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Geometric primitives for euclidean space.
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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.geometry.euclidean.oned;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.Objects;
import java.util.function.BiConsumer;
import org.apache.commons.geometry.core.RegionLocation;
import org.apache.commons.geometry.core.Transform;
import org.apache.commons.geometry.core.partitioning.Hyperplane;
import org.apache.commons.geometry.core.partitioning.Split;
import org.apache.commons.geometry.core.partitioning.bsp.AbstractBSPTree;
import org.apache.commons.geometry.core.partitioning.bsp.AbstractRegionBSPTree;
import org.apache.commons.geometry.core.partitioning.bsp.RegionCutRule;
/** Binary space partitioning (BSP) tree representing a region in one dimensional
* Euclidean space.
*/
public final class RegionBSPTree1D extends AbstractRegionBSPTree {
/** Comparator used to sort BoundaryPairs by ascending location. */
private static final Comparator BOUNDARY_PAIR_COMPARATOR =
Comparator.comparingDouble(BoundaryPair::getMinValue);
/** Create a new, empty region.
*/
public RegionBSPTree1D() {
this(false);
}
/** Create a new region. If {@code full} is true, then the region will
* represent the entire number line. Otherwise, it will be empty.
* @param full whether or not the region should contain the entire
* number line or be empty
*/
public RegionBSPTree1D(final boolean full) {
super(full);
}
/** Return a deep copy of this instance.
* @return a deep copy of this instance.
* @see #copy(org.apache.commons.geometry.core.partitioning.bsp.BSPTree)
*/
public RegionBSPTree1D copy() {
final RegionBSPTree1D result = RegionBSPTree1D.empty();
result.copy(this);
return result;
}
/** Add an interval to this region. The resulting region will be the
* union of the interval and the region represented by this instance.
* @param interval the interval to add
*/
public void add(final Interval interval) {
union(intervalToTree(interval));
}
/** Classify a point location with respect to the region.
* @param x the point to classify
* @return the location of the point with respect to the region
* @see #classify(org.apache.commons.geometry.core.Point)
*/
public RegionLocation classify(final double x) {
return classify(Vector1D.of(x));
}
/** Return true if the given point location is on the inside or boundary
* of the region.
* @param x the location to test
* @return true if the location is on the inside or boundary of the region
* @see #contains(org.apache.commons.geometry.core.Point)
*/
public boolean contains(final double x) {
return contains(Vector1D.of(x));
}
/** {@inheritDoc}
*
* This method simply returns 0 because boundaries in one dimension do not
* have any size.
*/
@Override
public double getBoundarySize() {
return 0;
}
/** {@inheritDoc} */
@Override
public Vector1D project(final Vector1D pt) {
// use our custom projector so that we can disambiguate points that are
// actually equidistant from the target point
final BoundaryProjector1D projector = new BoundaryProjector1D(pt);
accept(projector);
return projector.getProjected();
}
/** {@inheritDoc}
*
* When splitting trees representing single points with a splitter lying directly
* on the point, the result point is placed on one side of the splitter based on its
* orientation: if the splitter is positive-facing, the point is placed on the plus
* side of the split; if the splitter is negative-facing, the point is placed on the
* minus side of the split.
*/
@Override
public Split split(final Hyperplane splitter) {
return split(splitter, RegionBSPTree1D.empty(), RegionBSPTree1D.empty());
}
/** Get the minimum value on the inside of the region; returns {@link Double#NEGATIVE_INFINITY}
* if the region does not have a minimum value and {@link Double#POSITIVE_INFINITY} if
* the region is empty.
* @return the minimum value on the inside of the region
*/
public double getMin() {
double min = Double.POSITIVE_INFINITY;
RegionNode1D node = getRoot();
OrientedPoint pt;
while (!node.isLeaf()) {
pt = (OrientedPoint) node.getCutHyperplane();
min = pt.getLocation();
node = pt.isPositiveFacing() ? node.getMinus() : node.getPlus();
}
return node.isInside() ? Double.NEGATIVE_INFINITY : min;
}
/** Get the maximum value on the inside of the region; returns {@link Double#POSITIVE_INFINITY}
* if the region does not have a maximum value and {@link Double#NEGATIVE_INFINITY} if
* the region is empty.
* @return the maximum value on the inside of the region
*/
public double getMax() {
double max = Double.NEGATIVE_INFINITY;
RegionNode1D node = getRoot();
OrientedPoint pt;
while (!node.isLeaf()) {
pt = (OrientedPoint) node.getCutHyperplane();
max = pt.getLocation();
node = pt.isPositiveFacing() ? node.getPlus() : node.getMinus();
}
return node.isInside() ? Double.POSITIVE_INFINITY : max;
}
/** Convert the region represented by this tree into a list of separate
* {@link Interval}s, arranged in order of ascending min value.
* @return list of {@link Interval}s representing this region in order of
* ascending min value
*/
public List toIntervals() {
final List boundaryPairs = new ArrayList<>();
visitInsideIntervals((min, max) -> boundaryPairs.add(new BoundaryPair(min, max)));
boundaryPairs.sort(BOUNDARY_PAIR_COMPARATOR);
final List intervals = new ArrayList<>();
BoundaryPair start = null;
BoundaryPair end = null;
for (final BoundaryPair current : boundaryPairs) {
if (start == null) {
start = current;
end = current;
} else if (Objects.equals(end.getMax(), current.getMin())) {
// these intervals should be merged
end = current;
} else {
// these intervals should not be merged
intervals.add(createInterval(start, end));
// queue up the next pair
start = current;
end = current;
}
}
if (start != null) {
intervals.add(createInterval(start, end));
}
return intervals;
}
/** Create an interval instance from the min boundary from the start boundary pair and
* the max boundary from the end boundary pair. The hyperplane directions are adjusted
* as needed.
* @param start starting boundary pair
* @param end ending boundary pair
* @return an interval created from the min boundary of the given start pair and the
* max boundary from the given end pair
*/
private Interval createInterval(final BoundaryPair start, final BoundaryPair end) {
OrientedPoint min = start.getMin();
OrientedPoint max = end.getMax();
// flip the hyperplanes if needed since there's no
// guarantee that the inside will be on the minus side
// of the hyperplane (for example, if the region is complemented)
if (min != null && min.isPositiveFacing()) {
min = min.reverse();
}
if (max != null && !max.isPositiveFacing()) {
max = max.reverse();
}
return Interval.of(min, max);
}
/** Compute the min/max intervals for all interior convex regions in the tree and
* pass the values to the given visitor function.
* @param visitor the object that will receive the calculated min and max boundary for each
* insides node's convex region
*/
private void visitInsideIntervals(final BiConsumer visitor) {
for (final RegionNode1D node : nodes()) {
if (node.isInside()) {
node.visitNodeInterval(visitor);
}
}
}
/** {@inheritDoc} */
@Override
protected RegionNode1D createNode() {
return new RegionNode1D(this);
}
/** {@inheritDoc} */
@Override
protected RegionSizeProperties computeRegionSizeProperties() {
final RegionSizePropertiesVisitor visitor = new RegionSizePropertiesVisitor();
visitInsideIntervals(visitor);
return visitor.getRegionSizeProperties();
}
/** Returns true if the given transform would result in a swapping of the interior
* and exterior of the region if applied.
*
* This method always returns false since no swapping of this kind occurs in
* 1D.
*/
@Override
protected boolean swapsInsideOutside(final Transform transform) {
return false;
}
/** Return a new {@link RegionBSPTree1D} instance containing the entire space.
* @return a new {@link RegionBSPTree1D} instance containing the entire space
*/
public static RegionBSPTree1D full() {
return new RegionBSPTree1D(true);
}
/** Return a new, empty {@link RegionBSPTree1D} instance.
* @return a new, empty {@link RegionBSPTree1D} instance
*/
public static RegionBSPTree1D empty() {
return new RegionBSPTree1D(false);
}
/** Construct a new instance from one or more intervals. The returned tree
* represents the same region as the union of all of the input intervals.
* @param interval the input interval
* @param more additional intervals to add to the region
* @return a new instance representing the same region as the union
* of all of the given intervals
*/
public static RegionBSPTree1D from(final Interval interval, final Interval... more) {
final RegionBSPTree1D tree = intervalToTree(interval);
for (final Interval additional : more) {
tree.add(additional);
}
return tree;
}
/** Construct a new instance from the given collection of intervals.
* @param intervals the intervals to populate the region with
* @return a new instance constructed from the given collection of intervals
*/
public static RegionBSPTree1D from(final Iterable intervals) {
final RegionBSPTree1D tree = new RegionBSPTree1D(false);
for (final Interval interval : intervals) {
tree.add(interval);
}
return tree;
}
/** Return a tree representing the same region as the given interval.
* @param interval interval to create a tree from
* @return a tree representing the same region as the given interval
*/
private static RegionBSPTree1D intervalToTree(final Interval interval) {
final OrientedPoint minBoundary = interval.getMinBoundary();
final OrientedPoint maxBoundary = interval.getMaxBoundary();
final RegionBSPTree1D tree = full();
RegionNode1D node = tree.getRoot();
if (minBoundary != null) {
tree.setNodeCut(node, minBoundary.span(), tree.getSubtreeInitializer(RegionCutRule.MINUS_INSIDE));
node = node.getMinus();
}
if (maxBoundary != null) {
tree.setNodeCut(node, maxBoundary.span(), tree.getSubtreeInitializer(RegionCutRule.MINUS_INSIDE));
}
return tree;
}
/** BSP tree node for one dimensional Euclidean space.
*/
public static final class RegionNode1D extends AbstractRegionBSPTree.AbstractRegionNode {
/** Simple constructor.
* @param tree the owning tree instance
*/
private RegionNode1D(final AbstractBSPTree tree) {
super(tree);
}
/** Get the region represented by this node. The returned region contains
* the entire area contained in this node, regardless of the attributes of
* any child nodes.
* @return the region represented by this node
*/
public Interval getNodeRegion() {
final NodeRegionVisitor visitor = new NodeRegionVisitor();
visitNodeInterval(visitor);
return visitor.getInterval();
}
/** Determine the min/max boundaries for the convex region represented by this node and pass
* the values to the visitor function.
* @param visitor the object that will receive the min and max boundaries for the node's
* convex region
*/
private void visitNodeInterval(final BiConsumer visitor) {
OrientedPoint min = null;
OrientedPoint max = null;
OrientedPoint pt;
RegionNode1D child = this;
RegionNode1D parent;
while ((min == null || max == null) && (parent = child.getParent()) != null) {
pt = (OrientedPoint) parent.getCutHyperplane();
if ((pt.isPositiveFacing() && child.isMinus()) ||
(!pt.isPositiveFacing() && child.isPlus())) {
if (max == null) {
max = pt;
}
} else if (min == null) {
min = pt;
}
child = parent;
}
visitor.accept(min, max);
}
/** {@inheritDoc} */
@Override
protected RegionNode1D getSelf() {
return this;
}
}
/** Internal class containing pairs of interval boundaries.
*/
private static final class BoundaryPair {
/** The min boundary. */
private final OrientedPoint min;
/** The max boundary. */
private final OrientedPoint max;
/** Simple constructor.
* @param min min boundary hyperplane
* @param max max boundary hyperplane
*/
BoundaryPair(final OrientedPoint min, final OrientedPoint max) {
this.min = min;
this.max = max;
}
/** Get the minimum boundary hyperplane.
* @return the minimum boundary hyperplane.
*/
public OrientedPoint getMin() {
return min;
}
/** Get the maximum boundary hyperplane.
* @return the maximum boundary hyperplane.
*/
public OrientedPoint getMax() {
return max;
}
/** Get the minimum value of the interval or {@link Double#NEGATIVE_INFINITY}
* if no minimum value exists.
* @return the minimum value of the interval or {@link Double#NEGATIVE_INFINITY}
* if no minimum value exists.
*/
public double getMinValue() {
return (min != null) ? min.getLocation() : Double.NEGATIVE_INFINITY;
}
}
/** Class used to project points onto the region boundary.
*/
private static final class BoundaryProjector1D extends BoundaryProjector {
/** Simple constructor.
* @param point the point to project onto the region's boundary
*/
BoundaryProjector1D(final Vector1D point) {
super(point);
}
/** {@inheritDoc} */
@Override
protected Vector1D disambiguateClosestPoint(final Vector1D target, final Vector1D a, final Vector1D b) {
final int cmp = Vector1D.COORDINATE_ASCENDING_ORDER.compare(a, b);
if (target.isInfinite() && target.getX() > 0) {
// return the largest value (closest to +Infinity)
return cmp < 0 ? b : a;
}
// return the smallest value
return cmp < 0 ? a : b;
}
}
/** Internal class for calculating the region of a single tree node.
*/
private static final class NodeRegionVisitor implements BiConsumer {
/** The min boundary for the region. */
private OrientedPoint min;
/** The max boundary for the region. */
private OrientedPoint max;
/** {@inheritDoc} */
@Override
public void accept(final OrientedPoint minBoundary, final OrientedPoint maxBoundary) {
// reverse the oriented point directions if needed
this.min = (minBoundary != null && minBoundary.isPositiveFacing()) ? minBoundary.reverse() : minBoundary;
this.max = (maxBoundary != null && !maxBoundary.isPositiveFacing()) ? maxBoundary.reverse() : maxBoundary;
}
/** Return the computed interval.
* @return the computed interval.
*/
public Interval getInterval() {
return Interval.of(min, max);
}
}
/** Internal class for calculating size-related properties for a {@link RegionBSPTree1D}.
*/
private static final class RegionSizePropertiesVisitor implements BiConsumer {
/** Number of inside intervals visited. */
private int count;
/** Total computed size of all inside regions. */
private double size;
/** Raw sum of the centroids of each inside interval. */
private double rawCentroidSum;
/** The sum of the centroids of each inside interval, scaled by the size of the interval. */
private double scaledCentroidSum;
/** {@inheritDoc} */
@Override
public void accept(final OrientedPoint min, final OrientedPoint max) {
++count;
final double minLoc = (min != null) ? min.getLocation() : Double.NEGATIVE_INFINITY;
final double maxLoc = (max != null) ? max.getLocation() : Double.POSITIVE_INFINITY;
final double intervalSize = maxLoc - minLoc;
final double intervalCentroid = 0.5 * (maxLoc + minLoc);
size += intervalSize;
rawCentroidSum += intervalCentroid;
scaledCentroidSum += intervalSize * intervalCentroid;
}
/** Get the computed properties for the region. This must only be called after
* every inside interval has been visited.
* @return properties for the region
*/
public RegionSizeProperties getRegionSizeProperties() {
Vector1D centroid = null;
if (count > 0 && Double.isFinite(size)) {
if (size > 0) {
// use the scaled sum if we have a non-zero size
centroid = Vector1D.of(scaledCentroidSum / size);
} else {
// use the raw sum if we don't have a size; this will be
// the case if the region only contains points with zero size
centroid = Vector1D.of(rawCentroidSum / count);
}
}
return new RegionSizeProperties<>(size, centroid);
}
}
}