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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
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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 Line. 
Since:
3.0/** This class represents a sub-hyperplane for {@link Line}.
 * @since 3.0
 */
public class SubLine extends AbstractSubHyperplane<Euclidean2D, Euclidean1D> {

    
Default value for tolerance. /** Default value for tolerance. */
    private static final double DEFAULT_TOLERANCE = 1.0e-10;

    
Simple constructor.
Params:
hyperplane – underlying hyperplane
remainingRegion – remaining region of the hyperplane/** Simple constructor.
     * @param hyperplane underlying hyperplane
     * @param remainingRegion remaining region of the hyperplane
     */
    public SubLine(final Hyperplane<Euclidean2D> hyperplane,
                   final Region<Euclidean1D> remainingRegion) {
        super(hyperplane, remainingRegion);
    }

    
Create a sub-line from two endpoints.
Params:
start – start point
end – end point
tolerance – tolerance below which points are considered identical
Since:
3.3/** 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.
Params:
start – start point
end – end point
Deprecated:
as of 3.3, replaced with SubLine(Vector2D, Vector2D, double)/** 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.
Params:
segment – single segment forming the sub-line/** 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.

Returns:
list of segments endpoints/** Get the endpoints of the sub-line.
     * <p>
     * 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.
     * </p>
     * @return list of segments endpoints
     */
    public List<Segment> getSegments() {

        final Line line = (Line) getHyperplane();
        final List<Interval> list = ((IntervalsSet) getRemainingRegion()).asList();
        final List<Segment> segments = new ArrayList<Segment>(list.size());

        for (final Interval interval : list) {
            final Vector2D start = line.toSpace((Point<Euclidean1D>) new Vector1D(interval.getInf()));
            final Vector2D end   = line.toSpace((Point<Euclidean1D>) 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 
intersection method in the Line class, but in addition to compute the point along infinite lines, it also checks the point lies on both sub-line ranges. 
Params:
subLine – other sub-line which may intersect instance
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
Returns:
the intersection point if there is one, null if the sub-lines don't intersect/** Get the intersection of the instance and another sub-line.
     * <p>
     * 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.
     * </p>
     * @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<Euclidean2D>) v2D));

        // check location of point with respect to second sub-line
        Location loc2 = subLine.getRemainingRegion().checkPoint(line2.toSubSpace((Point<Euclidean2D>) 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.
Params:
start – start point
end – end point
tolerance – tolerance below which points are considered identical
Returns:
an interval set/** 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<Euclidean2D>) start).getX(),
                                line.toSubSpace((Point<Euclidean2D>) end).getX(),
                                tolerance);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    protected AbstractSubHyperplane<Euclidean2D, Euclidean1D> buildNew(final Hyperplane<Euclidean2D> hyperplane,
                                                                       final Region<Euclidean1D> remainingRegion) {
        return new SubLine(hyperplane, remainingRegion);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    public SplitSubHyperplane<Euclidean2D> split(final Hyperplane<Euclidean2D> 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<Euclidean2D>(null, this);
            } else if (global > tolerance) {
                return new SplitSubHyperplane<Euclidean2D>(this, null);
            } else {
                return new SplitSubHyperplane<Euclidean2D>(null, null);
            }
        }

        // the lines do intersect
        final boolean direct = FastMath.sin(thisLine.getAngle() - otherLine.getAngle()) < 0;
        final Vector1D x      = thisLine.toSubSpace((Point<Euclidean2D>) crossing);
        final SubHyperplane<Euclidean1D> subPlus  =
                new OrientedPoint(x, !direct, tolerance).wholeHyperplane();
        final SubHyperplane<Euclidean1D> subMinus =
                new OrientedPoint(x,  direct, tolerance).wholeHyperplane();

        final BSPTree<Euclidean1D> splitTree = getRemainingRegion().getTree(false).split(subMinus);
        final BSPTree<Euclidean1D> plusTree  = getRemainingRegion().isEmpty(splitTree.getPlus()) ?
                                               new BSPTree<Euclidean1D>(Boolean.FALSE) :
                                               new BSPTree<Euclidean1D>(subPlus, new BSPTree<Euclidean1D>(Boolean.FALSE),
                                                                        splitTree.getPlus(), null);
        final BSPTree<Euclidean1D> minusTree = getRemainingRegion().isEmpty(splitTree.getMinus()) ?
                                               new BSPTree<Euclidean1D>(Boolean.FALSE) :
                                               new BSPTree<Euclidean1D>(subMinus, new BSPTree<Euclidean1D>(Boolean.FALSE),
                                                                        splitTree.getMinus(), null);
        return new SplitSubHyperplane<Euclidean2D>(new SubLine(thisLine.copySelf(), new IntervalsSet(plusTree, tolerance)),
                                                   new SubLine(thisLine.copySelf(), new IntervalsSet(minusTree, tolerance)));

    }

}