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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.twod;
import java.util.ArrayList;
import java.util.List;
import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.euclidean.oned.Euclidean1D;
import org.apache.commons.math3.geometry.euclidean.oned.Interval;
import org.apache.commons.math3.geometry.euclidean.oned.IntervalsSet;
import org.apache.commons.math3.geometry.euclidean.oned.OrientedPoint;
import org.apache.commons.math3.geometry.euclidean.oned.Vector1D;
import org.apache.commons.math3.geometry.partitioning.AbstractSubHyperplane;
import org.apache.commons.math3.geometry.partitioning.BSPTree;
import org.apache.commons.math3.geometry.partitioning.Hyperplane;
import org.apache.commons.math3.geometry.partitioning.Region;
import org.apache.commons.math3.geometry.partitioning.Region.Location;
import org.apache.commons.math3.geometry.partitioning.SubHyperplane;
import org.apache.commons.math3.util.FastMath;
/** This class represents a sub-hyperplane for {@link Line}.
* @since 3.0
*/
public class SubLine extends AbstractSubHyperplane {
/** Default value for tolerance. */
private static final double DEFAULT_TOLERANCE = 1.0e-10;
/** Simple constructor.
* @param hyperplane underlying hyperplane
* @param remainingRegion remaining region of the hyperplane
*/
public SubLine(final Hyperplane hyperplane,
final Region remainingRegion) {
super(hyperplane, remainingRegion);
}
/** Create a sub-line from two endpoints.
* @param start start point
* @param end end point
* @param tolerance tolerance below which points are considered identical
* @since 3.3
*/
public SubLine(final Vector2D start, final Vector2D end, final double tolerance) {
super(new Line(start, end, tolerance), buildIntervalSet(start, end, tolerance));
}
/** Create a sub-line from two endpoints.
* @param start start point
* @param end end point
* @deprecated as of 3.3, replaced with {@link #SubLine(Vector2D, Vector2D, double)}
*/
@Deprecated
public SubLine(final Vector2D start, final Vector2D end) {
this(start, end, DEFAULT_TOLERANCE);
}
/** Create a sub-line from a segment.
* @param segment single segment forming the sub-line
*/
public SubLine(final Segment segment) {
super(segment.getLine(),
buildIntervalSet(segment.getStart(), segment.getEnd(), segment.getLine().getTolerance()));
}
/** Get the endpoints of the sub-line.
*
* A subline may be any arbitrary number of disjoints segments, so the endpoints
* are provided as a list of endpoint pairs. Each element of the list represents
* one segment, and each segment contains a start point at index 0 and an end point
* at index 1. If the sub-line is unbounded in the negative infinity direction,
* the start point of the first segment will have infinite coordinates. If the
* sub-line is unbounded in the positive infinity direction, the end point of the
* last segment will have infinite coordinates. So a sub-line covering the whole
* line will contain just one row and both elements of this row will have infinite
* coordinates. If the sub-line is empty, the returned list will contain 0 segments.
*
* @return list of segments endpoints
*/
public List getSegments() {
final Line line = (Line) getHyperplane();
final List list = ((IntervalsSet) getRemainingRegion()).asList();
final List segments = new ArrayList(list.size());
for (final Interval interval : list) {
final Vector2D start = line.toSpace((Point) new Vector1D(interval.getInf()));
final Vector2D end = line.toSpace((Point) new Vector1D(interval.getSup()));
segments.add(new Segment(start, end, line));
}
return segments;
}
/** Get the intersection of the instance and another sub-line.
*
* This method is related to the {@link Line#intersection(Line)
* intersection} method in the {@link Line Line} class, but in addition
* to compute the point along infinite lines, it also checks the point
* lies on both sub-line ranges.
*
* @param subLine other sub-line which may intersect instance
* @param includeEndPoints if true, endpoints are considered to belong to
* instance (i.e. they are closed sets) and may be returned, otherwise endpoints
* are considered to not belong to instance (i.e. they are open sets) and intersection
* occurring on endpoints lead to null being returned
* @return the intersection point if there is one, null if the sub-lines don't intersect
*/
public Vector2D intersection(final SubLine subLine, final boolean includeEndPoints) {
// retrieve the underlying lines
Line line1 = (Line) getHyperplane();
Line line2 = (Line) subLine.getHyperplane();
// compute the intersection on infinite line
Vector2D v2D = line1.intersection(line2);
if (v2D == null) {
return null;
}
// check location of point with respect to first sub-line
Location loc1 = getRemainingRegion().checkPoint(line1.toSubSpace((Point) v2D));
// check location of point with respect to second sub-line
Location loc2 = subLine.getRemainingRegion().checkPoint(line2.toSubSpace((Point) v2D));
if (includeEndPoints) {
return ((loc1 != Location.OUTSIDE) && (loc2 != Location.OUTSIDE)) ? v2D : null;
} else {
return ((loc1 == Location.INSIDE) && (loc2 == Location.INSIDE)) ? v2D : null;
}
}
/** Build an interval set from two points.
* @param start start point
* @param end end point
* @param tolerance tolerance below which points are considered identical
* @return an interval set
*/
private static IntervalsSet buildIntervalSet(final Vector2D start, final Vector2D end, final double tolerance) {
final Line line = new Line(start, end, tolerance);
return new IntervalsSet(line.toSubSpace((Point) start).getX(),
line.toSubSpace((Point) end).getX(),
tolerance);
}
/** {@inheritDoc} */
@Override
protected AbstractSubHyperplane buildNew(final Hyperplane hyperplane,
final Region remainingRegion) {
return new SubLine(hyperplane, remainingRegion);
}
/** {@inheritDoc} */
@Override
public SplitSubHyperplane split(final Hyperplane hyperplane) {
final Line thisLine = (Line) getHyperplane();
final Line otherLine = (Line) hyperplane;
final Vector2D crossing = thisLine.intersection(otherLine);
final double tolerance = thisLine.getTolerance();
if (crossing == null) {
// the lines are parallel
final double global = otherLine.getOffset(thisLine);
if (global < -tolerance) {
return new SplitSubHyperplane(null, this);
} else if (global > tolerance) {
return new SplitSubHyperplane(this, null);
} else {
return new SplitSubHyperplane(null, null);
}
}
// the lines do intersect
final boolean direct = FastMath.sin(thisLine.getAngle() - otherLine.getAngle()) < 0;
final Vector1D x = thisLine.toSubSpace((Point) crossing);
final SubHyperplane subPlus =
new OrientedPoint(x, !direct, tolerance).wholeHyperplane();
final SubHyperplane subMinus =
new OrientedPoint(x, direct, tolerance).wholeHyperplane();
final BSPTree splitTree = getRemainingRegion().getTree(false).split(subMinus);
final BSPTree plusTree = getRemainingRegion().isEmpty(splitTree.getPlus()) ?
new BSPTree(Boolean.FALSE) :
new BSPTree(subPlus, new BSPTree(Boolean.FALSE),
splitTree.getPlus(), null);
final BSPTree minusTree = getRemainingRegion().isEmpty(splitTree.getMinus()) ?
new BSPTree(Boolean.FALSE) :
new BSPTree(subMinus, new BSPTree(Boolean.FALSE),
splitTree.getMinus(), null);
return new SplitSubHyperplane(new SubLine(thisLine.copySelf(), new IntervalsSet(plusTree, tolerance)),
new SubLine(thisLine.copySelf(), new IntervalsSet(minusTree, tolerance)));
}
}