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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);
}
}
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