001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.math3.geometry.euclidean.oned;
018
019import java.util.ArrayList;
020import java.util.Collection;
021import java.util.List;
022
023import org.apache.commons.math3.geometry.partitioning.AbstractRegion;
024import org.apache.commons.math3.geometry.partitioning.BSPTree;
025import org.apache.commons.math3.geometry.partitioning.SubHyperplane;
026import org.apache.commons.math3.util.Precision;
027
028/** This class represents a 1D region: a set of intervals.
029 * @version $Id: IntervalsSet.java 1416643 2012-12-03 19:37:14Z tn $
030 * @since 3.0
031 */
032public class IntervalsSet extends AbstractRegion<Euclidean1D, Euclidean1D> {
033
034    /** Build an intervals set representing the whole real line.
035     */
036    public IntervalsSet() {
037        super();
038    }
039
040    /** Build an intervals set corresponding to a single interval.
041     * @param lower lower bound of the interval, must be lesser or equal
042     * to {@code upper} (may be {@code Double.NEGATIVE_INFINITY})
043     * @param upper upper bound of the interval, must be greater or equal
044     * to {@code lower} (may be {@code Double.POSITIVE_INFINITY})
045     */
046    public IntervalsSet(final double lower, final double upper) {
047        super(buildTree(lower, upper));
048    }
049
050    /** Build an intervals set from an inside/outside BSP tree.
051     * <p>The leaf nodes of the BSP tree <em>must</em> have a
052     * {@code Boolean} attribute representing the inside status of
053     * the corresponding cell (true for inside cells, false for outside
054     * cells). In order to avoid building too many small objects, it is
055     * recommended to use the predefined constants
056     * {@code Boolean.TRUE} and {@code Boolean.FALSE}</p>
057     * @param tree inside/outside BSP tree representing the intervals set
058     */
059    public IntervalsSet(final BSPTree<Euclidean1D> tree) {
060        super(tree);
061    }
062
063    /** Build an intervals set from a Boundary REPresentation (B-rep).
064     * <p>The boundary is provided as a collection of {@link
065     * SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the
066     * interior part of the region on its minus side and the exterior on
067     * its plus side.</p>
068     * <p>The boundary elements can be in any order, and can form
069     * several non-connected sets (like for example polygons with holes
070     * or a set of disjoints polyhedrons considered as a whole). In
071     * fact, the elements do not even need to be connected together
072     * (their topological connections are not used here). However, if the
073     * boundary does not really separate an inside open from an outside
074     * open (open having here its topological meaning), then subsequent
075     * calls to the {@link
076     * org.apache.commons.math3.geometry.partitioning.Region#checkPoint(org.apache.commons.math3.geometry.Vector)
077     * checkPoint} method will not be meaningful anymore.</p>
078     * <p>If the boundary is empty, the region will represent the whole
079     * space.</p>
080     * @param boundary collection of boundary elements
081     */
082    public IntervalsSet(final Collection<SubHyperplane<Euclidean1D>> boundary) {
083        super(boundary);
084    }
085
086    /** Build an inside/outside tree representing a single interval.
087     * @param lower lower bound of the interval, must be lesser or equal
088     * to {@code upper} (may be {@code Double.NEGATIVE_INFINITY})
089     * @param upper upper bound of the interval, must be greater or equal
090     * to {@code lower} (may be {@code Double.POSITIVE_INFINITY})
091     * @return the built tree
092     */
093    private static BSPTree<Euclidean1D> buildTree(final double lower, final double upper) {
094        if (Double.isInfinite(lower) && (lower < 0)) {
095            if (Double.isInfinite(upper) && (upper > 0)) {
096                // the tree must cover the whole real line
097                return new BSPTree<Euclidean1D>(Boolean.TRUE);
098            }
099            // the tree must be open on the negative infinity side
100            final SubHyperplane<Euclidean1D> upperCut =
101                new OrientedPoint(new Vector1D(upper), true).wholeHyperplane();
102            return new BSPTree<Euclidean1D>(upperCut,
103                               new BSPTree<Euclidean1D>(Boolean.FALSE),
104                               new BSPTree<Euclidean1D>(Boolean.TRUE),
105                               null);
106        }
107        final SubHyperplane<Euclidean1D> lowerCut =
108            new OrientedPoint(new Vector1D(lower), false).wholeHyperplane();
109        if (Double.isInfinite(upper) && (upper > 0)) {
110            // the tree must be open on the positive infinity side
111            return new BSPTree<Euclidean1D>(lowerCut,
112                                            new BSPTree<Euclidean1D>(Boolean.FALSE),
113                                            new BSPTree<Euclidean1D>(Boolean.TRUE),
114                                            null);
115        }
116
117        // the tree must be bounded on the two sides
118        final SubHyperplane<Euclidean1D> upperCut =
119            new OrientedPoint(new Vector1D(upper), true).wholeHyperplane();
120        return new BSPTree<Euclidean1D>(lowerCut,
121                                        new BSPTree<Euclidean1D>(Boolean.FALSE),
122                                        new BSPTree<Euclidean1D>(upperCut,
123                                                                 new BSPTree<Euclidean1D>(Boolean.FALSE),
124                                                                 new BSPTree<Euclidean1D>(Boolean.TRUE),
125                                                                 null),
126                                        null);
127
128    }
129
130    /** {@inheritDoc} */
131    @Override
132    public IntervalsSet buildNew(final BSPTree<Euclidean1D> tree) {
133        return new IntervalsSet(tree);
134    }
135
136    /** {@inheritDoc} */
137    @Override
138    protected void computeGeometricalProperties() {
139        if (getTree(false).getCut() == null) {
140            setBarycenter(Vector1D.NaN);
141            setSize(((Boolean) getTree(false).getAttribute()) ? Double.POSITIVE_INFINITY : 0);
142        } else {
143            double size = 0.0;
144            double sum = 0.0;
145            for (final Interval interval : asList()) {
146                size += interval.getSize();
147                sum  += interval.getSize() * interval.getBarycenter();
148            }
149            setSize(size);
150            if (Double.isInfinite(size)) {
151                setBarycenter(Vector1D.NaN);
152            } else if (size >= Precision.SAFE_MIN) {
153                setBarycenter(new Vector1D(sum / size));
154            } else {
155                setBarycenter(((OrientedPoint) getTree(false).getCut().getHyperplane()).getLocation());
156            }
157        }
158    }
159
160    /** Get the lowest value belonging to the instance.
161     * @return lowest value belonging to the instance
162     * ({@code Double.NEGATIVE_INFINITY} if the instance doesn't
163     * have any low bound, {@code Double.POSITIVE_INFINITY} if the
164     * instance is empty)
165     */
166    public double getInf() {
167        BSPTree<Euclidean1D> node = getTree(false);
168        double  inf  = Double.POSITIVE_INFINITY;
169        while (node.getCut() != null) {
170            final OrientedPoint op = (OrientedPoint) node.getCut().getHyperplane();
171            inf  = op.getLocation().getX();
172            node = op.isDirect() ? node.getMinus() : node.getPlus();
173        }
174        return ((Boolean) node.getAttribute()) ? Double.NEGATIVE_INFINITY : inf;
175    }
176
177    /** Get the highest value belonging to the instance.
178     * @return highest value belonging to the instance
179     * ({@code Double.POSITIVE_INFINITY} if the instance doesn't
180     * have any high bound, {@code Double.NEGATIVE_INFINITY} if the
181     * instance is empty)
182     */
183    public double getSup() {
184        BSPTree<Euclidean1D> node = getTree(false);
185        double  sup  = Double.NEGATIVE_INFINITY;
186        while (node.getCut() != null) {
187            final OrientedPoint op = (OrientedPoint) node.getCut().getHyperplane();
188            sup  = op.getLocation().getX();
189            node = op.isDirect() ? node.getPlus() : node.getMinus();
190        }
191        return ((Boolean) node.getAttribute()) ? Double.POSITIVE_INFINITY : sup;
192    }
193
194    /** Build an ordered list of intervals representing the instance.
195     * <p>This method builds this intervals set as an ordered list of
196     * {@link Interval Interval} elements. If the intervals set has no
197     * lower limit, the first interval will have its low bound equal to
198     * {@code Double.NEGATIVE_INFINITY}. If the intervals set has
199     * no upper limit, the last interval will have its upper bound equal
200     * to {@code Double.POSITIVE_INFINITY}. An empty tree will
201     * build an empty list while a tree representing the whole real line
202     * will build a one element list with both bounds beeing
203     * infinite.</p>
204     * @return a new ordered list containing {@link Interval Interval}
205     * elements
206     */
207    public List<Interval> asList() {
208        final List<Interval> list = new ArrayList<Interval>();
209        recurseList(getTree(false), list,
210                    Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);
211        return list;
212    }
213
214    /** Update an intervals list.
215     * @param node current node
216     * @param list list to update
217     * @param lower lower bound of the current convex cell
218     * @param upper upper bound of the current convex cell
219     */
220    private void recurseList(final BSPTree<Euclidean1D> node,
221                             final List<Interval> list,
222                             final double lower, final double upper) {
223
224        if (node.getCut() == null) {
225            if ((Boolean) node.getAttribute()) {
226                // this leaf cell is an inside cell: an interval
227                list.add(new Interval(lower, upper));
228            }
229        } else {
230            final OrientedPoint op  = (OrientedPoint) node.getCut().getHyperplane();
231            final Vector1D       loc = op.getLocation();
232            double              x   = loc.getX();
233
234            // make sure we explore the tree in increasing order
235            final BSPTree<Euclidean1D> low  =
236                op.isDirect() ? node.getMinus() : node.getPlus();
237            final BSPTree<Euclidean1D> high =
238                op.isDirect() ? node.getPlus()  : node.getMinus();
239
240            recurseList(low, list, lower, x);
241            if ((checkPoint(low,  loc) == Location.INSIDE) &&
242                (checkPoint(high, loc) == Location.INSIDE)) {
243                // merge the last interval added and the first one of the high sub-tree
244                x = list.remove(list.size() - 1).getInf();
245            }
246            recurseList(high, list, x, upper);
247
248        }
249
250    }
251
252}