology of the graph formed by the edges.

To support graphs where the edges are sequences of coordinates each edge may also have a direction point supplied. This is used to determine the ordering of the edges around the origin. HalfEdges with the same origin are ordered so that the ring of edges formed by them is oriented CCW.

By design HalfEdges carry minimal information about the actual usage of the graph they represent. They can be subclassed to carry more information if required.

HalfEdges form a complete and consistent data structure by themselves, but an EdgeGraph is useful to allow retrieving edges by vertex and edge location, as well as ensuring edges are created and linked appropriately.

Authors:: Martin Davis

public HalfEdge(Coordinate orig)

Creates a half-edge originating from a given coordinate.

Parameters:: orig - orig the origin coordinate

public static HalfEdge create(Coordinate p0, Coordinate p1)

Creates a HalfEdge pair representing an edge between two vertices located at coordinates p0 and p1.

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

Returns:: the HalfEdge with origin at p0

public void link(HalfEdge sym)

Links this edge with its sym (opposite) edge. This must be done for each pair of edges created.

Parameters:: e - e the sym edge to link.

public Coordinate orig()

Gets the origin coordinate of this edge.

Returns:: the origin coordinate

public Coordinate dest()

Gets the destination coordinate of this edge.

Returns:: the destination coordinate

protected Coordinate directionPt()

Gets the direction point of this edge. In the base case this is the dest coordinate of the edge. Subclasses may override to allow a HalfEdge to represent an edge with more than two coordinates.

Returns:: the direction point for the edge

public HalfEdge sym()

Gets the symmetric pair edge of this edge.

Returns:: the symmetric pair edge

public HalfEdge next()

Gets the next edge CCW around the destination vertex of this edge, with the dest vertex as its origin. If the vertex has degree 1 then this is the sym edge.

Returns:: the next edge

public HalfEdge prev()

Gets the edge previous to this one (with dest being the same as this orig).

Returns:: the previous edge to this one

public HalfEdge oNext()

Gets the next edge CCW around the origin of this edge, with the same origin.

Returns:: the next edge around the origin

public void setNext(HalfEdge e)

Sets the next edge CCW around the destination vertex of this edge.

Parameters:: e - e the next edge

public HalfEdge find(Coordinate dest)

Finds the edge starting at the origin of this edge with the given dest vertex, if any.

Parameters:: dest - dest the dest vertex to search for

Returns:: the edge with the required dest vertex, if it exists, or null

public boolean equals(Coordinate p0, Coordinate p1)

Tests whether this edge has the given orig and dest vertices.

Parameters:: p0 - p0 the origin vertex to test; p1 - p1 the destination vertex to test

Returns:: true if the vertices are equal to the ones of this edge

public void insert(HalfEdge eAdd)

Inserts an edge into the ring of edges around the origin vertex of this edge, ensuring that the edges remain ordered CCW. The inserted edge must have the same origin as this edge.

Parameters:: eAdd - eAdd the edge to insert

public boolean isEdgesSorted()

Tests whether the edges around the origin are sorted correctly. Note that edges must be strictly increasing, which implies no two edges can have the same direction point.

Returns:: true if the origin edges are sorted correctly

public int compareTo(Object obj)

Compares edges which originate at the same vertex based on the angle they make at their origin vertex with the positive X-axis. This allows sorting edges around their origin vertex in CCW order.

public int compareAngularDirection(HalfEdge e)

Implements the total order relation:

The angle of edge a is greater than the angle of edge b, where the angle of an edge is the angle made by the first segment of the edge with the positive x-axis

When applied to a list of edges originating at the same point, this produces a CCW ordering of the edges around the point.

Using the obvious algorithm of computing the angle is not robust, since the angle calculation is susceptible to roundoff error. A robust algorithm is:

First, compare the quadrants the edge vectors lie in. If the quadrants are different, it is trivial to determine which edge has a greater angle.
if the vectors lie in the same quadrant, the Orientation.index(Coordinate, Coordinate, Coordinate) function can be used to determine the relative orientation of the vectors.

public String toString()

Computes a string representation of a HalfEdge.

Returns:: a string representation

public String toStringNode()

public int degree()

Computes the degree of the origin vertex. The degree is the number of edges originating from the vertex.

Returns:: the degree of the origin vertex

public HalfEdge prevNode()

Finds the first node previous to this edge, if any. If no such node exists (i.e. the edge is part of a ring) then null is returned.

Returns:: an edge originating at the node prior to this edge, if any, or null if no node exists