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Open-source Java libraries, supporting generalized smart arrays and matrices with elements
of any types, including a wide set of 2D-, 3D- and multidimensional image processing
and other algorithms, working with arrays and matrices.
/*
* The MIT License (MIT)
*
* Copyright (c) 2007-2024 Daniel Alievsky, AlgART Laboratory (http://algart.net)
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
package net.algart.math.patterns;
import net.algart.math.Point;
import net.algart.math.Range;
import net.algart.math.RectangularArea;
import java.lang.ref.Reference;
import java.lang.ref.SoftReference;
import java.util.*;
final class MinkowskiSum extends AbstractPattern implements Pattern {
private final Pattern[] summands;
private final List optimizedSummands;
private final Pattern[] projections;
private volatile Reference> points = null;
MinkowskiSum(Pattern[] patterns) {
this(patterns, null);
}
private MinkowskiSum(Pattern[] patterns, List optimizedSummands) {
super(getDimCountAndCheck(patterns));
List allSummands = new ArrayList<>();
for (Pattern ptn : patterns) {
if (ptn instanceof MinkowskiSum) {
allSummands.addAll(Arrays.asList(((MinkowskiSum) ptn).summands));
} else {
allSummands.add(ptn);
}
// An alternate idea could be using ptn.minkowskiDecomposition always.
// But it requires to choose minimalPointCount, which is unknown here:
// for example, maybe we do not want to decompose little rectangular patterns.
}
double[] minCoord = new double[dimCount]; // zero-filled (for further summing)
double[] maxCoord = new double[dimCount]; // zero-filled (for further summing)
for (Pattern ptn : allSummands) {
for (int k = 0; k < dimCount; k++) {
Range range = ptn.coordRange(k);
minCoord[k] += range.min();
maxCoord[k] += range.max();
}
}
for (int k = 0; k < dimCount; k++) {
this.coordRanges[k] = Range.valueOf(minCoord[k], maxCoord[k]);
checkCoordRange(this.coordRanges[k]);
}
this.summands = allSummands.toArray(new Pattern[allSummands.size()]);
if (optimizedSummands == null) {
this.optimizedSummands = optimizeMinkowskiSum(allSummands);
} else {
this.optimizedSummands = optimizedSummands;
}
this.projections = new Pattern[dimCount]; //null-filled
}
@Override
public long pointCount() {
return points().size();
}
// @Override
// public boolean contains(IPoint point) {
// return points().contains(point.toPoint());
// }
@Override
public Set points() {
Set resultPoints = points == null ? null : points.get();
if (resultPoints == null) {
Pattern ptn = new SimplePattern(optimizedSummands.get(0).points());
// this actualization is necessary for a case when minkowskiAdd method just returns MinkowskiSum instance
for (int k = 1, n = optimizedSummands.size(); k < n; k++) {
ptn = ptn.minkowskiAdd(optimizedSummands.get(k));
}
resultPoints = ptn.points(); // immutable set
points = new SoftReference<>(resultPoints);
}
return resultPoints;
}
@Override
public Range coordRange(int coordIndex) {
return coordRanges[coordIndex];
}
@Override
public RectangularArea coordArea() {
return RectangularArea.valueOf(coordRanges);
}
@Override
public boolean isSurelySinglePoint() {
for (Pattern p : optimizedSummands) {
if (!p.isSurelySinglePoint()) {
return false;
}
}
return true;
}
@Override
public boolean isSurelyInteger() {
if (surelyInteger == null) {
boolean allInteger = true;
for (Pattern p : optimizedSummands) {
if (!p.isSurelyInteger()) {
allInteger = false;
break;
}
}
surelyInteger = allInteger;
}
return surelyInteger;
}
@Override
public Pattern projectionAlongAxis(int coordIndex) {
checkCoordIndex(coordIndex);
assert dimCount > 0;
if (dimCount == 1) {
throw new IllegalStateException("Cannot perform projection for 1-dimensional pattern");
}
synchronized (projections) {
if (projections[coordIndex] == null) {
Pattern[] newSummands = new Pattern[summands.length];
for (int k = 0; k < newSummands.length; k++) {
newSummands[k] = summands[k].projectionAlongAxis(coordIndex);
}
projections[coordIndex] = new MinkowskiSum(newSummands);
}
return projections[coordIndex];
}
}
// We could also optimize minBound()/maxBound() here
@Override
public Pattern shift(Point shift) {
if (shift.coordCount() != dimCount) {
throw new IllegalArgumentException("The number of shift coordinates " + shift.coordCount()
+ " is not equal to the number of pattern coordinates " + dimCount);
}
if (shift.isOrigin()) {
return this;
}
Pattern[] newSummands = summands.clone();
newSummands[0] = newSummands[0].shift(shift);
List newOptimizedSummands = new ArrayList<>(optimizedSummands);
newOptimizedSummands.set(0, newOptimizedSummands.get(0).shift(shift));
return new MinkowskiSum(newSummands, newOptimizedSummands);
}
@Override
public Pattern scale(double... multipliers) {
Objects.requireNonNull(multipliers, "Null multipliers argument");
if (multipliers.length != dimCount) {
throw new IllegalArgumentException("Illegal number of multipliers: "
+ multipliers.length + " instead of " + dimCount);
}
Pattern[] newSummands = new Pattern[summands.length];
for (int k = 0; k < newSummands.length; k++) {
newSummands[k] = summands[k].scale(multipliers);
}
return new MinkowskiSum(newSummands);
}
@Override
public Pattern minkowskiAdd(Pattern added) {
Objects.requireNonNull(added, "Null added argument");
Pattern[] newSummands = new Pattern[summands.length + 1];
System.arraycopy(summands, 0, newSummands, 0, summands.length);
newSummands[summands.length] = added;
return new MinkowskiSum(newSummands);
}
@Override
public List minkowskiDecomposition(int minimalPointCount) {
ArrayList result = new ArrayList<>();
for (Pattern summand : optimizedSummands) {
result.addAll(summand.minkowskiDecomposition(minimalPointCount));
}
int numberOfPatternsWithAtLeast2Points = 0;
for (Pattern ptn : result) {
long pointCount = ptn.pointCount();
if (pointCount >= 3) {
return Collections.unmodifiableList(result);
}
if (pointCount >= 2) {
numberOfPatternsWithAtLeast2Points++;
}
}
if (numberOfPatternsWithAtLeast2Points <= 1) {
return Collections.singletonList(this);
}
return Collections.unmodifiableList(result);
}
@Override
public String toString() {
int n = optimizedSummands.size();
StringBuilder sb = new StringBuilder(dimCount + "D Minkowski sum of " + n + " patterns: ");
for (int k = 0; k < n; k++) {
if (k > 0) {
sb.append(" (+) ");
}
sb.append(optimizedSummands.get(k));
}
return sb.toString();
}
@Override
public int hashCode() {
return Arrays.hashCode(summands) ^ getClass().getName().hashCode();
}
@Override
public boolean equals(Object obj) {
return obj instanceof MinkowskiSum && (obj == this || Arrays.equals(summands, ((MinkowskiSum) obj).summands));
}
static int getDimCountAndCheck(Pattern[] patterns) {
Objects.requireNonNull(patterns, "Null patterns argument");
if (patterns.length == 0) {
throw new IllegalArgumentException("Empty patterns array");
}
Objects.requireNonNull(patterns[0], "Null pattern is the array");
int result = patterns[0].dimCount();
for (int k = 1; k < patterns.length; k++) {
Objects.requireNonNull(patterns[k], "Null pattern #" + k + " is the array");
if (patterns[k].dimCount() != result) {
throw new IllegalArgumentException("Patterns dimensions mismatch: the first pattern has "
+ result + " dimensions, but pattern #" + k + " has " + patterns[k].dimCount());
}
}
return result;
}
private static List optimizeMinkowskiSum(List patterns) {
Map numbersOfEquals = new HashMap<>();
Map rectangularSummands = new HashMap<>();
Pattern onePointSummand = null;
for (Pattern pattern : patterns) {
if (pattern instanceof OnePointPattern) {
onePointSummand = onePointSummand == null ? pattern : onePointSummand.minkowskiAdd(pattern);
if (!(onePointSummand instanceof OnePointPattern)) {
throw new AssertionError("Invalid OnePointPattern.minkowskiAdd implementation");
}
} else if (pattern instanceof UniformGridPattern ugPattern
&& ((UniformGridPattern) pattern).isActuallyRectangular())
{
ugPattern = new BasicRectangularPattern(ugPattern.originOfGrid(), ugPattern.stepsOfGrid(),
ugPattern.gridIndexArea().ranges());
Point steps = Point.valueOf(ugPattern.stepsOfGrid());
UniformGridPattern previousSummand = rectangularSummands.get(steps);
pattern = previousSummand == null ? ugPattern : previousSummand.minkowskiAdd(ugPattern);
if (!(pattern instanceof BasicRectangularPattern)) {
throw new AssertionError("Invalid RectangularUniformGridPattern.minkowskiAdd implementation");
}
rectangularSummands.put(steps, (BasicRectangularPattern) pattern);
} else {
Integer previousNumber = numbersOfEquals.get(pattern);
if (previousNumber == null) {
numbersOfEquals.put(pattern, 1);
} else {
numbersOfEquals.put(pattern, previousNumber + 1);
}
}
}
List> multiPatterns =
new ArrayList<>(numbersOfEquals.entrySet());
// Sorting by decreasing number of points
multiPatterns.sort((o1, o2) -> {
long pointCount1 = o1.getKey().pointCount();
long pointCount2 = o2.getKey().pointCount();
return Long.compare(pointCount2, pointCount1);
});
List result = new ArrayList<>(rectangularSummands.values());
if (onePointSummand != null) {
if (result.isEmpty()) {
result.add(onePointSummand);
} else {
result.set(0, onePointSummand.minkowskiAdd(result.get(0)));
}
}
Pattern last = null;
for (Map.Entry multiPattern : multiPatterns) {
Pattern p = multiPattern.getKey();
int n = multiPattern.getValue();
Pattern c = null;
if (n > 1 || last != null) {
c = p.carcass();
}
if (last != null && last.minkowskiAdd(p).equals(last.minkowskiAdd(c))) {
// probably true, because patterns were sorted
result.add(c);
} else {
result.add(p);
}
n--; // 1 pattern used (included into result);
if (n > 0) {
int maxMultiplier = p.maxCarcassMultiplier();
for (int m = 1; ; ) {
if (m > n) {
m = n;
}
assert c != null; // because n > 0 after n--
result.add(c.multiply(m));
n -= m; // m patterns used now
if (n == 0) {
break;
}
assert n >= 0 : "Counter overflow while optimizing Minkowski sum";
if (2 * m >= 0 && // no overflow yet
2 * m <= maxMultiplier)
{
m *= 2;
}
}
}
last = p;
}
return result;
}
}