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* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
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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.
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).
The implementation is not sensitive to collinear points on the hull. The parameter includeCollinearPoints allows to control the behavior with regard to collinear points. If 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.
The tolerance parameter (default: 1e-10) is used as epsilon criteria to determine identical and collinear points.
See Also: Since: 3.3
/**
* 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.
/**
* Create a new MonotoneChain instance.
*/
public MonotoneChain() {
this(false);
}
Create a new MonotoneChain instance.
Params: - includeCollinearPoints – whether collinear points shall be added as hull vertices
/**
* 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.
Params: - includeCollinearPoints – whether collinear points shall be added as hull vertices
- tolerance – tolerance below which points are considered identical
/**
* 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} /** {@inheritDoc} */
@Override
public Collection<Vector2D> findHullVertices(final Collection<Vector2D> points) {
final List<Vector2D> pointsSortedByXAxis = new ArrayList<Vector2D>(points);
// sort the points in increasing order on the x-axis
Collections.sort(pointsSortedByXAxis, new Comparator<Vector2D>() {
{@inheritDoc} /** {@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<Vector2D>();
for (Vector2D p : pointsSortedByXAxis) {
updateHull(p, lowerHull);
}
// build upper hull
final List<Vector2D> upperHull = new ArrayList<Vector2D>();
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<Vector2D>(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.
Params: - point – the current point
- hull – the partial hull
/**
* 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);
}
}