IncrementalDelaunayTriangulator.java
/*
* Copyright (c) 2016 Vivid Solutions.
*
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License 2.0
* and Eclipse Distribution License v. 1.0 which accompanies this distribution.
* The Eclipse Public License is available at http://www.eclipse.org/legal/epl-v20.html
* and the Eclipse Distribution License is available at
*
* http://www.eclipse.org/org/documents/edl-v10.php.
*/
package org.locationtech.jts.triangulate;
import java.util.Collection;
import java.util.Iterator;
import org.locationtech.jts.algorithm.Orientation;
import org.locationtech.jts.geom.Coordinate;
import org.locationtech.jts.triangulate.quadedge.LocateFailureException;
import org.locationtech.jts.triangulate.quadedge.QuadEdge;
import org.locationtech.jts.triangulate.quadedge.QuadEdgeSubdivision;
import org.locationtech.jts.triangulate.quadedge.Vertex;
/**
* Computes a Delaunay Triangulation of a set of {@link Vertex}es, using an
* incremental insertion algorithm.
*
* @author Martin Davis
* @version 1.0
*/
public class IncrementalDelaunayTriangulator
{
private QuadEdgeSubdivision subdiv;
private boolean isUsingTolerance = false;
private boolean isForceConvex = true;
/**
* Creates a new triangulator using the given {@link QuadEdgeSubdivision}.
* The triangulator uses the tolerance of the supplied subdivision.
*
* @param subdiv
* a subdivision in which to build the TIN
*/
public IncrementalDelaunayTriangulator(QuadEdgeSubdivision subdiv) {
this.subdiv = subdiv;
isUsingTolerance = subdiv.getTolerance() > 0.0;
}
/**
* Sets whether the triangulation is forced to have a convex boundary. Because
* of the use of a finite-size frame, this condition requires special logic to
* enforce. The default is true, since this is a requirement for some uses of
* Delaunay Triangulations (such as Concave Hull generation). However, forcing
* the triangulation boundary to be convex may cause the overall frame
* triangulation to be non-Delaunay. This can cause a problem for Voronoi
* generation, so the logic can be disabled via this method.
*
* @param isForceConvex true if the triangulation boundary is forced to be
* convex
*/
public void forceConvex(boolean isForceConvex) {
this.isForceConvex = isForceConvex;
}
/**
* Inserts all sites in a collection. The inserted vertices <b>MUST</b> be
* unique up to the provided tolerance value. (i.e. no two vertices should be
* closer than the provided tolerance value). They do not have to be rounded
* to the tolerance grid, however.
*
* @param vertices a Collection of Vertex
*
* @throws LocateFailureException if the location algorithm fails to converge in a reasonable number of iterations
*/
public void insertSites(Collection vertices) {
for (Iterator i = vertices.iterator(); i.hasNext();) {
Vertex v = (Vertex) i.next();
insertSite(v);
}
}
/**
* Inserts a new point into a subdivision representing a Delaunay
* triangulation, and fixes the affected edges so that the result is still a
* Delaunay triangulation.
* <p>
*
* @return a quadedge containing the inserted vertex
*/
public QuadEdge insertSite(Vertex v) {
/**
* This code is based on Guibas and Stolfi (1985), with minor modifications
* and a bug fix from Dani Lischinski (Graphic Gems 1993). (The modification
* I believe is the test for the inserted site falling exactly on an
* existing edge. Without this test zero-width triangles have been observed
* to be created)
*/
QuadEdge e = subdiv.locate(v);
if (subdiv.isVertexOfEdge(e, v)) {
// point is already in subdivision.
return e;
}
else if (subdiv.isOnEdge(e, v.getCoordinate())) {
// the point lies exactly on an edge, so delete the edge
// (it will be replaced by a pair of edges which have the point as a vertex)
e = e.oPrev();
subdiv.delete(e.oNext());
}
/**
* Connect the new point to the vertices of the containing triangle
* (or quadrilateral, if the new point fell on an existing edge.)
*/
QuadEdge base = subdiv.makeEdge(e.orig(), v);
QuadEdge.splice(base, e);
QuadEdge startEdge = base;
do {
base = subdiv.connect(e, base.sym());
e = base.oPrev();
} while (e.lNext() != startEdge);
/**
* Examine suspect edges to ensure that the Delaunay condition is satisfied.
* If it is not, flip the edge and continue scanning.
*
* Since the frame is not infinitely far away,
* edges which touch the frame or are adjacent to it require special logic
* to ensure the inner triangulation maintains a convex boundary.
*/
do {
//-- general case - flip if vertex is in circumcircle
QuadEdge t = e.oPrev();
boolean doFlip = t.dest().rightOf(e) && v.isInCircle(e.orig(), t.dest(), e.dest());
if (isForceConvex) {
//-- special cases to ensure triangulation boundary is convex
if (isConcaveBoundary(e)) {
//-- flip if the triangulation boundary is concave
doFlip = true;
}
else if (isBetweenFrameAndInserted(e, v)) {
//-- don't flip if edge lies between the inserted vertex and a frame vertex
doFlip = false;
}
}
if (doFlip) {
//-- flip the edge within its quadrilateral
QuadEdge.swap(e);
e = e.oPrev();
continue;
}
if (e.oNext() == startEdge) {
return base; // no more suspect edges.
}
//-- check next edge
e = e.oNext().lPrev();
} while (true);
}
/**
* Tests if a edge touching a frame vertex
* creates a concavity in the triangulation boundary.
*
* @param e the edge to test
* @return true if the triangulation boundary is concave at the edge
*/
private boolean isConcaveBoundary(QuadEdge e) {
if (subdiv.isFrameVertex(e.dest())) {
return isConcaveAtOrigin(e);
}
if (subdiv.isFrameVertex(e.orig())) {
return isConcaveAtOrigin(e.sym());
}
return false;
}
/**
* Tests if the quadrilateral surrounding an edge is concave at the edge origin.
* Used to determine if the triangulation boundary has a concavity.
* @param e
* @return
*/
private static boolean isConcaveAtOrigin(QuadEdge e) {
Coordinate p = e.orig().getCoordinate();
Coordinate pp = e.oPrev().dest().getCoordinate();
Coordinate pn = e.oNext().dest().getCoordinate();
boolean isConcave = Orientation.COUNTERCLOCKWISE == Orientation.index(pp, pn, p);
return isConcave;
}
/**
* Edges whose adjacent triangles contain
* a frame vertex and the inserted vertex must not be flipped.
*
* @param e the edge to test
* @param vInsert the inserted vertex
* @return true if the edge is between the frame and inserted vertex
*/
private boolean isBetweenFrameAndInserted(QuadEdge e, Vertex vInsert) {
Vertex v1 = e.oNext().dest();
Vertex v2 = e.oPrev().dest();
return (v1 == vInsert && subdiv.isFrameVertex(v2))
|| (v2 == vInsert && subdiv.isFrameVertex(v1));
}
}