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Java example source code file (WelzlEncloser.java)

This example Java source code file (WelzlEncloser.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arraylist, enclosingball, iterable, list, mathinternalerror, point, space, supportballgenerator, util, welzlencloser

The WelzlEncloser.java Java example source code

 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *      http://www.apache.org/licenses/LICENSE-2.0
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * See the License for the specific language governing permissions and
 * limitations under the License.
package org.apache.commons.math3.geometry.enclosing;

import java.util.ArrayList;
import java.util.List;

import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.Space;

/** Class implementing Emo Welzl algorithm to find the smallest enclosing ball in linear time.
 * <p>
 * The class implements the algorithm described in paper <a
 * href="http://www.inf.ethz.ch/personal/emo/PublFiles/SmallEnclDisk_LNCS555_91.pdf">Smallest
 * Enclosing Disks (Balls and Ellipsoids)</a> by Emo Welzl, Lecture Notes in Computer Science
 * 555 (1991) 359-370. The pivoting improvement published in the paper <a
 * href="http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf">Fast and
 * Robust Smallest Enclosing Balls</a>, by Bernd Gärtner and further modified in
 * paper <a
 * href=http://www.idt.mdh.se/kurser/ct3340/ht12/MINICONFERENCE/FinalPapers/ircse12_submission_30.pdf">
 * Efficient Computation of Smallest Enclosing Balls in Three Dimensions</a> by Linus Källberg
 * to avoid performing local copies of data have been included.
 * </p>
 * @param <S> Space type.
 * @param <P> Point type.
 * @since 3.3
public class WelzlEncloser<S extends Space, P extends Point implements Encloser {

    /** Tolerance below which points are consider to be identical. */
    private final double tolerance;

    /** Generator for balls on support. */
    private final SupportBallGenerator<S, P> generator;

    /** Simple constructor.
     * @param tolerance below which points are consider to be identical
     * @param generator generator for balls on support
    public WelzlEncloser(final double tolerance, final SupportBallGenerator<S, P> generator) {
        this.tolerance = tolerance;
        this.generator = generator;

    /** {@inheritDoc} */
    public EnclosingBall<S, P> enclose(final Iterable

points) { if (points == null || !points.iterator().hasNext()) { // return an empty ball return generator.ballOnSupport(new ArrayList<P>()); } // Emo Welzl algorithm with Bernd Gärtner and Linus Källberg improvements return pivotingBall(points); } /** Compute enclosing ball using Gärtner's pivoting heuristic. * @param points points to be enclosed * @return enclosing ball */ private EnclosingBall<S, P> pivotingBall(final Iterable

points) { final P first = points.iterator().next(); final List<P> extreme = new ArrayList

(first.getSpace().getDimension() + 1); final List<P> support = new ArrayList

(first.getSpace().getDimension() + 1); // start with only first point selected as a candidate support extreme.add(first); EnclosingBall<S, P> ball = moveToFrontBall(extreme, extreme.size(), support); while (true) { // select the point farthest to current ball final P farthest = selectFarthest(points, ball); if (ball.contains(farthest, tolerance)) { // we have found a ball containing all points return ball; } // recurse search, restricted to the small subset containing support and farthest point support.clear(); support.add(farthest); EnclosingBall<S, P> savedBall = ball; ball = moveToFrontBall(extreme, extreme.size(), support); if (ball.getRadius() < savedBall.getRadius()) { // this should never happen throw new MathInternalError(); } // it was an interesting point, move it to the front // according to Gärtner's heuristic extreme.add(0, farthest); // prune the least interesting points extreme.subList(ball.getSupportSize(), extreme.size()).clear(); } } /** Compute enclosing ball using Welzl's move to front heuristic. * @param extreme subset of extreme points * @param nbExtreme number of extreme points to consider * @param support points that must belong to the ball support * @return enclosing ball, for the extreme subset only */ private EnclosingBall<S, P> moveToFrontBall(final List

extreme, final int nbExtreme, final List<P> support) { // create a new ball on the prescribed support EnclosingBall<S, P> ball = generator.ballOnSupport(support); if (ball.getSupportSize() <= ball.getCenter().getSpace().getDimension()) { for (int i = 0; i < nbExtreme; ++i) { final P pi = extreme.get(i); if (!ball.contains(pi, tolerance)) { // we have found an outside point, // enlarge the ball by adding it to the support support.add(pi); ball = moveToFrontBall(extreme, i, support); support.remove(support.size() - 1); // it was an interesting point, move it to the front // according to Welzl's heuristic for (int j = i; j > 0; --j) { extreme.set(j, extreme.get(j - 1)); } extreme.set(0, pi); } } } return ball; } /** Select the point farthest to the current ball. * @param points points to be enclosed * @param ball current ball * @return farthest point */ public P selectFarthest(final Iterable<P> points, final EnclosingBall ball) { final P center = ball.getCenter(); P farthest = null; double dMax = -1.0; for (final P point : points) { final double d = point.distance(center); if (d > dMax) { farthest = point; dMax = d; } } return farthest; } }

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