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/* * 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.io.Serializable; import org.apache.commons.math3.exception.InsufficientDataException; import org.apache.commons.math3.exception.MathIllegalArgumentException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.geometry.euclidean.twod.Euclidean2D; import org.apache.commons.math3.geometry.euclidean.twod.Line; import org.apache.commons.math3.geometry.euclidean.twod.Segment; import org.apache.commons.math3.geometry.euclidean.twod.Vector2D; import org.apache.commons.math3.geometry.hull.ConvexHull; import org.apache.commons.math3.geometry.partitioning.Region; import org.apache.commons.math3.geometry.partitioning.RegionFactory; import org.apache.commons.math3.util.MathArrays; import org.apache.commons.math3.util.Precision; /** * This class represents a convex hull in an two-dimensional euclidean space. * * @since 3.3 */ public class ConvexHull2D implements ConvexHull<Euclidean2D, Vector2D>, Serializable { /** Serializable UID. */ private static final long serialVersionUID = 20140129L; /** Vertices of the hull. */ private final Vector2D[] vertices; /** Tolerance threshold used during creation of the hull vertices. */ private final double tolerance; /** * Line segments of the hull. * The array is not serialized and will be created from the vertices on first access. */ private transient Segment[] lineSegments; /** * Simple constructor. * @param vertices the vertices of the convex hull, must be ordered * @param tolerance tolerance below which points are considered identical * @throws MathIllegalArgumentException if the vertices do not form a convex hull */ public ConvexHull2D(final Vector2D[] vertices, final double tolerance) throws MathIllegalArgumentException { // assign tolerance as it will be used by the isConvex method this.tolerance = tolerance; if (!isConvex(vertices)) { throw new MathIllegalArgumentException(LocalizedFormats.NOT_CONVEX); } this.vertices = vertices.clone(); } /** * Checks whether the given hull vertices form a convex hull. * @param hullVertices the hull vertices * @return {@code true} if the vertices form a convex hull, {@code false} otherwise */ private boolean isConvex(final Vector2D[] hullVertices) { if (hullVertices.length < 3) { return true; } int sign = 0; for (int i = 0; i < hullVertices.length; i++) { final Vector2D p1 = hullVertices[i == 0 ? hullVertices.length - 1 : i - 1]; final Vector2D p2 = hullVertices[i]; final Vector2D p3 = hullVertices[i == hullVertices.length - 1 ? 0 : i + 1]; final Vector2D d1 = p2.subtract(p1); final Vector2D d2 = p3.subtract(p2); final double crossProduct = MathArrays.linearCombination(d1.getX(), d2.getY(), -d1.getY(), d2.getX()); final int cmp = Precision.compareTo(crossProduct, 0.0, tolerance); // in case of collinear points the cross product will be zero if (cmp != 0.0) { if (sign != 0.0 && cmp != sign) { return false; } sign = cmp; } } return true; } /** {@inheritDoc} */ public Vector2D[] getVertices() { return vertices.clone(); } /** * Get the line segments of the convex hull, ordered. * @return the line segments of the convex hull */ public Segment[] getLineSegments() { return retrieveLineSegments().clone(); } /** * Retrieve the line segments from the cached array or create them if needed. * * @return the array of line segments */ private Segment[] retrieveLineSegments() { if (lineSegments == null) { // construct the line segments - handle special cases of 1 or 2 points final int size = vertices.length; if (size <= 1) { this.lineSegments = new Segment[0]; } else if (size == 2) { this.lineSegments = new Segment[1]; final Vector2D p1 = vertices[0]; final Vector2D p2 = vertices[1]; this.lineSegments[0] = new Segment(p1, p2, new Line(p1, p2, tolerance)); } else { this.lineSegments = new Segment[size]; Vector2D firstPoint = null; Vector2D lastPoint = null; int index = 0; for (Vector2D point : vertices) { if (lastPoint == null) { firstPoint = point; lastPoint = point; } else { this.lineSegments[index++] = new Segment(lastPoint, point, new Line(lastPoint, point, tolerance)); lastPoint = point; } } this.lineSegments[index] = new Segment(lastPoint, firstPoint, new Line(lastPoint, firstPoint, tolerance)); } } return lineSegments; } /** {@inheritDoc} */ public Region<Euclidean2D> createRegion() throws InsufficientDataException { if (vertices.length < 3) { throw new InsufficientDataException(); } final RegionFactory<Euclidean2D> factory = new RegionFactory<Euclidean2D>(); final Segment[] segments = retrieveLineSegments(); final Line[] lineArray = new Line[segments.length]; for (int i = 0; i < segments.length; i++) { lineArray[i] = segments[i].getLine(); } return factory.buildConvex(lineArray); } }