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Java example source code file (MonotoneChain.java)

This example Java source code file (MonotoneChain.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

abstractconvexhullgenerator2d, arraylist, collection, comparator, line, list, monotonechain, override, util, vector2d

The MonotoneChain.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,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.geometry.euclidean.twod.hull;

import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;

import org.apache.commons.math3.geometry.euclidean.twod.Line;
import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;

/**
 * Implements Andrew's monotone chain method to generate the convex hull of a finite set of
 * points in the two-dimensional euclidean space.
 * <p>
 * The runtime complexity is O(n log n), with n being the number of input points. If the
 * point set is already sorted (by x-coordinate), the runtime complexity is O(n).
 * <p>
 * The implementation is not sensitive to collinear points on the hull. The parameter
 * {@code includeCollinearPoints} allows to control the behavior with regard to collinear points.
 * If {@code true}, all points on the boundary of the hull will be added to the hull vertices,
 * otherwise only the extreme points will be present. By default, collinear points are not added
 * as hull vertices.
 * <p>
 * The {@code tolerance} parameter (default: 1e-10) is used as epsilon criteria to determine
 * identical and collinear points.
 *
 * @see <a href="http://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain">
 * Andrew's monotone chain algorithm (Wikibooks)</a>
 * @since 3.3
 */
public class MonotoneChain extends AbstractConvexHullGenerator2D {

    /**
     * Create a new MonotoneChain instance.
     */
    public MonotoneChain() {
        this(false);
    }

    /**
     * Create a new MonotoneChain instance.
     * @param includeCollinearPoints whether collinear points shall be added as hull vertices
     */
    public MonotoneChain(final boolean includeCollinearPoints) {
        super(includeCollinearPoints);
    }

    /**
     * Create a new MonotoneChain instance.
     * @param includeCollinearPoints whether collinear points shall be added as hull vertices
     * @param tolerance tolerance below which points are considered identical
     */
    public MonotoneChain(final boolean includeCollinearPoints, final double tolerance) {
        super(includeCollinearPoints, tolerance);
    }

    /** {@inheritDoc} */
    @Override
    public Collection<Vector2D> findHullVertices(final Collection points) {

        final List<Vector2D> pointsSortedByXAxis = new ArrayList(points);

        // sort the points in increasing order on the x-axis
        Collections.sort(pointsSortedByXAxis, new Comparator<Vector2D>() {
            /** {@inheritDoc} */
            public int compare(final Vector2D o1, final Vector2D o2) {
                final double tolerance = getTolerance();
                // need to take the tolerance value into account, otherwise collinear points
                // will not be handled correctly when building the upper/lower hull
                final int diff = Precision.compareTo(o1.getX(), o2.getX(), tolerance);
                if (diff == 0) {
                    return Precision.compareTo(o1.getY(), o2.getY(), tolerance);
                } else {
                    return diff;
                }
            }
        });

        // build lower hull
        final List<Vector2D> lowerHull = new ArrayList();
        for (Vector2D p : pointsSortedByXAxis) {
            updateHull(p, lowerHull);
        }

        // build upper hull
        final List<Vector2D> upperHull = new ArrayList();
        for (int idx = pointsSortedByXAxis.size() - 1; idx >= 0; idx--) {
            final Vector2D p = pointsSortedByXAxis.get(idx);
            updateHull(p, upperHull);
        }

        // concatenate the lower and upper hulls
        // the last point of each list is omitted as it is repeated at the beginning of the other list
        final List<Vector2D> hullVertices = new ArrayList(lowerHull.size() + upperHull.size() - 2);
        for (int idx = 0; idx < lowerHull.size() - 1; idx++) {
            hullVertices.add(lowerHull.get(idx));
        }
        for (int idx = 0; idx < upperHull.size() - 1; idx++) {
            hullVertices.add(upperHull.get(idx));
        }

        // special case: if the lower and upper hull may contain only 1 point if all are identical
        if (hullVertices.isEmpty() && ! lowerHull.isEmpty()) {
            hullVertices.add(lowerHull.get(0));
        }

        return hullVertices;
    }

    /**
     * Update the partial hull with the current point.
     *
     * @param point the current point
     * @param hull the partial hull
     */
    private void updateHull(final Vector2D point, final List<Vector2D> hull) {
        final double tolerance = getTolerance();

        if (hull.size() == 1) {
            // ensure that we do not add an identical point
            final Vector2D p1 = hull.get(0);
            if (p1.distance(point) < tolerance) {
                return;
            }
        }

        while (hull.size() >= 2) {
            final int size = hull.size();
            final Vector2D p1 = hull.get(size - 2);
            final Vector2D p2 = hull.get(size - 1);

            final double offset = new Line(p1, p2, tolerance).getOffset(point);
            if (FastMath.abs(offset) < tolerance) {
                // the point is collinear to the line (p1, p2)

                final double distanceToCurrent = p1.distance(point);
                if (distanceToCurrent < tolerance || p2.distance(point) < tolerance) {
                    // the point is assumed to be identical to either p1 or p2
                    return;
                }

                final double distanceToLast = p1.distance(p2);
                if (isIncludeCollinearPoints()) {
                    final int index = distanceToCurrent < distanceToLast ? size - 1 : size;
                    hull.add(index, point);
                } else {
                    if (distanceToCurrent > distanceToLast) {
                        hull.remove(size - 1);
                        hull.add(point);
                    }
                }
                return;
            } else if (offset > 0) {
                hull.remove(size - 1);
            } else {
                break;
            }
        }
        hull.add(point);
    }

}

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