A class that represents the edge data structure which implements the quadedge algebra. The quadedge algebra was described in a well-known paper by Guibas and Stolfi, "Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams", ACM Transactions on Graphics, 4(2), 1985, 75-123.

Each edge object is part of a quartet of 4 edges, linked via their rot references. Any edge in the group may be accessed using a series of rot() operations. Quadedges in a subdivision are linked together via their next references. The linkage between the quadedge quartets determines the topology of the subdivision.

The edge class does not contain separate information for vertices or faces; a vertex is implicitly defined as a ring of edges (created using the next field).

Authors:: David Skea; Martin Davis

public static QuadEdge makeEdge(Vertex o, Vertex d)

Creates a new QuadEdge quartet from Vertex o to Vertex d.

Parameters:: o - o the origin Vertex; d - d the destination Vertex

Returns:: the new QuadEdge quartet

public static 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. Additionally, the data pointers of the new edge are set.

Returns:: the connected edge.

public static void splice(QuadEdge a, QuadEdge b)

Splices two edges together or apart. Splice affects the two edge rings around the origins of a and b, and, independently, the two edge rings around the left faces of a and b. In each case, (i) if the two rings are distinct, Splice will combine them into one, or (ii) if the two are the same ring, Splice will break it into two separate pieces. Thus, Splice can be used both to attach the two edges together, and to break them apart.

Parameters:: a - a an edge to splice; b - b an edge to splice

public static void swap(QuadEdge e)

Turns an edge counterclockwise inside its enclosing quadrilateral.

Parameters:: e - e the quadedge to turn

public QuadEdge getPrimary()

Gets the primary edge of this quadedge and its sym. The primary edge is the one for which the origin and destination coordinates are ordered according to the standard Coordinate ordering

Returns:: the primary quadedge

public void setData(Object data)

Sets the external data value for this edge.

Parameters:: data - data an object containing external data

public Object getData()

Gets the external data value for this edge.

Returns:: the data object

public void delete()

Marks this quadedge as being deleted. This does not free the memory used by this quadedge quartet, but indicates that this edge no longer participates in a subdivision.

public boolean isLive()

Tests whether this edge has been deleted.

Returns:: true if this edge has not been deleted.

public void setNext(QuadEdge next)

Sets the connected edge

Parameters:: next - next edge

public final QuadEdge rot()

Gets the dual of this edge, directed from its right to its left.

Returns:: the rotated edge

public final QuadEdge invRot()

Gets the dual of this edge, directed from its left to its right.

Returns:: the inverse rotated edge.

public final QuadEdge sym()

Gets the edge from the destination to the origin of this edge.

Returns:: the sym of the edge

public final QuadEdge oNext()

Gets the next CCW edge around the origin of this edge.

Returns:: the next linked edge.

public final QuadEdge oPrev()

Gets the next CW edge around (from) the origin of this edge.

Returns:: the previous edge.

public final QuadEdge dNext()

Gets the next CCW edge around (into) the destination of this edge.

Returns:: the next destination edge.

public final QuadEdge dPrev()

Gets the next CW edge around (into) the destination of this edge.

Returns:: the previous destination edge.

public final QuadEdge lNext()

Gets the CCW edge around the left face following this edge.

Returns:: the next left face edge.

public final QuadEdge lPrev()

Gets the CCW edge around the left face before this edge.

Returns:: the previous left face edge.

public final QuadEdge rNext()

Gets the edge around the right face ccw following this edge.

Returns:: the next right face edge.

public final QuadEdge rPrev()

Gets the edge around the right face ccw before this edge.

Returns:: the previous right face edge.

public final Vertex orig()

Gets the vertex for the edge's origin

Returns:: the origin vertex

public final Vertex dest()

Gets the vertex for the edge's destination

Returns:: the destination vertex

public double getLength()

Gets the length of the geometry of this quadedge.

Returns:: the length of the quadedge

public boolean equalsNonOriented(QuadEdge qe)

Tests if this quadedge and another have the same line segment geometry, regardless of orientation.

Parameters:: qe - qe a quadedge

Returns:: true if the quadedges are based on the same line segment regardless of orientation

public boolean equalsOriented(QuadEdge qe)

Tests if this quadedge and another have the same line segment geometry with the same orientation.

Parameters:: qe - qe a quadedge

Returns:: true if the quadedges are based on the same line segment

public LineSegment toLineSegment()

Creates a LineSegment representing the geometry of this edge.

Returns:: a LineSegment

public String toString()

Converts this edge to a WKT two-point LINESTRING indicating the geometry of this edge.

Returns:: a String representing this edge's geometry