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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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.oned;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;
import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.partitioning.AbstractRegion;
import org.apache.commons.math3.geometry.partitioning.BSPTree;
import org.apache.commons.math3.geometry.partitioning.BoundaryProjection;
import org.apache.commons.math3.geometry.partitioning.SubHyperplane;
import org.apache.commons.math3.util.Precision;
/** This class represents a 1D region: a set of intervals.
* @since 3.0
*/
public class IntervalsSet extends AbstractRegion implements Iterable {
/** Default value for tolerance. */
private static final double DEFAULT_TOLERANCE = 1.0e-10;
/** Build an intervals set representing the whole real line.
* @param tolerance tolerance below which points are considered identical.
* @since 3.3
*/
public IntervalsSet(final double tolerance) {
super(tolerance);
}
/** Build an intervals set corresponding to a single interval.
* @param lower lower bound of the interval, must be lesser or equal
* to {@code upper} (may be {@code Double.NEGATIVE_INFINITY})
* @param upper upper bound of the interval, must be greater or equal
* to {@code lower} (may be {@code Double.POSITIVE_INFINITY})
* @param tolerance tolerance below which points are considered identical.
* @since 3.3
*/
public IntervalsSet(final double lower, final double upper, final double tolerance) {
super(buildTree(lower, upper, tolerance), tolerance);
}
/** Build an intervals set from an inside/outside BSP tree.
* The leaf nodes of the BSP tree must have a
* {@code Boolean} attribute representing the inside status of
* the corresponding cell (true for inside cells, false for outside
* cells). In order to avoid building too many small objects, it is
* recommended to use the predefined constants
* {@code Boolean.TRUE} and {@code Boolean.FALSE}
* @param tree inside/outside BSP tree representing the intervals set
* @param tolerance tolerance below which points are considered identical.
* @since 3.3
*/
public IntervalsSet(final BSPTree tree, final double tolerance) {
super(tree, tolerance);
}
/** Build an intervals set from a Boundary REPresentation (B-rep).
* The boundary is provided as a collection of {@link
* SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the
* interior part of the region on its minus side and the exterior on
* its plus side.
* The boundary elements can be in any order, and can form
* several non-connected sets (like for example polygons with holes
* or a set of disjoints polyhedrons considered as a whole). In
* fact, the elements do not even need to be connected together
* (their topological connections are not used here). However, if the
* boundary does not really separate an inside open from an outside
* open (open having here its topological meaning), then subsequent
* calls to the {@link
* org.apache.commons.math3.geometry.partitioning.Region#checkPoint(org.apache.commons.math3.geometry.Point)
* checkPoint} method will not be meaningful anymore.
* If the boundary is empty, the region will represent the whole
* space.
* @param boundary collection of boundary elements
* @param tolerance tolerance below which points are considered identical.
* @since 3.3
*/
public IntervalsSet(final Collection> boundary,
final double tolerance) {
super(boundary, tolerance);
}
/** Build an intervals set representing the whole real line.
* @deprecated as of 3.1 replaced with {@link #IntervalsSet(double)}
*/
@Deprecated
public IntervalsSet() {
this(DEFAULT_TOLERANCE);
}
/** Build an intervals set corresponding to a single interval.
* @param lower lower bound of the interval, must be lesser or equal
* to {@code upper} (may be {@code Double.NEGATIVE_INFINITY})
* @param upper upper bound of the interval, must be greater or equal
* to {@code lower} (may be {@code Double.POSITIVE_INFINITY})
* @deprecated as of 3.3 replaced with {@link #IntervalsSet(double, double, double)}
*/
@Deprecated
public IntervalsSet(final double lower, final double upper) {
this(lower, upper, DEFAULT_TOLERANCE);
}
/** Build an intervals set from an inside/outside BSP tree.
* The leaf nodes of the BSP tree must have a
* {@code Boolean} attribute representing the inside status of
* the corresponding cell (true for inside cells, false for outside
* cells). In order to avoid building too many small objects, it is
* recommended to use the predefined constants
* {@code Boolean.TRUE} and {@code Boolean.FALSE}
* @param tree inside/outside BSP tree representing the intervals set
* @deprecated as of 3.3, replaced with {@link #IntervalsSet(BSPTree, double)}
*/
@Deprecated
public IntervalsSet(final BSPTree tree) {
this(tree, DEFAULT_TOLERANCE);
}
/** Build an intervals set from a Boundary REPresentation (B-rep).
* The boundary is provided as a collection of {@link
* SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the
* interior part of the region on its minus side and the exterior on
* its plus side.
* The boundary elements can be in any order, and can form
* several non-connected sets (like for example polygons with holes
* or a set of disjoints polyhedrons considered as a whole). In
* fact, the elements do not even need to be connected together
* (their topological connections are not used here). However, if the
* boundary does not really separate an inside open from an outside
* open (open having here its topological meaning), then subsequent
* calls to the {@link
* org.apache.commons.math3.geometry.partitioning.Region#checkPoint(org.apache.commons.math3.geometry.Point)
* checkPoint} method will not be meaningful anymore.
* If the boundary is empty, the region will represent the whole
* space.
* @param boundary collection of boundary elements
* @deprecated as of 3.3, replaced with {@link #IntervalsSet(Collection, double)}
*/
@Deprecated
public IntervalsSet(final Collection> boundary) {
this(boundary, DEFAULT_TOLERANCE);
}
/** Build an inside/outside tree representing a single interval.
* @param lower lower bound of the interval, must be lesser or equal
* to {@code upper} (may be {@code Double.NEGATIVE_INFINITY})
* @param upper upper bound of the interval, must be greater or equal
* to {@code lower} (may be {@code Double.POSITIVE_INFINITY})
* @param tolerance tolerance below which points are considered identical.
* @return the built tree
*/
private static BSPTree buildTree(final double lower, final double upper,
final double tolerance) {
if (Double.isInfinite(lower) && (lower < 0)) {
if (Double.isInfinite(upper) && (upper > 0)) {
// the tree must cover the whole real line
return new BSPTree(Boolean.TRUE);
}
// the tree must be open on the negative infinity side
final SubHyperplane upperCut =
new OrientedPoint(new Vector1D(upper), true, tolerance).wholeHyperplane();
return new BSPTree(upperCut,
new BSPTree(Boolean.FALSE),
new BSPTree(Boolean.TRUE),
null);
}
final SubHyperplane lowerCut =
new OrientedPoint(new Vector1D(lower), false, tolerance).wholeHyperplane();
if (Double.isInfinite(upper) && (upper > 0)) {
// the tree must be open on the positive infinity side
return new BSPTree(lowerCut,
new BSPTree(Boolean.FALSE),
new BSPTree(Boolean.TRUE),
null);
}
// the tree must be bounded on the two sides
final SubHyperplane upperCut =
new OrientedPoint(new Vector1D(upper), true, tolerance).wholeHyperplane();
return new BSPTree(lowerCut,
new BSPTree(Boolean.FALSE),
new BSPTree(upperCut,
new BSPTree(Boolean.FALSE),
new BSPTree(Boolean.TRUE),
null),
null);
}
/** {@inheritDoc} */
@Override
public IntervalsSet buildNew(final BSPTree tree) {
return new IntervalsSet(tree, getTolerance());
}
/** {@inheritDoc} */
@Override
protected void computeGeometricalProperties() {
if (getTree(false).getCut() == null) {
setBarycenter((Point) Vector1D.NaN);
setSize(((Boolean) getTree(false).getAttribute()) ? Double.POSITIVE_INFINITY : 0);
} else {
double size = 0.0;
double sum = 0.0;
for (final Interval interval : asList()) {
size += interval.getSize();
sum += interval.getSize() * interval.getBarycenter();
}
setSize(size);
if (Double.isInfinite(size)) {
setBarycenter((Point) Vector1D.NaN);
} else if (size >= Precision.SAFE_MIN) {
setBarycenter((Point) new Vector1D(sum / size));
} else {
setBarycenter((Point) ((OrientedPoint) getTree(false).getCut().getHyperplane()).getLocation());
}
}
}
/** Get the lowest value belonging to the instance.
* @return lowest value belonging to the instance
* ({@code Double.NEGATIVE_INFINITY} if the instance doesn't
* have any low bound, {@code Double.POSITIVE_INFINITY} if the
* instance is empty)
*/
public double getInf() {
BSPTree node = getTree(false);
double inf = Double.POSITIVE_INFINITY;
while (node.getCut() != null) {
final OrientedPoint op = (OrientedPoint) node.getCut().getHyperplane();
inf = op.getLocation().getX();
node = op.isDirect() ? node.getMinus() : node.getPlus();
}
return ((Boolean) node.getAttribute()) ? Double.NEGATIVE_INFINITY : inf;
}
/** Get the highest value belonging to the instance.
* @return highest value belonging to the instance
* ({@code Double.POSITIVE_INFINITY} if the instance doesn't
* have any high bound, {@code Double.NEGATIVE_INFINITY} if the
* instance is empty)
*/
public double getSup() {
BSPTree node = getTree(false);
double sup = Double.NEGATIVE_INFINITY;
while (node.getCut() != null) {
final OrientedPoint op = (OrientedPoint) node.getCut().getHyperplane();
sup = op.getLocation().getX();
node = op.isDirect() ? node.getPlus() : node.getMinus();
}
return ((Boolean) node.getAttribute()) ? Double.POSITIVE_INFINITY : sup;
}
/** {@inheritDoc}
* @since 3.3
*/
@Override
public BoundaryProjection projectToBoundary(final Point point) {
// get position of test point
final double x = ((Vector1D) point).getX();
double previous = Double.NEGATIVE_INFINITY;
for (final double[] a : this) {
if (x < a[0]) {
// the test point lies between the previous and the current intervals
// offset will be positive
final double previousOffset = x - previous;
final double currentOffset = a[0] - x;
if (previousOffset < currentOffset) {
return new BoundaryProjection(point, finiteOrNullPoint(previous), previousOffset);
} else {
return new BoundaryProjection(point, finiteOrNullPoint(a[0]), currentOffset);
}
} else if (x <= a[1]) {
// the test point lies within the current interval
// offset will be negative
final double offset0 = a[0] - x;
final double offset1 = x - a[1];
if (offset0 < offset1) {
return new BoundaryProjection(point, finiteOrNullPoint(a[1]), offset1);
} else {
return new BoundaryProjection(point, finiteOrNullPoint(a[0]), offset0);
}
}
previous = a[1];
}
// the test point if past the last sub-interval
return new BoundaryProjection(point, finiteOrNullPoint(previous), x - previous);
}
/** Build a finite point.
* @param x abscissa of the point
* @return a new point for finite abscissa, null otherwise
*/
private Vector1D finiteOrNullPoint(final double x) {
return Double.isInfinite(x) ? null : new Vector1D(x);
}
/** Build an ordered list of intervals representing the instance.
* This method builds this intervals set as an ordered list of
* {@link Interval Interval} elements. If the intervals set has no
* lower limit, the first interval will have its low bound equal to
* {@code Double.NEGATIVE_INFINITY}. If the intervals set has
* no upper limit, the last interval will have its upper bound equal
* to {@code Double.POSITIVE_INFINITY}. An empty tree will
* build an empty list while a tree representing the whole real line
* will build a one element list with both bounds being
* infinite.
* @return a new ordered list containing {@link Interval Interval}
* elements
*/
public List asList() {
final List list = new ArrayList();
for (final double[] a : this) {
list.add(new Interval(a[0], a[1]));
}
return list;
}
/** Get the first leaf node of a tree.
* @param root tree root
* @return first leaf node
*/
private BSPTree getFirstLeaf(final BSPTree root) {
if (root.getCut() == null) {
return root;
}
// find the smallest internal node
BSPTree smallest = null;
for (BSPTree n = root; n != null; n = previousInternalNode(n)) {
smallest = n;
}
return leafBefore(smallest);
}
/** Get the node corresponding to the first interval boundary.
* @return smallest internal node,
* or null if there are no internal nodes (i.e. the set is either empty or covers the real line)
*/
private BSPTree getFirstIntervalBoundary() {
// start search at the tree root
BSPTree node = getTree(false);
if (node.getCut() == null) {
return null;
}
// walk tree until we find the smallest internal node
node = getFirstLeaf(node).getParent();
// walk tree until we find an interval boundary
while (node != null && !(isIntervalStart(node) || isIntervalEnd(node))) {
node = nextInternalNode(node);
}
return node;
}
/** Check if an internal node corresponds to the start abscissa of an interval.
* @param node internal node to check
* @return true if the node corresponds to the start abscissa of an interval
*/
private boolean isIntervalStart(final BSPTree node) {
if ((Boolean) leafBefore(node).getAttribute()) {
// it has an inside cell before it, it may end an interval but not start it
return false;
}
if (!(Boolean) leafAfter(node).getAttribute()) {
// it has an outside cell after it, it is a dummy cut away from real intervals
return false;
}
// the cell has an outside before and an inside after it
// it is the start of an interval
return true;
}
/** Check if an internal node corresponds to the end abscissa of an interval.
* @param node internal node to check
* @return true if the node corresponds to the end abscissa of an interval
*/
private boolean isIntervalEnd(final BSPTree node) {
if (!(Boolean) leafBefore(node).getAttribute()) {
// it has an outside cell before it, it may start an interval but not end it
return false;
}
if ((Boolean) leafAfter(node).getAttribute()) {
// it has an inside cell after it, it is a dummy cut in the middle of an interval
return false;
}
// the cell has an inside before and an outside after it
// it is the end of an interval
return true;
}
/** Get the next internal node.
* @param node current internal node
* @return next internal node in ascending order, or null
* if this is the last internal node
*/
private BSPTree nextInternalNode(BSPTree node) {
if (childAfter(node).getCut() != null) {
// the next node is in the sub-tree
return leafAfter(node).getParent();
}
// there is nothing left deeper in the tree, we backtrack
while (isAfterParent(node)) {
node = node.getParent();
}
return node.getParent();
}
/** Get the previous internal node.
* @param node current internal node
* @return previous internal node in ascending order, or null
* if this is the first internal node
*/
private BSPTree previousInternalNode(BSPTree node) {
if (childBefore(node).getCut() != null) {
// the next node is in the sub-tree
return leafBefore(node).getParent();
}
// there is nothing left deeper in the tree, we backtrack
while (isBeforeParent(node)) {
node = node.getParent();
}
return node.getParent();
}
/** Find the leaf node just before an internal node.
* @param node internal node at which the sub-tree starts
* @return leaf node just before the internal node
*/
private BSPTree leafBefore(BSPTree node) {
node = childBefore(node);
while (node.getCut() != null) {
node = childAfter(node);
}
return node;
}
/** Find the leaf node just after an internal node.
* @param node internal node at which the sub-tree starts
* @return leaf node just after the internal node
*/
private BSPTree leafAfter(BSPTree node) {
node = childAfter(node);
while (node.getCut() != null) {
node = childBefore(node);
}
return node;
}
/** Check if a node is the child before its parent in ascending order.
* @param node child node considered
* @return true is the node has a parent end is before it in ascending order
*/
private boolean isBeforeParent(final BSPTree node) {
final BSPTree parent = node.getParent();
if (parent == null) {
return false;
} else {
return node == childBefore(parent);
}
}
/** Check if a node is the child after its parent in ascending order.
* @param node child node considered
* @return true is the node has a parent end is after it in ascending order
*/
private boolean isAfterParent(final BSPTree node) {
final BSPTree parent = node.getParent();
if (parent == null) {
return false;
} else {
return node == childAfter(parent);
}
}
/** Find the child node just before an internal node.
* @param node internal node at which the sub-tree starts
* @return child node just before the internal node
*/
private BSPTree childBefore(BSPTree node) {
if (isDirect(node)) {
// smaller abscissas are on minus side, larger abscissas are on plus side
return node.getMinus();
} else {
// smaller abscissas are on plus side, larger abscissas are on minus side
return node.getPlus();
}
}
/** Find the child node just after an internal node.
* @param node internal node at which the sub-tree starts
* @return child node just after the internal node
*/
private BSPTree childAfter(BSPTree node) {
if (isDirect(node)) {
// smaller abscissas are on minus side, larger abscissas are on plus side
return node.getPlus();
} else {
// smaller abscissas are on plus side, larger abscissas are on minus side
return node.getMinus();
}
}
/** Check if an internal node has a direct oriented point.
* @param node internal node to check
* @return true if the oriented point is direct
*/
private boolean isDirect(final BSPTree node) {
return ((OrientedPoint) node.getCut().getHyperplane()).isDirect();
}
/** Get the abscissa of an internal node.
* @param node internal node to check
* @return abscissa
*/
private double getAngle(final BSPTree node) {
return ((OrientedPoint) node.getCut().getHyperplane()).getLocation().getX();
}
/** {@inheritDoc}
*
* The iterator returns the limit values of sub-intervals in ascending order.
*
*
* The iterator does not support the optional {@code remove} operation.
*
* @since 3.3
*/
public Iterator iterator() {
return new SubIntervalsIterator();
}
/** Local iterator for sub-intervals. */
private class SubIntervalsIterator implements Iterator {
/** Current node. */
private BSPTree current;
/** Sub-interval no yet returned. */
private double[] pending;
/** Simple constructor.
*/
SubIntervalsIterator() {
current = getFirstIntervalBoundary();
if (current == null) {
// all the leaf tree nodes share the same inside/outside status
if ((Boolean) getFirstLeaf(getTree(false)).getAttribute()) {
// it is an inside node, it represents the full real line
pending = new double[] {
Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY
};
} else {
pending = null;
}
} else if (isIntervalEnd(current)) {
// the first boundary is an interval end,
// so the first interval starts at infinity
pending = new double[] {
Double.NEGATIVE_INFINITY, getAngle(current)
};
} else {
selectPending();
}
}
/** Walk the tree to select the pending sub-interval.
*/
private void selectPending() {
// look for the start of the interval
BSPTree start = current;
while (start != null && !isIntervalStart(start)) {
start = nextInternalNode(start);
}
if (start == null) {
// we have exhausted the iterator
current = null;
pending = null;
return;
}
// look for the end of the interval
BSPTree end = start;
while (end != null && !isIntervalEnd(end)) {
end = nextInternalNode(end);
}
if (end != null) {
// we have identified the interval
pending = new double[] {
getAngle(start), getAngle(end)
};
// prepare search for next interval
current = end;
} else {
// the final interval is open toward infinity
pending = new double[] {
getAngle(start), Double.POSITIVE_INFINITY
};
// there won't be any other intervals
current = null;
}
}
/** {@inheritDoc} */
public boolean hasNext() {
return pending != null;
}
/** {@inheritDoc} */
public double[] next() {
if (pending == null) {
throw new NoSuchElementException();
}
final double[] next = pending;
selectPending();
return next;
}
/** {@inheritDoc} */
public void remove() {
throw new UnsupportedOperationException();
}
}
}