package org.djutils.draw.line;
   
   import java.awt.geom.Path2D;
   import java.awt.geom.PathIterator;
   import java.util.ArrayList;
   import java.util.Arrays;
   import java.util.Iterator;
   import java.util.List;
   import java.util.Locale;
  import java.util.NoSuchElementException;
  import java.util.function.Function;
  
  import org.djutils.draw.DrawRuntimeException;
  import org.djutils.draw.Drawable2d;
  import org.djutils.draw.bounds.Bounds2d;
  import org.djutils.draw.point.Point2d;
  import org.djutils.exceptions.Throw;
  import org.djutils.logger.CategoryLogger;
  
  /**
   * Implementation of PolyLine for 2D space.
   * <p>
   * Copyright (c) 2020-2022 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved. <br>
   * BSD-style license. See <a href="https://djutils.org/docs/current/djutils/licenses.html">DJUTILS License</a>.
   * </p>
   * @author <a href="https://www.tudelft.nl/averbraeck">Alexander Verbraeck</a>
   * @author <a href="https://www.tudelft.nl/pknoppers">Peter Knoppers</a>
   */
  public class PolyLine2d implements Drawable2d, PolyLine<PolyLine2d, Point2d, Ray2d, LineSegment2d>
  {
      /** */
      private static final long serialVersionUID = 20200911L;
  
      /** X-coordinates of the points. */
      private final double[] x;
  
      /** Y-coordinates of the points. */
      private final double[] y;
  
      /** The cumulative length of the line at point 'i'. */
      private final double[] lengthIndexedLine;
  
      /** The length. */
      private final double length;
  
      /** Bounding rectangle of this PolyLine2d. */
      private final Bounds2d bounds;
  
      /** Heading at start point (only needed for degenerate PolyLine2d). */
      private final double startHeading;
  
      /**
       * Construct a new PolyLine2d from an array of double x values and an array of double y values.
       * @param copyNeeded boolean; if true; a deep copy of the points array is stored instead of the provided array
       * @param x double[]; the x-coordinates of the points
       * @param y double[]; the y-coordinates of the points
       * @throws NullPointerException when iterator is null
       * @throws DrawRuntimeException when the provided points do not constitute a valid line (too few points or identical
       *             adjacent points)
       */
      PolyLine2d(final boolean copyNeeded, final double[] x, final double[] y) throws NullPointerException, DrawRuntimeException
      {
          Throw.whenNull(x, "x array may not be null");
          Throw.whenNull(y, "y array may not be null");
          Throw.when(x.length != y.length, DrawRuntimeException.class, "x and y arrays must have same length");
          Throw.when(x.length < 2, DrawRuntimeException.class, "Need at least two points");
          this.x = copyNeeded ? Arrays.copyOf(x, x.length) : x;
          this.y = copyNeeded ? Arrays.copyOf(y, y.length) : y;
          double minX = x[0];
          double minY = y[0];
          double maxX = x[0];
          double maxY = y[0];
          this.lengthIndexedLine = new double[x.length];
          this.lengthIndexedLine[0] = 0.0;
          for (int i = 1; i < x.length; i++)
          {
              minX = Math.min(minX, x[i]);
              minY = Math.min(minY, y[i]);
              maxX = Math.max(maxX, x[i]);
              maxY = Math.max(maxY, y[i]);
              if (x[i - 1] == x[i] && y[i - 1] == y[i])
              {
                  throw new DrawRuntimeException(
                          "Degenerate PolyLine2d; point " + (i - 1) + " has the same x and y as point " + i);
              }
              this.lengthIndexedLine[i] = this.lengthIndexedLine[i - 1] + Math.hypot(x[i] - x[i - 1], y[i] - y[i - 1]);
          }
          this.length = this.lengthIndexedLine[this.lengthIndexedLine.length - 1];
          this.bounds = new Bounds2d(minX, maxX, minY, maxY);
          this.startHeading = Double.NaN;
      }
  
      /**
       * Construct a degenerate PolyLine2d (consisting of only one point).
       * @param x double; the x-coordinate
       * @param y double; the y-coordinate
       * @param heading double; the heading in radians
       * @throws DrawRuntimeException when x, y, or heading is NaN, or heading is infinite
       */
     public PolyLine2d(final double x, final double y, final double heading) throws DrawRuntimeException
     {
         Throw.when(Double.isNaN(x), DrawRuntimeException.class, "x may not be NaN");
         Throw.when(Double.isNaN(y), DrawRuntimeException.class, "y may not be NaN");
         Throw.when(Double.isNaN(heading), DrawRuntimeException.class, "heading may not be NaN");
         Throw.when(Double.isInfinite(heading), DrawRuntimeException.class, "heading must be finite");
         this.x = new double[] { x };
         this.y = new double[] { y };
         this.startHeading = heading;
         this.length = 0;
         this.bounds = new Bounds2d(x, x, y, y);
         this.lengthIndexedLine = new double[] { 0.0 };
     }
 
     /**
      * Construct a degenerate PolyLine2d (consisting of only one point).
      * @param p Point2d; the point of the degenerate PolyLine2d
      * @param heading double; the heading in radians
      * @throws NullPointerException when p is null
      * @throws DrawRuntimeException when heading is infinite
      */
     public PolyLine2d(final Point2d p, final double heading) throws NullPointerException, DrawRuntimeException
     {
         this(Throw.whenNull(p, "p may not be null").x, p.y, heading);
     }
 
     /**
      * Construct a degenerate PolyLine2d (consisting of only one point).
      * @param r Ray2d; point and heading of the degenerate PolyLine2d
      * @throws NullPointerException when p is null
      * @throws DrawRuntimeException when heading is infinite
      */
     public PolyLine2d(final Ray2d r) throws NullPointerException, DrawRuntimeException
     {
         this(Throw.whenNull(r, "r may not be NaN").x, r.y, r.phi);
     }
 
     /**
      * Construct a new PolyLine2d from an array of Point2d. This constructor makes a deep copy of the parameters.
      * @param x double[]; the x-coordinates of the points
      * @param y double[]; the y-coordinates of the points
      * @throws NullPointerException when iterator is null
      * @throws DrawRuntimeException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine2d(final double[] x, final double[] y) throws NullPointerException, DrawRuntimeException
     {
         this(true, x, y);
     }
 
     /**
      * Construct a new PolyLine2d from an array of Point2d.
      * @param points Point2d[]; the array of points to construct this PolyLine2d from.
      * @throws NullPointerException when the array is null
      * @throws DrawRuntimeException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine2d(final Point2d[] points) throws NullPointerException, DrawRuntimeException
     {
         this(false, makeArray(Throw.whenNull(points, "points may not be null"), p -> p.x), makeArray(points, p -> p.y));
     }
 
     /**
      * Make an array of double an fill it with the appropriate coordinate of points.
      * @param points Point2d[]; array of points
      * @param getter Function&lt;Point2d, Double&gt;; function that obtains the intended coordinate
      * @return double[]; array of double filled with the requested coordinate values
      */
     protected static double[] makeArray(final Point2d[] points, final Function<Point2d, Double> getter)
     {
         double[] array = new double[points.length];
         for (int index = 0; index < points.length; index++)
         {
             array[index] = getter.apply(points[index]);
         }
         return array;
     }
 
     /**
      * Construct a new PolyLine2d from an array of Point2d.
      * @param point1 Point2d; starting point of the PolyLine2d
      * @param point2 Point2d; second point of the PolyLine2d
      * @param otherPoints Point2d...; additional points of the PolyLine2d (may be null)
      * @throws NullPointerException when iterator is null
      * @throws DrawRuntimeException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine2d(final Point2d point1, final Point2d point2, final Point2d... otherPoints)
             throws NullPointerException, DrawRuntimeException
     {
         this(spliceArray(Throw.whenNull(point1, "point1 may not be null"), Throw.whenNull(point2, "point2 may not be null"),
                 otherPoints));
     }
 
     /**
      * Construct an array of Point2d from two points plus an array of Point2d.
      * @param point1 Point2d; the first point (ends up at index 0 of the result)
      * @param point2 Point2d; the second point (ends up at index 1 of the result)
      * @param otherPoints Point2d...; may be null, may be empty. If non empty, the elements in otherPoints end up at index 2 and
      *            up in the result
      * @return Point2d[]; the combined array
      */
     private static Point2d[] spliceArray(final Point2d point1, final Point2d point2, final Point2d... otherPoints)
     {
         Point2d[] result = new Point2d[2 + (otherPoints == null ? 0 : otherPoints.length)];
         result[0] = point1;
         result[1] = point2;
         if (otherPoints != null)
         {
             for (int i = 0; i < otherPoints.length; i++)
             {
                 result[i + 2] = otherPoints[i];
             }
         }
         return result;
     }
 
     /**
      * Construct a new PolyLine2d from an iterator that yields Point2d objects.
      * @param iterator Iterator&lt;Point2d&gt;; iterator that will provide all points that constitute the new PolyLine2d
      * @throws NullPointerException when iterator is null
      * @throws DrawRuntimeException when the iterator provides too few points, or some adjacent identical points)
      */
     public PolyLine2d(final Iterator<Point2d> iterator) throws NullPointerException, DrawRuntimeException
     {
         this(iteratorToList(Throw.whenNull(iterator, "iterator cannot be null")));
     }
 
     /**
      * Construct a new PolyLine2d from a List&lt;Point2d&gt;.
      * @param pointList List&lt;Point2d&gt;; the list of points to construct this PolyLine2d from.
      * @throws DrawRuntimeException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      * @throws NullPointerException when pointList is null
      */
     public PolyLine2d(final List<Point2d> pointList) throws DrawRuntimeException, NullPointerException
     {
         this(pointList.toArray(new Point2d[Throw.whenNull(pointList, "pointList may not be null").size()]));
     }
 
     /**
      * Construct a new PolyLine2d (closed shape) from a Path2D.
      * @param path Path2D; the Path2D to construct this PolyLine2d from.
      * @throws DrawRuntimeException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      * @throws NullPointerException when path is null
      */
     public PolyLine2d(final Path2D path) throws DrawRuntimeException, NullPointerException
     {
         this(path2DtoArray(Throw.whenNull(path, "path may not be null")));
     }
 
     /**
      * Convert a path2D to a Point2d[] array to construct the line.
      * @param path Path2D; the path to convert
      * @return Point2d[]; an array of points based on MOVETO and LINETO elements of the Path2D
      * @throws DrawRuntimeException when the pathIterator of the path returns an unsupported command
      */
     private static Point2d[] path2DtoArray(final Path2D path) throws DrawRuntimeException
     {
         List<Point2d> result = new ArrayList<>();
         for (PathIterator pi = path.getPathIterator(null); !pi.isDone(); pi.next())
         {
             double[] p = new double[6];
             int segType = pi.currentSegment(p);
             if (segType == PathIterator.SEG_MOVETO || segType == PathIterator.SEG_LINETO)
             {
                 result.add(new Point2d(p[0], p[1]));
             }
             else if (segType == PathIterator.SEG_CLOSE)
             {
                 if (!result.get(0).equals(result.get(result.size() - 1)))
                 {
                     result.add(result.get(0));
                 }
                 break;
             }
             else
             {
                 throw new DrawRuntimeException("path2DtoArray only handles SEG_MOVETO, SEG_LINETO and SEG_CLOSE");
             }
         }
         return result.toArray(new Point2d[result.size() - 1]);
     }
 
     /**
      * Build a list from the Point2d objects that an iterator provides.
      * @param iterator Iterator&lt;Point2d&gt;; the iterator that will provide the points
      * @return List&lt;Point2d&gt;; a list of the points provided by the iterator
      */
     protected static List<Point2d> iteratorToList(final Iterator<Point2d> iterator)
     {
         List<Point2d> result = new ArrayList<>();
         iterator.forEachRemaining(result::add);
         return result;
     }
 
     /**
      * Create a new PolyLine2d, optionally filtering out repeating successive points.
      * @param filterDuplicates boolean; if true; filter out successive repeated points; otherwise do not filter
      * @param points Point2d...; the coordinates of the line as Point2d
      * @throws DrawRuntimeException when number of points &lt; 2
      */
     public PolyLine2d(final boolean filterDuplicates, final Point2d... points) throws DrawRuntimeException
     {
         this(PolyLine2d.cleanPoints(filterDuplicates, Arrays.stream(points).iterator()));
     }
 
     /**
      * Create a new PolyLine2d, optionally filtering out repeating successive points.
      * @param filterDuplicates boolean; if true; filter out successive repeated points; otherwise do not filter
      * @param pointList List&lt;Point2d&gt;; list of the coordinates of the line as Point3d; any duplicate points in this list
      *            are removed (this method may modify the provided list)
      * @throws DrawRuntimeException when number of non-equal points &lt; 2
      */
     public PolyLine2d(final boolean filterDuplicates, final List<Point2d> pointList) throws DrawRuntimeException
     {
         this(PolyLine2d.cleanPoints(filterDuplicates, pointList.iterator()));
     }
 
     /**
      * Return an iterator that optionally skips identical successive points.
      * @param filter boolean; if true; filter out itentical successive points; if false; do not filter
      * @param iterator Iterator&lt;Point2d&gt;; iterator that generates points, potentially with successive duplicates
      * @return Iterator&lt;Point2d&gt;; iterator that skips identical successive points
      */
     static Iterator<Point2d> cleanPoints(final boolean filter, final Iterator<Point2d> iterator)
     {
         Throw.whenNull(iterator, "Iterator may not be null");
         Throw.when(!iterator.hasNext(), DrawRuntimeException.class, "Iterator has no points to return");
         if (!filter)
         {
             return iterator;
         }
         return new Iterator<Point2d>()
         {
             private Point2d currentPoint = iterator.next();
 
             @Override
             public boolean hasNext()
             {
                 return this.currentPoint != null;
             }
 
             @Override
             public Point2d next()
             {
                 Throw.when(this.currentPoint == null, NoSuchElementException.class, "Out of input");
                 Point2d result = this.currentPoint;
                 this.currentPoint = null;
                 while (iterator.hasNext())
                 {
                     this.currentPoint = iterator.next();
                     if (result.x != this.currentPoint.x || result.y != this.currentPoint.y)
                     {
                         break;
                     }
                     this.currentPoint = null;
                 }
                 return result;
             }
         };
     }
 
     /** {@inheritDoc} */
     @Override
     public PolyLine2d instantiate(final List<Point2d> pointList) throws NullPointerException, DrawRuntimeException
     {
         return new PolyLine2d(pointList);
     }
 
     /** {@inheritDoc} */
     @Override
     public int size()
     {
         return this.x.length;
     }
 
     /** {@inheritDoc} */
     @Override
     public final Point2d get(final int i) throws IndexOutOfBoundsException
     {
         return new Point2d(this.x[i], this.y[i]);
     }
 
     /** {@inheritDoc} */
     @Override
     public final double getX(final int i) throws IndexOutOfBoundsException
     {
         return this.x[i];
     }
 
     /** {@inheritDoc} */
     @Override
     public final double getY(final int i) throws IndexOutOfBoundsException
     {
         return this.y[i];
     }
 
     /** {@inheritDoc} */
     @Override
     public LineSegment2d getSegment(final int index)
     {
         Throw.when(index < 0 || index >= this.x.length - 1, DrawRuntimeException.class, "index must be in range 0..size() - 1");
         return new LineSegment2d(this.x[index], this.y[index], this.x[index + 1], this.y[index + 1]);
     }
 
     /** {@inheritDoc} */
     @Override
     public final double lengthAtIndex(final int index)
     {
         return this.lengthIndexedLine[index];
     }
 
     /** {@inheritDoc} */
     @Override
     public double getLength()
     {
         return this.length;
     }
 
     /** {@inheritDoc} */
     @Override
     public Iterator<Point2d> getPoints()
     {
         return new Iterator<Point2d>()
         {
             private int nextIndex = 0;
 
             /** {@inheritDoc} */
             @Override
             public boolean hasNext()
             {
                 return this.nextIndex < size();
             }
 
             /** {@inheritDoc} */
             @Override
             public Point2d next()
             {
                 return get(this.nextIndex++);
             }
         };
     }
 
     /** {@inheritDoc} */
     @Override
     public Bounds2d getBounds()
     {
         return this.bounds;
     }
 
     /** {@inheritDoc} */
     @Override
     public final PolyLine2d noiseFilteredLine(final double noiseLevel)
     {
         if (this.size() <= 2)
         {
             return this; // Except for some cached fields; a PolyLine2d is immutable; so safe to return
         }
         Point2d prevPoint = null;
         List<Point2d> list = new ArrayList<>();
         for (int index = 0; index < this.size(); index++)
         {
             Point2d currentPoint = get(index);
             if (null != prevPoint && prevPoint.distance(currentPoint) < noiseLevel)
             {
                 if (index == this.size() - 1)
                 {
                     if (list.size() > 1)
                     {
                         // Replace the last point of the result by the last point of this PolyLine2d
                         list.set(list.size() - 1, currentPoint);
                     }
                     else
                     {
                         // Append the last point of this even though it is close to the first point than the noise value to
                         // comply with the requirement that first and last point of this are ALWAYS included in the result.
                         list.add(currentPoint);
                     }
                 }
                 continue; // Do not replace prevPoint by currentPoint
             }
             list.add(currentPoint);
             prevPoint = currentPoint;
         }
         if (list.size() == this.x.length)
         {
             return this;
         }
         if (list.size() == 2 && list.get(0).equals(list.get(1)))
         {
             // Insert point 1 of this; it MUST be different from point 0; so we don't have to test for anything.
             list.add(1, get(1));
         }
         try
         {
             return new PolyLine2d(list);
         }
         catch (DrawRuntimeException exception)
         {
             // Cannot happen
             CategoryLogger.always().error(exception);
             throw new Error(exception);
         }
     }
 
     /**
      * Concatenate several PolyLine2d instances.
      * @param lines PolyLine2d...; One or more PolyLine2d objects. The last point of the first &lt;strong&gt;must&lt;/strong&gt;
      *            match the first of the second, etc.
      * @return PolyLine2d
      * @throws DrawRuntimeException if zero lines are given, or when there is a gap between consecutive lines
      */
     public static PolyLine2d concatenate(final PolyLine2d... lines) throws DrawRuntimeException
     {
         return concatenate(0.0, lines);
     }
 
     /**
      * Concatenate two PolyLine2d instances. This method is separate for efficiency reasons.
      * @param tolerance double; the tolerance between the end point of a line and the first point of the next line
      * @param line1 PolyLine2d; first line
      * @param line2 PolyLine2d; second line
      * @return PolyLine2d; the concatenation of the two lines
      * @throws DrawRuntimeException if zero lines are given, or when there is a gap between consecutive lines
      */
     public static PolyLine2d concatenate(final double tolerance, final PolyLine2d line1, final PolyLine2d line2)
             throws DrawRuntimeException
     {
         if (line1.getLast().distance(line2.getFirst()) > tolerance)
         {
             throw new DrawRuntimeException("Lines are not connected: " + line1.getLast() + " to " + line2.getFirst()
                     + " distance is " + line1.getLast().distance(line2.getFirst()) + " > " + tolerance);
         }
         int size = line1.size() + line2.size() - 1;
         Point2d[] points = new Point2d[size];
         int nextIndex = 0;
         for (int j = 0; j < line1.size(); j++)
         {
             points[nextIndex++] = line1.get(j);
         }
         for (int j = 1; j < line2.size(); j++)
         {
             points[nextIndex++] = line2.get(j);
         }
         return new PolyLine2d(points);
     }
 
     /**
      * Concatenate several PolyLine2d instances.
      * @param tolerance double; the tolerance between the end point of a line and the first point of the next line
      * @param lines PolyLine2d...; one or more PolyLine2d objects. The last point of the first &lt;strong&gt;must&lt;/strong&gt;
      *            match the first of the second, etc.
      * @return PolyLine2d; the concatenation of the lines
      * @throws DrawRuntimeException if zero lines are given, or when there is a gap between consecutive lines
      */
     public static PolyLine2d concatenate(final double tolerance, final PolyLine2d... lines) throws DrawRuntimeException
     {
         if (0 == lines.length)
         {
             throw new DrawRuntimeException("Empty argument list");
         }
         else if (1 == lines.length)
         {
             return lines[0];
         }
         int size = lines[0].size();
         for (int i = 1; i < lines.length; i++)
         {
             if (lines[i - 1].getLast().distance(lines[i].getFirst()) > tolerance)
             {
                 throw new DrawRuntimeException(
                         "Lines are not connected: " + lines[i - 1].getLast() + " to " + lines[i].getFirst() + " distance is "
                                 + lines[i - 1].getLast().distance(lines[i].getFirst()) + " > " + tolerance);
             }
             size += lines[i].size() - 1;
         }
         Point2d[] points = new Point2d[size];
         int nextIndex = 0;
         for (int i = 0; i < lines.length; i++)
         {
             PolyLine2d line = lines[i];
             for (int j = 0 == i ? 0 : 1; j < line.size(); j++)
             {
                 points[nextIndex++] = line.get(j);
             }
         }
         return new PolyLine2d(points);
     }
 
     /** {@inheritDoc} */
     @Override
     public final Ray2d getLocationExtended(final double position)
     {
         if (position >= 0.0 && position <= getLength())
         {
             try
             {
                 return getLocation(position);
             }
             catch (DrawRuntimeException exception)
             {
                 // cannot happen
             }
         }
 
         // position before start point -- extrapolate using direction from first point to second point of this PolyLine2d
         if (position < 0.0)
         {
             double fraction = position / (this.lengthIndexedLine[1] - this.lengthIndexedLine[0]);
             return new Ray2d(this.x[0] + fraction * (this.x[1] - this.x[0]), this.y[0] + fraction * (this.y[1] - this.y[0]),
                     this.x[1], this.y[1]);
         }
 
         // position beyond end point -- extrapolate using the direction from the before last point to the last point of this
         // PolyLine2d
         int n1 = this.x.length - 1; // index of last point
         int n2 = this.x.length - 2; // index of before last point
         double len = position - getLength();
         double fraction = len / (this.lengthIndexedLine[n1] - this.lengthIndexedLine[n2]);
         while (Double.isInfinite(fraction))
         {
             // Overflow occurred; move n2 back another point; if possible
             if (--n2 < 0)
             {
                 CategoryLogger.always().error("lengthIndexedLine of {} is invalid", this);
                 return new Ray2d(this.x[n1], this.y[n1], 0.0); // Bogus direction
             }
             fraction = len / (this.lengthIndexedLine[n1] - this.lengthIndexedLine[n2]);
         }
         return new Ray2d(this.x[n1] + fraction * (this.x[n1] - this.x[n2]), this.y[n1] + fraction * (this.y[n1] - this.y[n2]),
                 Math.atan2(this.y[n1] - this.y[n2], this.x[n1] - this.x[n2]));
     }
 
     /** {@inheritDoc} */
     @Override
     public final Ray2d getLocation(final double position) throws DrawRuntimeException
     {
         Throw.when(Double.isNaN(position), DrawRuntimeException.class, "position may not be NaN");
         Throw.when(position < 0.0 || position > getLength(), DrawRuntimeException.class,
                 "getLocation for line: position < 0.0 or > line length. Position = " + position + "; length = " + getLength());
         // handle special cases: position == 0.0, or position == length
         if (position == 0.0)
         {
             if (this.lengthIndexedLine.length == 1) // Extra special case; degenerate PolyLine2d
             {
                 return new Ray2d(this.x[0], this.y[0], this.startHeading);
             }
             return new Ray2d(this.x[0], this.y[0], this.x[1], this.y[1]);
         }
         if (position == getLength())
         {
             return new Ray2d(this.x[this.x.length - 1], this.y[this.x.length - 1],
                     2 * this.x[this.x.length - 1] - this.x[this.x.length - 2],
                     2 * this.y[this.x.length - 1] - this.y[this.x.length - 2]);
         }
         // find the index of the line segment, use binary search
         int index = find(position);
         double remainder = position - this.lengthIndexedLine[index];
         double fraction = remainder / (this.lengthIndexedLine[index + 1] - this.lengthIndexedLine[index]);
         // if (fraction >= 1.0 && index < this.x.length - 1)
         // {
         // // Rounding problem; move to the next segment.
         // index++;
         // remainder = position - this.lengthIndexedLine[index];
         // fraction = remainder / (this.lengthIndexedLine[index + 1] - this.lengthIndexedLine[index]);
         // }
         return new Ray2d(this.x[index] + fraction * (this.x[index + 1] - this.x[index]),
                 this.y[index] + fraction * (this.y[index + 1] - this.y[index]), 2 * this.x[index + 1] - this.x[index],
                 2 * this.y[index + 1] - this.y[index]);
     }
 
     /**
      * Perform the orthogonal projection operation.
      * @param point Point2d; the point to project
      * @param limitHandling Boolean; if Null; results outside the interval 0.0 .. 1.0 are replaced by NaN, if false, results
      *            outside that interval are returned as is; if true results outside the interval are truncated to the interval
      *            and therefore not truly orthogonal
      * @return double; the fractional position on this PolyLine that is closest to point, or NaN
      */
     private double projectOrthogonalFractional(final Point2d point, final Boolean limitHandling)
     {
         Throw.whenNull(point, "point may not be null");
         double result = Double.NaN;
         if (this.lengthIndexedLine.length == 1)
         {
             // This is a degenerate PolyLine2d
             if (null != limitHandling && limitHandling)
             {
                 return 0.0;
             }
             result = getLocation(0.0).projectOrthogonalFractionalExtended(point);
             if (null == limitHandling)
             {
                 return result == 0.0 ? 0.0 : Double.NaN;
             }
             // limitHanling is false
             if (result == 0.0)
             {
                 return 0.0;
             }
             return result > 0 ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
         }
         double bestDistance = Double.POSITIVE_INFINITY;
         double bestDistanceExtended = Double.POSITIVE_INFINITY;
         for (int index = 1; index < this.size(); index++)
         {
             double fraction = point.fractionalPositionOnLine(this.x[index - 1], this.y[index - 1], this.x[index], this.y[index],
                     false, false);
             double distance = Math.hypot(point.x - (this.x[index - 1] + fraction * (this.x[index] - this.x[index - 1])),
                     point.y - (this.y[index - 1] + fraction * (this.y[index] - this.y[index - 1])));
             if (distance < bestDistanceExtended && (fraction >= 0.0 && fraction <= 1.0 || (fraction < 0.0 && index == 1)
                     || fraction > 1.0 && index == this.size() - 1))
             {
                 bestDistanceExtended = distance;
             }
             if (distance < bestDistance && (fraction >= 0.0 || index == 1 && limitHandling != null && !limitHandling)
                     && (fraction <= 1.0 || index == this.size() - 1 && limitHandling != null && !limitHandling))
             {
                 bestDistance = distance;
                 result = lengthAtIndex(index - 1) + fraction * (lengthAtIndex(index) - lengthAtIndex(index - 1));
             }
             else if (fraction < 0.0 && limitHandling != null && limitHandling)
             {
                 distance = Math.hypot(point.x - this.x[index - 1], point.y - this.y[index - 1]);
                 if (distance < bestDistance)
                 {
                     bestDistance = distance;
                     result = lengthAtIndex(index - 1);
                 }
             }
             else if (index == this.size() - 1 && limitHandling != null && limitHandling)
             {
                 distance = Math.hypot(point.x - this.x[index], point.y - this.y[index]);
                 if (distance < bestDistance)
                 {
                     bestDistance = distance;
                     result = lengthAtIndex(index);
                 }
             }
         }
         if (bestDistance > bestDistanceExtended && (limitHandling == null || !limitHandling))
         {
             return Double.NaN;
         }
         return result / getLength();
     }
 
     /** {@inheritDoc} */
     @Override
     public Point2d closestPointOnPolyLine(final Point2d point)
     {
         try
         {
             return getLocation(projectOrthogonalFractional(point, true) * getLength());
         }
         catch (DrawRuntimeException e)
         {
             // Cannot happen
             e.printStackTrace();
             return null;
         }
     }
 
     /**
      * Perform the project orthogonal operation.
      * @param point Point2d; the point to project
      * @param limitHandling Boolean; if Null; results outside this PolyLin2de are replaced by Null, if false, results outside
      *            that interval are returned as is; if true results outside this PolyLine2d are truncated to the first or last
      *            point of this PolyLine2d and therefore not truly orthogonal
      * @return Point2d; the orthogonal projection of point on this PolyLine2d
      */
     private Point2d projectOrthogonal(final Point2d point, final Boolean limitHandling)
     {
         Throw.whenNull(point, "point may not be null");
         if (this.lengthIndexedLine.length == 1) // Handle degenerate case
         {
             // limitHandling == true is not handled because it cannot happen
             Point2d result = this.getLocation(0.0).projectOrthogonalExtended(point);
             if (null == limitHandling)
             {
                 return result.x != this.x[0] || result.y != this.y[0] ? null : get(0);
             }
             // limitHandling is false
             return result;
         }
         double fraction = projectOrthogonalFractional(point, limitHandling);
         if (Double.isNaN(fraction))
         {
             return null;
         }
         return getLocationExtended(fraction * getLength());
     }
 
     /** {@inheritDoc} */
     @Override
     public Point2d projectOrthogonal(final Point2d point) throws NullPointerException
     {
         return projectOrthogonal(point, null);
     }
 
     /** {@inheritDoc} */
     @Override
     public Point2d projectOrthogonalExtended(final Point2d point) throws NullPointerException
     {
         return projectOrthogonal(point, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public final double projectOrthogonalFractional(final Point2d point) throws NullPointerException
     {
         return projectOrthogonalFractional(point, null);
     }
 
     /** {@inheritDoc} */
     @Override
     public double projectOrthogonalFractionalExtended(final Point2d point) throws NullPointerException
     {
         return projectOrthogonalFractional(point, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public PolyLine2d extract(final double start, final double end) throws DrawRuntimeException
     {
         if (Double.isNaN(start) || Double.isNaN(end) || start < 0 || start >= end || end > getLength())
         {
             throw new DrawRuntimeException(
                     "Bad interval (" + start + ".." + end + "; length of this PolyLine2d is " + this.getLength() + ")");
         }
         double cumulativeLength = 0;
         double nextCumulativeLength = 0;
         double segmentLength = 0;
         int index = 0;
         List<Point2d> pointList = new ArrayList<>();
         while (start > cumulativeLength)
         {
             Point2d fromPoint = get(index);
             index++;
             Point2d toPoint = get(index);
             segmentLength = fromPoint.distance(toPoint);
             cumulativeLength = nextCumulativeLength;
             nextCumulativeLength = cumulativeLength + segmentLength;
             if (nextCumulativeLength >= start)
             {
                 break;
             }
         }
         if (start == nextCumulativeLength)
         {
             pointList.add(get(index));
         }
         else
         {
             pointList.add(get(index - 1).interpolate(get(index), (start - cumulativeLength) / segmentLength));
             if (end > nextCumulativeLength)
             {
                 pointList.add(get(index));
             }
         }
         while (end > nextCumulativeLength)
         {
             Point2d fromPoint = get(index);
             index++;
             if (index >= size())
             {
                 break; // rounding error
             }
             Point2d toPoint = get(index);
             segmentLength = fromPoint.distance(toPoint);
             cumulativeLength = nextCumulativeLength;
             nextCumulativeLength = cumulativeLength + segmentLength;
             if (nextCumulativeLength >= end)
             {
                 break;
             }
             pointList.add(toPoint);
         }
         if (end == nextCumulativeLength)
         {
             pointList.add(get(index));
         }
         else if (index < this.x.length)
         {
             Point2d point = get(index - 1).interpolate(get(index), (end - cumulativeLength) / segmentLength);
             // can be the same due to rounding
             if (!point.equals(pointList.get(pointList.size() - 1)))
             {
                 pointList.add(point);
             }
         }
         // else rounding error
         try
         {
             return instantiate(pointList);
         }
         catch (DrawRuntimeException exception)
         {
             CategoryLogger.always().error(exception, "interval " + start + ".." + end + " too short");
             throw new DrawRuntimeException("interval " + start + ".." + end + "too short");
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public PolyLine2d truncate(final double position) throws DrawRuntimeException
     {
         if (position <= 0.0 || position > getLength())
         {
             throw new DrawRuntimeException("truncate for line: position <= 0.0 or > line length. Position = " + position
                     + ". Length = " + getLength() + " m.");
         }
 
         // handle special case: position == length
         if (position == getLength())
         {
             return this;
         }
 
         // find the index of the line segment
         int index = find(position);
         double remainder = position - lengthAtIndex(index);
         double fraction = remainder / (lengthAtIndex(index + 1) - lengthAtIndex(index));
         Point2d p1 = get(index);
         Point2d lastPoint;
         if (0.0 == fraction)
         {
             lastPoint = p1;
         }
         else
         {
             Point2d p2 = get(index + 1);
             lastPoint = p1.interpolate(p2, fraction);
             index++;
         }
         double[] truncatedX = new double[index + 1];
         double[] truncatedY = new double[index + 1];
         for (int i = 0; i < index; i++)
         {
             truncatedX[i] = this.x[i];
             truncatedY[i] = this.y[i];
         }
         truncatedX[index] = lastPoint.x;
         truncatedY[index] = lastPoint.y;
         return new PolyLine2d(truncatedX, truncatedY);
     }
 
     /** {@inheritDoc} */
     @Override
     @SuppressWarnings("checkstyle:methodlength")
     public PolyLine2d offsetLine(final double offset, final double circlePrecision, final double offsetMinimumFilterValue,
             final double offsetMaximumFilterValue, final double offsetFilterRatio, final double minimumOffset)
             throws IllegalArgumentException
     {
         Throw.when(Double.isNaN(offset), IllegalArgumentException.class, "Offset may not be NaN");
         Throw.when(Double.isNaN(circlePrecision) || circlePrecision <= 0, IllegalArgumentException.class,
                 "bad circlePrecision");
         Throw.when(Double.isNaN(offsetMinimumFilterValue) || offsetMinimumFilterValue <= 0, IllegalArgumentException.class,
                 "bad offsetMinimumFilterValue");
         Throw.when(Double.isNaN(offsetMaximumFilterValue) || offsetMaximumFilterValue <= 0, IllegalArgumentException.class,
                 "bad offsetMaximumFilterValue");
         Throw.when(Double.isNaN(offsetFilterRatio) || offsetFilterRatio <= 0, IllegalArgumentException.class,
                 "bad offsetFilterRatio");
         Throw.when(Double.isNaN(minimumOffset) || minimumOffset <= 0, IllegalArgumentException.class, "bad minimumOffset");
         Throw.when(offsetMinimumFilterValue >= offsetMaximumFilterValue, IllegalArgumentException.class,
                 "bad offset filter values; minimum must be less than maximum");
         double bufferOffset = Math.abs(offset);
         if (bufferOffset < minimumOffset)
         {
             return this;
         }
 
         PolyLine2d filteredReferenceLine = noiseFilteredLine(
                 Math.max(offsetMinimumFilterValue, Math.min(bufferOffset / offsetFilterRatio, offsetMaximumFilterValue)));
         List<Point2d> tempPoints = new ArrayList<>();
         // Make good use of the fact that PolyLine3d cannot have consecutive duplicate points and has > 1 points
         Point2d prevPoint = filteredReferenceLine.get(0);
         Double prevAngle = null;
         for (int index = 0; index < filteredReferenceLine.size() - 1; index++)
         {
             Point2d nextPoint = filteredReferenceLine.get(index + 1);
             double angle = Math.atan2(nextPoint.y - prevPoint.y, nextPoint.x - prevPoint.x);
             Point2d segmentFrom = new Point2d(prevPoint.x - Math.sin(angle) * offset, prevPoint.y + Math.cos(angle) * offset);
             Point2d segmentTo = new Point2d(nextPoint.x - Math.sin(angle) * offset, nextPoint.y + Math.cos(angle) * offset);
             boolean addSegment = true;
             if (index > 0)
             {
                 double deltaAngle = angle - prevAngle;
                 if (Math.abs(deltaAngle) > Math.PI)
                 {
                     deltaAngle -= Math.signum(deltaAngle) * 2 * Math.PI;
                 }
                 if (deltaAngle * offset <= 0)
                 {
                     // Outside of curve of reference line
                     // Approximate an arc using straight segments.
                     // Determine how many segments are needed.
                     int numSegments = 1;
                     if (Math.abs(deltaAngle) > Math.PI / 2)
                     {
                         numSegments = 2;
                     }
                     while (true)
                     {
                         double maxError = bufferOffset * (1 - Math.abs(Math.cos(deltaAngle / numSegments / 2)));
                         if (maxError < circlePrecision)
                         {
                             break; // required precision reached
                         }
                         numSegments *= 2;
                     }
                     Point2d prevArcPoint = tempPoints.get(tempPoints.size() - 1);
                     // Generate the intermediate points
                     for (int additionalPoint = 1; additionalPoint < numSegments; additionalPoint++)
                     {
                         double intermediateAngle =
                                 (additionalPoint * angle + (numSegments - additionalPoint) * prevAngle) / numSegments;
                         if (prevAngle * angle < 0 && Math.abs(prevAngle) > Math.PI / 2 && Math.abs(angle) > Math.PI / 2)
                         {
                             intermediateAngle += Math.PI;
                         }
                         Point2d intermediatePoint = new Point2d(prevPoint.x - Math.sin(intermediateAngle) * offset,
                                 prevPoint.y + Math.cos(intermediateAngle) * offset);
                         // Find any intersection points of the new segment and all previous segments
                         Point2d prevSegFrom = null;
                         int stopAt = tempPoints.size();
                         for (int i = 0; i < stopAt; i++)
                         {
                             Point2d prevSegTo = tempPoints.get(i);
                             if (null != prevSegFrom)
                             {
                                 Point2d prevSegIntersection = Point2d.intersectionOfLineSegments(prevArcPoint,
                                         intermediatePoint, prevSegFrom, prevSegTo);
                                 if (null != prevSegIntersection && prevSegIntersection.distance(prevArcPoint) > circlePrecision
                                         && prevSegIntersection.distance(prevSegFrom) > circlePrecision
                                         && prevSegIntersection.distance(prevSegTo) > circlePrecision)
                                 {
                                     tempPoints.add(prevSegIntersection);
                                     // System.out.println(new OTSLine3D(tempPoints).toPlot());
                                 }
                             }
                             prevSegFrom = prevSegTo;
                         }
                         Point2d nextSegmentIntersection =
                                 Point2d.intersectionOfLineSegments(prevSegFrom, intermediatePoint, segmentFrom, segmentTo);
                         if (null != nextSegmentIntersection)
                         {
                             tempPoints.add(nextSegmentIntersection);
                             // System.out.println(new OTSLine3D(tempPoints).toPlot());
                         }
                         tempPoints.add(intermediatePoint);
                         // System.out.println(new OTSLine3D(tempPoints).toPlot());
                         prevArcPoint = intermediatePoint;
                     }
                 }
                 // Inside of curve of reference line.
                 // Add the intersection point of each previous segment and the next segment
                 Point2d pPoint = null;
                 int currentSize = tempPoints.size(); // PK DO NOT use the "dynamic" limit
                 for (int i = 0; i < currentSize /* tempPoints.size() */; i++)
                 {
                     Point2d p = tempPoints.get(i);
                     if (null != pPoint)
                     {
                         double pAngle = Math.atan2(p.y - pPoint.y, p.x - pPoint.x);
                         double angleDifference = angle - pAngle;
                         if (Math.abs(angleDifference) > Math.PI)
                         {
                             angleDifference -= Math.signum(angleDifference) * 2 * Math.PI;
                         }
                         if (Math.abs(angleDifference) > 0)// 0.01)
                         {
                             Point2d intersection = Point2d.intersectionOfLineSegments(pPoint, p, segmentFrom, segmentTo);
                             if (null != intersection)
                             {
                                 if (tempPoints.size() - 1 == i)
                                 {
                                     tempPoints.remove(tempPoints.size() - 1);
                                     segmentFrom = intersection;
                                 }
                                 else
                                 {
                                     tempPoints.add(intersection);
                                 }
                             }
                         }
                         else
                         {
                             // This is where things went very wrong in the TestGeometry demo.
                             if (i == tempPoints.size() - 1)
                             {
                                 tempPoints.remove(tempPoints.size() - 1);
                                 segmentFrom = tempPoints.get(tempPoints.size() - 1);
                                 tempPoints.remove(tempPoints.size() - 1);
                             }
                         }
                     }
                     pPoint = p;
                 }
             }
             if (addSegment)
             {
                 tempPoints.add(segmentFrom);
                 tempPoints.add(segmentTo);
                 prevPoint = nextPoint;
                 prevAngle = angle;
             }
         }
         // Remove points that are closer than the specified offset
         for (int index = 1; index < tempPoints.size() - 1; index++)
         {
             Point2d checkPoint = tempPoints.get(index);
             prevPoint = null;
             boolean tooClose = false;
             boolean somewhereAtCorrectDistance = false;
             for (int i = 0; i < filteredReferenceLine.size(); i++)
             {
                 Point2d p = filteredReferenceLine.get(i);
                 if (null != prevPoint)
                 {
                     Point2d closestPoint = checkPoint.closestPointOnSegment(prevPoint, p);
                     double distance = closestPoint.distance(checkPoint);
                     if (distance < bufferOffset - circlePrecision)
                     {
                         tooClose = true;
                         break;
                     }
                     else if (distance < bufferOffset + minimumOffset)
                     {
                         somewhereAtCorrectDistance = true;
                     }
                 }
                 prevPoint = p;
             }
             if (tooClose || !somewhereAtCorrectDistance)
             {
                 tempPoints.remove(index);
                 index--;
             }
         }
         try
         {
             return new PolyLine2d(true, tempPoints);
         }
         catch (DrawRuntimeException exception)
         {
             exception.printStackTrace();
         }
         return null;
     }
 
     /** {@inheritDoc} */
     @Override
     public PolyLine2d offsetLine(final double offsetAtStart, final double offsetAtEnd, final double circlePrecision,
             final double offsetMinimumFilterValue, final double offsetMaximumFilterValue, final double offsetFilterRatio,
             final double minimumOffset) throws IllegalArgumentException, DrawRuntimeException
     {
         if (offsetAtStart == offsetAtEnd)
         {
             return offsetLine(offsetAtStart, circlePrecision, offsetMinimumFilterValue, offsetMaximumFilterValue,
                     offsetFilterRatio, minimumOffset);
         }
         PolyLine2d atStart = offsetLine(offsetAtStart, circlePrecision, offsetMinimumFilterValue, offsetMaximumFilterValue,
                 offsetFilterRatio, minimumOffset);
         PolyLine2d atEnd = offsetLine(offsetAtEnd, circlePrecision, offsetMinimumFilterValue, offsetMaximumFilterValue,
                 offsetFilterRatio, minimumOffset);
         return atStart.transitionLine(atEnd, new TransitionFunction()
         {
             @Override
             public double function(final double fraction)
             {
                 return fraction;
             }
         });
     }
 
     /** {@inheritDoc} */
     @Override
     public PolyLine2d transitionLine(final PolyLine2d endLine, final TransitionFunction transition) throws DrawRuntimeException
     {
         Throw.whenNull(endLine, "endLine may not be null");
         Throw.whenNull(transition, "transition may not be null");
         List<Point2d> pointList = new ArrayList<>();
         int indexInStart = 0;
         int indexInEnd = 0;
         while (indexInStart < this.size() && indexInEnd < endLine.size())
         {
             double fractionInStart = lengthAtIndex(indexInStart) / getLength();
             double fractionInEnd = endLine.lengthAtIndex(indexInEnd) / endLine.getLength();
             if (fractionInStart < fractionInEnd)
             {
                 pointList.add(get(indexInStart).interpolate(endLine.getLocation(fractionInStart * endLine.getLength()),
                         transition.function(fractionInStart)));
                 indexInStart++;
             }
             else if (fractionInStart > fractionInEnd)
             {
                 pointList.add(this.getLocation(fractionInEnd * getLength()).interpolate(endLine.get(indexInEnd),
                         transition.function(fractionInEnd)));
                 indexInEnd++;
             }
             else
             {
                 pointList.add(this.get(indexInStart).interpolate(endLine.getLocation(fractionInEnd * endLine.getLength()),
                         transition.function(fractionInStart)));
                 indexInStart++;
                 indexInEnd++;
             }
         }
         return new PolyLine2d(true, pointList);
     }
 
     /**
      * Find a location on this PolyLine2d that is a reasonable projection of a Ray on this line. The result (if not NaN) lies on
      * a line perpendicular to the direction of the Ray and on some segment of this PolyLine. This method attempts to give
      * continuous results for continuous changes of the Ray that must be projected. There are cases where this is simply
      * impossible, or the optimal result is ambiguous. In these cases this method will return something that is hopefully good
      * enough.
      * @param ray Ray2d; the Ray
      * @return double; length along this PolyLine (some value between 0 and the length of this PolyLine) where ray projects, or
      *         NaN if there is no solution
      * @throws NullPointerException when ray is null
      */
     public double projectRay(final Ray2d ray) throws NullPointerException
     {
         Throw.whenNull(ray, "ray may not be null");
         double bestDistance = Double.POSITIVE_INFINITY;
         double positionAtBestDistance = Double.NaN;
         // Point2d prevPoint = null;
         // Define the line that is perpendicular to directedPoint, passing through directedPoint
         double perpendicularX = ray.x - Math.sin(ray.phi);
         double perpendicularY = ray.y + Math.cos(ray.phi);
         for (int index = 1; index < this.x.length; index++)
         {
             Point2d intersection = Point2d.intersectionOfLines(ray.x, ray.y, perpendicularX, perpendicularY, false, false,
                     this.x[index - 1], this.y[index - 1], this.x[index], this.y[index], true, true);
             if (intersection != null) // Intersection is on the segment
             {
                 double thisDistance = intersection.distance(ray);
                 if (thisDistance < bestDistance)
                 {
                     double distanceToPrevPoint =
                             Math.hypot(intersection.x - this.x[index - 1], intersection.y - this.y[index - 1]);
                     positionAtBestDistance = lengthAtIndex(index - 1) + distanceToPrevPoint;
                     bestDistance = thisDistance;
                 }
             }
         }
         return positionAtBestDistance;
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString()
     {
         return toString("%f", false);
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString(final String doubleFormat, final boolean doNotIncludeClassName)
     {
         StringBuilder result = new StringBuilder();
         if (!doNotIncludeClassName)
         {
             result.append("PolyLine2d ");
         }
         String format = String.format("%%sx=%1$s, y=%1$s", doubleFormat);
         for (int index = 0; index < this.x.length; index++)
         {
             result.append(String.format(Locale.US, format, index == 0 ? "[" : ", ", this.x[index], this.y[index]));
         }
         if (this.lengthIndexedLine.length == 1)
         {
             format = String.format(", startHeading=%1$s", doubleFormat);
             result.append(String.format(Locale.US, format, this.startHeading));
         }
         result.append("]");
         return result.toString();
     }
 
     /** {@inheritDoc} */
     @Override
     public String toExcel()
     {
         StringBuffer s = new StringBuffer();
         for (int i = 0; i < this.x.length; i++)
         {
             s.append(this.x[i] + "\t" + this.y[i] + "\n");
         }
         return s.toString();
     }
 
     /**
      * Convert this PolyLine3D to Peter's plot format.
      * @return Peter's format plot output
      */
     public String toPlot()
     {
         StringBuffer result = new StringBuffer();
         for (int i = 0; i < this.x.length; i++)
         {
             result.append(String.format(Locale.US, "%s%.3f,%.3f", 0 == result.length() ? "M" : " L", this.x[i], this.y[i]));
         }
         result.append("\n");
         return result.toString();
     }
 
     /** {@inheritDoc} */
     @Override
     public int hashCode()
     {
         final int prime = 31;
         int result = 1;
         long temp;
         temp = Double.doubleToLongBits(this.startHeading);
         result = prime * result + (int) (temp ^ (temp >>> 32));
         result = prime * result + Arrays.hashCode(this.x);
         result = prime * result + Arrays.hashCode(this.y);
         return result;
     }
 
     /** {@inheritDoc} */
     @SuppressWarnings("checkstyle:needbraces")
     @Override
     public boolean equals(final Object obj)
     {
         if (this == obj)
             return true;
         if (obj == null)
             return false;
         if (getClass() != obj.getClass())
             return false;
         PolyLine2d other = (PolyLine2d) obj;
         if (Double.doubleToLongBits(this.startHeading) != Double.doubleToLongBits(other.startHeading))
             return false;
         if (!Arrays.equals(this.x, other.x))
             return false;
         if (!Arrays.equals(this.y, other.y))
             return false;
         return true;
     }
 
 }