com.vividsolutions.jts.algorithm.ConvexHull Maven / Gradle / Ivy
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/*
* The JTS Topology Suite is a collection of Java classes that
* implement the fundamental operations required to validate a given
* geo-spatial data set to a known topological specification.
*
* Copyright (C) 2001 Vivid Solutions
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* For more information, contact:
*
* Vivid Solutions
* Suite #1A
* 2328 Government Street
* Victoria BC V8T 5G5
* Canada
*
* (250)385-6040
* www.vividsolutions.com
*/
package com.vividsolutions.jts.algorithm;
import com.vividsolutions.jts.geom.*;
import com.vividsolutions.jts.util.Assert;
import java.util.*;
import com.vividsolutions.jts.util.UniqueCoordinateArrayFilter;
/**
* Computes the convex hull of a {@link Geometry}.
* The convex hull is the smallest convex Geometry that contains all the
* points in the input Geometry.
*
* Uses the Graham Scan algorithm.
*
*@version 1.7
*/
public class ConvexHull
{
private GeometryFactory geomFactory;
private Coordinate[] inputPts;
/**
* Create a new convex hull construction for the input {@link Geometry}.
*/
public ConvexHull(Geometry geometry)
{
this(extractCoordinates(geometry), geometry.getFactory());
}
/**
* Create a new convex hull construction for the input {@link Coordinate} array.
*/
public ConvexHull(Coordinate[] pts, GeometryFactory geomFactory)
{
inputPts = pts;
this.geomFactory = geomFactory;
}
private static Coordinate[] extractCoordinates(Geometry geom)
{
UniqueCoordinateArrayFilter filter = new UniqueCoordinateArrayFilter();
geom.apply(filter);
return filter.getCoordinates();
}
/**
* Returns a {@link Geometry} that represents the convex hull of the input
* geometry.
* The returned geometry contains the minimal number of points needed to
* represent the convex hull. In particular, no more than two consecutive
* points will be collinear.
*
* @return if the convex hull contains 3 or more points, a {@link Polygon};
* 2 points, a {@link LineString};
* 1 point, a {@link Point};
* 0 points, an empty {@link GeometryCollection}.
*/
public Geometry getConvexHull() {
if (inputPts.length == 0) {
return geomFactory.createGeometryCollection(null);
}
if (inputPts.length == 1) {
return geomFactory.createPoint(inputPts[0]);
}
if (inputPts.length == 2) {
return geomFactory.createLineString(inputPts);
}
Coordinate[] reducedPts = inputPts;
// use heuristic to reduce points, if large
if (inputPts.length > 50) {
reducedPts = reduce(inputPts);
}
// sort points for Graham scan.
Coordinate[] sortedPts = preSort(reducedPts);
// Use Graham scan to find convex hull.
Stack cHS = grahamScan(sortedPts);
// Convert stack to an array.
Coordinate[] cH = toCoordinateArray(cHS);
// Convert array to appropriate output geometry.
return lineOrPolygon(cH);
}
/**
* An alternative to Stack.toArray, which is not present in earlier versions
* of Java.
*/
protected Coordinate[] toCoordinateArray(Stack stack) {
Coordinate[] coordinates = new Coordinate[stack.size()];
for (int i = 0; i < stack.size(); i++) {
Coordinate coordinate = (Coordinate) stack.get(i);
coordinates[i] = coordinate;
}
return coordinates;
}
/**
* Uses a heuristic to reduce the number of points scanned
* to compute the hull.
* The heuristic is to find a polygon guaranteed to
* be in (or on) the hull, and eliminate all points inside it.
* A quadrilateral defined by the extremal points
* in the four orthogonal directions
* can be used, but even more inclusive is
* to use an octilateral defined by the points in the 8 cardinal directions.
*
* Note that even if the method used to determine the polygon vertices
* is not 100% robust, this does not affect the robustness of the convex hull.
*
* To satisfy the requirements of the Graham Scan algorithm,
* the returned array has at least 3 entries.
*
* @param pts the points to reduce
* @return the reduced list of points (at least 3)
*/
private Coordinate[] reduce(Coordinate[] inputPts)
{
//Coordinate[] polyPts = computeQuad(inputPts);
Coordinate[] polyPts = computeOctRing(inputPts);
//Coordinate[] polyPts = null;
// unable to compute interior polygon for some reason
if (polyPts == null)
return inputPts;
// LinearRing ring = geomFactory.createLinearRing(polyPts);
// System.out.println(ring);
// add points defining polygon
TreeSet reducedSet = new TreeSet();
for (int i = 0; i < polyPts.length; i++) {
reducedSet.add(polyPts[i]);
}
/**
* Add all unique points not in the interior poly.
* CGAlgorithms.isPointInRing is not defined for points actually on the ring,
* but this doesn't matter since the points of the interior polygon
* are forced to be in the reduced set.
*/
for (int i = 0; i < inputPts.length; i++) {
if (! CGAlgorithms.isPointInRing(inputPts[i], polyPts)) {
reducedSet.add(inputPts[i]);
}
}
Coordinate[] reducedPts = CoordinateArrays.toCoordinateArray(reducedSet);
// ensure that computed array has at least 3 points (not necessarily unique)
if (reducedPts.length < 3)
return padArray3(reducedPts);
return reducedPts;
}
private Coordinate[] padArray3(Coordinate[] pts)
{
Coordinate[] pad = new Coordinate[3];
for (int i = 0; i < pad.length; i++) {
if (i < pts.length) {
pad[i] = pts[i];
}
else
pad[i] = pts[0];
}
return pad;
}
private Coordinate[] preSort(Coordinate[] pts) {
Coordinate t;
// find the lowest point in the set. If two or more points have
// the same minimum y coordinate choose the one with the minimu x.
// This focal point is put in array location pts[0].
for (int i = 1; i < pts.length; i++) {
if ((pts[i].y < pts[0].y) || ((pts[i].y == pts[0].y) && (pts[i].x < pts[0].x))) {
t = pts[0];
pts[0] = pts[i];
pts[i] = t;
}
}
// sort the points radially around the focal point.
Arrays.sort(pts, 1, pts.length, new RadialComparator(pts[0]));
//radialSort(pts);
return pts;
}
/**
* Uses the Graham Scan algorithm to compute the convex hull vertices.
*
* @param c a list of points, with at least 3 entries
* @return a Stack containing the ordered points of the convex hull ring
*/
private Stack grahamScan(Coordinate[] c) {
Coordinate p;
Stack ps = new Stack();
p = (Coordinate) ps.push(c[0]);
p = (Coordinate) ps.push(c[1]);
p = (Coordinate) ps.push(c[2]);
for (int i = 3; i < c.length; i++) {
p = (Coordinate) ps.pop();
while (CGAlgorithms.computeOrientation((Coordinate) ps.peek(), p, c[i]) > 0) {
p = (Coordinate) ps.pop();
}
p = (Coordinate) ps.push(p);
p = (Coordinate) ps.push(c[i]);
}
p = (Coordinate) ps.push(c[0]);
return ps;
}
/**
*@return whether the three coordinates are collinear and c2 lies between
* c1 and c3 inclusive
*/
private boolean isBetween(Coordinate c1, Coordinate c2, Coordinate c3) {
if (CGAlgorithms.computeOrientation(c1, c2, c3) != 0) {
return false;
}
if (c1.x != c3.x) {
if (c1.x <= c2.x && c2.x <= c3.x) {
return true;
}
if (c3.x <= c2.x && c2.x <= c1.x) {
return true;
}
}
if (c1.y != c3.y) {
if (c1.y <= c2.y && c2.y <= c3.y) {
return true;
}
if (c3.y <= c2.y && c2.y <= c1.y) {
return true;
}
}
return false;
}
private Coordinate[] computeOctRing(Coordinate[] inputPts) {
Coordinate[] octPts = computeOctPts(inputPts);
CoordinateList coordList = new CoordinateList();
coordList.add(octPts, false);
// points must all lie in a line
if (coordList.size() < 3) {
return null;
}
coordList.closeRing();
return coordList.toCoordinateArray();
}
private Coordinate[] computeOctPts(Coordinate[] inputPts)
{
Coordinate[] pts = new Coordinate[8];
for (int j = 0; j < pts.length; j++) {
pts[j] = inputPts[0];
}
for (int i = 1; i < inputPts.length; i++) {
if (inputPts[i].x < pts[0].x) {
pts[0] = inputPts[i];
}
if (inputPts[i].x - inputPts[i].y < pts[1].x - pts[1].y) {
pts[1] = inputPts[i];
}
if (inputPts[i].y > pts[2].y) {
pts[2] = inputPts[i];
}
if (inputPts[i].x + inputPts[i].y > pts[3].x + pts[3].y) {
pts[3] = inputPts[i];
}
if (inputPts[i].x > pts[4].x) {
pts[4] = inputPts[i];
}
if (inputPts[i].x - inputPts[i].y > pts[5].x - pts[5].y) {
pts[5] = inputPts[i];
}
if (inputPts[i].y < pts[6].y) {
pts[6] = inputPts[i];
}
if (inputPts[i].x + inputPts[i].y < pts[7].x + pts[7].y) {
pts[7] = inputPts[i];
}
}
return pts;
}
/*
// MD - no longer used, but keep for reference purposes
private Coordinate[] computeQuad(Coordinate[] inputPts) {
BigQuad bigQuad = bigQuad(inputPts);
// Build a linear ring defining a big poly.
ArrayList bigPoly = new ArrayList();
bigPoly.add(bigQuad.westmost);
if (! bigPoly.contains(bigQuad.northmost)) {
bigPoly.add(bigQuad.northmost);
}
if (! bigPoly.contains(bigQuad.eastmost)) {
bigPoly.add(bigQuad.eastmost);
}
if (! bigPoly.contains(bigQuad.southmost)) {
bigPoly.add(bigQuad.southmost);
}
// points must all lie in a line
if (bigPoly.size() < 3) {
return null;
}
// closing point
bigPoly.add(bigQuad.westmost);
Coordinate[] bigPolyArray = CoordinateArrays.toCoordinateArray(bigPoly);
return bigPolyArray;
}
private BigQuad bigQuad(Coordinate[] pts) {
BigQuad bigQuad = new BigQuad();
bigQuad.northmost = pts[0];
bigQuad.southmost = pts[0];
bigQuad.westmost = pts[0];
bigQuad.eastmost = pts[0];
for (int i = 1; i < pts.length; i++) {
if (pts[i].x < bigQuad.westmost.x) {
bigQuad.westmost = pts[i];
}
if (pts[i].x > bigQuad.eastmost.x) {
bigQuad.eastmost = pts[i];
}
if (pts[i].y < bigQuad.southmost.y) {
bigQuad.southmost = pts[i];
}
if (pts[i].y > bigQuad.northmost.y) {
bigQuad.northmost = pts[i];
}
}
return bigQuad;
}
private static class BigQuad {
public Coordinate northmost;
public Coordinate southmost;
public Coordinate westmost;
public Coordinate eastmost;
}
*/
/**
*@param vertices the vertices of a linear ring, which may or may not be
* flattened (i.e. vertices collinear)
*@return a 2-vertex LineString if the vertices are
* collinear; otherwise, a Polygon with unnecessary
* (collinear) vertices removed
*/
private Geometry lineOrPolygon(Coordinate[] coordinates) {
coordinates = cleanRing(coordinates);
if (coordinates.length == 3) {
return geomFactory.createLineString(new Coordinate[]{coordinates[0], coordinates[1]});
// return new LineString(new Coordinate[]{coordinates[0], coordinates[1]},
// geometry.getPrecisionModel(), geometry.getSRID());
}
LinearRing linearRing = geomFactory.createLinearRing(coordinates);
return geomFactory.createPolygon(linearRing, null);
}
/**
*@param vertices the vertices of a linear ring, which may or may not be
* flattened (i.e. vertices collinear)
*@return the coordinates with unnecessary (collinear) vertices
* removed
*/
private Coordinate[] cleanRing(Coordinate[] original) {
Assert.equals(original[0], original[original.length - 1]);
ArrayList cleanedRing = new ArrayList();
Coordinate previousDistinctCoordinate = null;
for (int i = 0; i <= original.length - 2; i++) {
Coordinate currentCoordinate = original[i];
Coordinate nextCoordinate = original[i+1];
if (currentCoordinate.equals(nextCoordinate)) {
continue;
}
if (previousDistinctCoordinate != null
&& isBetween(previousDistinctCoordinate, currentCoordinate, nextCoordinate)) {
continue;
}
cleanedRing.add(currentCoordinate);
previousDistinctCoordinate = currentCoordinate;
}
cleanedRing.add(original[original.length - 1]);
Coordinate[] cleanedRingCoordinates = new Coordinate[cleanedRing.size()];
return (Coordinate[]) cleanedRing.toArray(cleanedRingCoordinates);
}
/**
* Compares {@link Coordinate}s for their angle and distance
* relative to an origin.
*
* @author Martin Davis
* @version 1.7
*/
private static class RadialComparator
implements Comparator
{
private Coordinate origin;
public RadialComparator(Coordinate origin)
{
this.origin = origin;
}
public int compare(Object o1, Object o2)
{
Coordinate p1 = (Coordinate) o1;
Coordinate p2 = (Coordinate) o2;
return polarCompare(origin, p1, p2);
}
/**
* Given two points p and q compare them with respect to their radial
* ordering about point o. First checks radial ordering.
* If points are collinear, the comparison is based
* on their distance to the origin.
*
* p < q iff
*
* - ang(o-p) < ang(o-q) (e.g. o-p-q is CCW)
*
- or ang(o-p) == ang(o-q) && dist(o,p) < dist(o,q)
*
*
* @param o the origin
* @param p a point
* @param q another point
* @return -1, 0 or 1 depending on whether p is less than,
* equal to or greater than q
*/
private static int polarCompare(Coordinate o, Coordinate p, Coordinate q)
{
double dxp = p.x - o.x;
double dyp = p.y - o.y;
double dxq = q.x - o.x;
double dyq = q.y - o.y;
/*
// MD - non-robust
int result = 0;
double alph = Math.atan2(dxp, dyp);
double beta = Math.atan2(dxq, dyq);
if (alph < beta) {
result = -1;
}
if (alph > beta) {
result = 1;
}
if (result != 0) return result;
//*/
int orient = CGAlgorithms.computeOrientation(o, p, q);
if (orient == CGAlgorithms.COUNTERCLOCKWISE) return 1;
if (orient == CGAlgorithms.CLOCKWISE) return -1;
// points are collinear - check distance
double op = dxp * dxp + dyp * dyp;
double oq = dxq * dxq + dyq * dyq;
if (op < oq) {
return -1;
}
if (op > oq) {
return 1;
}
return 0;
}
}
}