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Java example source code file (AklToussaintHeuristic.java)

This example Java source code file (AklToussaintHeuristic.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.

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Java - Java tags/keywords

akltoussaintheuristic, arraylist, collection, list, util, vector2d

The AklToussaintHeuristic.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.euclidean.twod.hull;

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

import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;

 * A simple heuristic to improve the performance of convex hull algorithms.
 * <p>
 * The heuristic is based on the idea of a convex quadrilateral, which is formed by
 * four points with the lowest and highest x / y coordinates. Any point that lies inside
 * this quadrilateral can not be part of the convex hull and can thus be safely discarded
 * before generating the convex hull itself.
 * <p>
 * The complexity of the operation is O(n), and may greatly improve the time it takes to
 * construct the convex hull afterwards, depending on the point distribution.
 * @see <a href="http://en.wikipedia.org/wiki/Convex_hull_algorithms#Akl-Toussaint_heuristic">
 * Akl-Toussaint heuristic (Wikipedia)</a>
 * @since 3.3
public final class AklToussaintHeuristic {

    /** Hide utility constructor. */
    private AklToussaintHeuristic() {

     * Returns a point set that is reduced by all points for which it is safe to assume
     * that they are not part of the convex hull.
     * @param points the original point set
     * @return a reduced point set, useful as input for convex hull algorithms
    public static Collection<Vector2D> reducePoints(final Collection points) {

        // find the leftmost point
        int size = 0;
        Vector2D minX = null;
        Vector2D maxX = null;
        Vector2D minY = null;
        Vector2D maxY = null;
        for (Vector2D p : points) {
            if (minX == null || p.getX() < minX.getX()) {
                minX = p;
            if (maxX == null || p.getX() > maxX.getX()) {
                maxX = p;
            if (minY == null || p.getY() < minY.getY()) {
                minY = p;
            if (maxY == null || p.getY() > maxY.getY()) {
                maxY = p;

        if (size < 4) {
            return points;

        final List<Vector2D> quadrilateral = buildQuadrilateral(minY, maxX, maxY, minX);
        // if the quadrilateral is not well formed, e.g. only 2 points, do not attempt to reduce
        if (quadrilateral.size() < 3) {
            return points;

        final List<Vector2D> reducedPoints = new ArrayList(quadrilateral);
        for (final Vector2D p : points) {
            // check all points if they are within the quadrilateral
            // in which case they can not be part of the convex hull
            if (!insideQuadrilateral(p, quadrilateral)) {

        return reducedPoints;

     * Build the convex quadrilateral with the found corner points (with min/max x/y coordinates).
     * @param points the respective points with min/max x/y coordinate
     * @return the quadrilateral
    private static List<Vector2D> buildQuadrilateral(final Vector2D... points) {
        List<Vector2D> quadrilateral = new ArrayList();
        for (Vector2D p : points) {
            if (!quadrilateral.contains(p)) {
        return quadrilateral;

     * Checks if the given point is located within the convex quadrilateral.
     * @param point the point to check
     * @param quadrilateralPoints the convex quadrilateral, represented by 4 points
     * @return {@code true} if the point is inside the quadrilateral, {@code false} otherwise
    private static boolean insideQuadrilateral(final Vector2D point,
                                               final List<Vector2D> quadrilateralPoints) {

        Vector2D p1 = quadrilateralPoints.get(0);
        Vector2D p2 = quadrilateralPoints.get(1);

        if (point.equals(p1) || point.equals(p2)) {
            return true;

        // get the location of the point relative to the first two vertices
        final double last = point.crossProduct(p1, p2);
        final int size = quadrilateralPoints.size();
        // loop through the rest of the vertices
        for (int i = 1; i < size; i++) {
            p1 = p2;
            p2 = quadrilateralPoints.get((i + 1) == size ? 0 : i + 1);

            if (point.equals(p1) || point.equals(p2)) {
                return true;

            // do side of line test: multiply the last location with this location
            // if they are the same sign then the operation will yield a positive result
            // -x * -y = +xy, x * y = +xy, -x * y = -xy, x * -y = -xy
            if (last * point.crossProduct(p1, p2) < 0) {
                return false;
        return true;


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