Centroid.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.algorithm;
import org.locationtech.jts.geom.Coordinate;
import org.locationtech.jts.geom.Geometry;
import org.locationtech.jts.geom.GeometryCollection;
import org.locationtech.jts.geom.LineString;
import org.locationtech.jts.geom.Point;
import org.locationtech.jts.geom.Polygon;
/**
* Computes the centroid of a {@link Geometry} of any dimension.
* For collections the centroid is computed for the collection of
* non-empty elements of highest dimension.
* The centroid of an empty geometry is {@code null}.
*
* <h3>Algorithm</h3>
*
* <ul>
* <li><b>Dimension 2</b> - the centroid is computed
* as the weighted sum of the centroids
* of a decomposition of the area into (possibly overlapping) triangles.
* Holes and multipolygons are handled correctly.
* See http://www.faqs.org/faqs/graphics/algorithms-faq/
* for further details of the basic approach.
*
* <li><b>Dimension 1</b> - Computes the average of the midpoints
* of all line segments weighted by the segment length.
* Zero-length lines are treated as points.
*
* <li><b>Dimension 0</b> - Compute the average coordinate over all points.
* Repeated points are all included in the average.
* </ul>
*
* @see InteriorPoint
* @see org.locationtech.jts.algorithm.construct.MaximumInscribedCircle
* @see org.locationtech.jts.algorithm.construct.LargestEmptyCircle
*
* @version 1.7
*/
public class Centroid
{
/**
* Computes the centroid point of a geometry.
*
* @param geom the geometry to use
* @return the centroid point, or null if the geometry is empty
*/
public static Coordinate getCentroid(Geometry geom)
{
Centroid cent = new Centroid(geom);
return cent.getCentroid();
}
private Coordinate areaBasePt = null;// the point all triangles are based at
private Coordinate triangleCent3 = new Coordinate();// temporary variable to hold centroid of triangle
private double areasum2 = 0; /* Partial area sum */
private Coordinate cg3 = new Coordinate(); // partial centroid sum
// data for linear centroid computation, if needed
private Coordinate lineCentSum = new Coordinate();
private double totalLength = 0.0;
private int ptCount = 0;
private Coordinate ptCentSum = new Coordinate();
/**
* Creates a new instance for computing the centroid of a geometry
*/
public Centroid(Geometry geom)
{
areaBasePt = null;
add(geom);
}
/**
* Adds a Geometry to the centroid total.
*
* @param geom the geometry to add
*/
private void add(Geometry geom)
{
if (geom.isEmpty())
return;
if (geom instanceof Point) {
addPoint(geom.getCoordinate());
}
else if (geom instanceof LineString) {
addLineSegments(geom.getCoordinates());
}
else if (geom instanceof Polygon) {
Polygon poly = (Polygon) geom;
add(poly);
}
else if (geom instanceof GeometryCollection) {
GeometryCollection gc = (GeometryCollection) geom;
for (int i = 0; i < gc.getNumGeometries(); i++) {
add(gc.getGeometryN(i));
}
}
}
/**
* Gets the computed centroid.
*
* @return the computed centroid, or null if the input is empty
*/
public Coordinate getCentroid()
{
/*
* The centroid is computed from the highest dimension components present in the input.
* I.e. areas dominate lineal geometry, which dominates points.
* Degenerate geometry are computed using their effective dimension
* (e.g. areas may degenerate to lines or points)
*/
Coordinate cent = new Coordinate();
if (Math.abs(areasum2) > 0.0) {
/*
* Input contains areal geometry
*/
cent.x = cg3.x / 3 / areasum2;
cent.y = cg3.y / 3 / areasum2;
}
else if (totalLength > 0.0) {
/*
* Input contains lineal geometry
*/
cent.x = lineCentSum.x / totalLength;
cent.y = lineCentSum.y / totalLength;
}
else if (ptCount > 0){
/*
* Input contains puntal geometry only
*/
cent.x = ptCentSum.x / ptCount;
cent.y = ptCentSum.y / ptCount;
}
else {
return null;
}
return cent;
}
private void setAreaBasePoint(Coordinate basePt)
{
this.areaBasePt = basePt;
}
private void add(Polygon poly)
{
addShell(poly.getExteriorRing().getCoordinates());
for (int i = 0; i < poly.getNumInteriorRing(); i++) {
addHole(poly.getInteriorRingN(i).getCoordinates());
}
}
private void addShell(Coordinate[] pts)
{
if (pts.length > 0)
setAreaBasePoint(pts[0]);
boolean isPositiveArea = ! Orientation.isCCW(pts);
for (int i = 0; i < pts.length - 1; i++) {
addTriangle(areaBasePt, pts[i], pts[i+1], isPositiveArea);
}
addLineSegments(pts);
}
private void addHole(Coordinate[] pts)
{
boolean isPositiveArea = Orientation.isCCW(pts);
for (int i = 0; i < pts.length - 1; i++) {
addTriangle(areaBasePt, pts[i], pts[i+1], isPositiveArea);
}
addLineSegments(pts);
}
private void addTriangle(Coordinate p0, Coordinate p1, Coordinate p2, boolean isPositiveArea)
{
double sign = (isPositiveArea) ? 1.0 : -1.0;
centroid3( p0, p1, p2, triangleCent3 );
double area2 = area2( p0, p1, p2 );
cg3.x += sign * area2 * triangleCent3.x;
cg3.y += sign * area2 * triangleCent3.y;
areasum2 += sign * area2;
}
/**
* Computes three times the centroid of the triangle p1-p2-p3.
* The factor of 3 is
* left in to permit division to be avoided until later.
*/
private static void centroid3( Coordinate p1, Coordinate p2, Coordinate p3, Coordinate c )
{
c.x = p1.x + p2.x + p3.x;
c.y = p1.y + p2.y + p3.y;
return;
}
/**
* Returns twice the signed area of the triangle p1-p2-p3.
* The area is positive if the triangle is oriented CCW, and negative if CW.
*/
private static double area2( Coordinate p1, Coordinate p2, Coordinate p3 )
{
return
(p2.x - p1.x) * (p3.y - p1.y) -
(p3.x - p1.x) * (p2.y - p1.y);
}
/**
* Adds the line segments defined by an array of coordinates
* to the linear centroid accumulators.
*
* @param pts an array of {@link Coordinate}s
*/
private void addLineSegments(Coordinate[] pts)
{
double lineLen = 0.0;
for (int i = 0; i < pts.length - 1; i++) {
double segmentLen = pts[i].distance(pts[i + 1]);
if (segmentLen == 0.0)
continue;
lineLen += segmentLen;
double midx = (pts[i].x + pts[i + 1].x) / 2;
lineCentSum.x += segmentLen * midx;
double midy = (pts[i].y + pts[i + 1].y) / 2;
lineCentSum.y += segmentLen * midy;
}
totalLength += lineLen;
if (lineLen == 0.0 && pts.length > 0)
addPoint(pts[0]);
}
/**
* Adds a point to the point centroid accumulator.
* @param pt a {@link Coordinate}
*/
private void addPoint(Coordinate pt)
{
ptCount += 1;
ptCentSum.x += pt.x;
ptCentSum.y += pt.y;
}
}