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 org.djutils.draw.DrawException;
  import org.djutils.draw.DrawRuntimeException;
  import org.djutils.draw.Drawable2d;
  import org.djutils.draw.Space2d;
  import org.djutils.draw.bounds.Bounds2d;
  import org.djutils.draw.point.Point2d;
  import org.djutils.exceptions.Throw;
  import org.djutils.logger.CategoryLogger;
  
  /**
   * Implementation of Line for 2D space.
   * <p>
   * Copyright (c) 2020-2021 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, Space2d, Ray2d>
  {
      /** */
      private static final long serialVersionUID = 20200911L;
  
      /** The points of the line. */
      private final Point2d[] points;
  
      /** The cumulative length of the line at point 'i'. */
      private final double[] lengthIndexedLine;
  
      /** The length. */
      private final double length;
  
      /** Bounding rectangle of this Line2d. */
      private final Bounds2d bounds;
  
      /**
       * Construct a new Line2D from an array of Point2d.
       * @param copyNeeded boolean; if true; a deep copy of the points array is stored instead of the provided array
       * @param points Point2d[]; the array of points to construct this Line2d from.
       * @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)
       */
      private PolyLine2d(final boolean copyNeeded, final Point2d[] points) throws NullPointerException, DrawRuntimeException
      {
          Throw.whenNull(points, "points may not be null");
          Throw.when(points.length < 2, DrawRuntimeException.class, "Need at least two points");
          this.points = copyNeeded ? Arrays.copyOf(points, points.length) : points;
          Point2d prevPoint = points[0];
          double minX = prevPoint.x;
          double minY = prevPoint.y;
          double maxX = prevPoint.x;
          double maxY = prevPoint.y;
          this.lengthIndexedLine = new double[points.length];
          this.lengthIndexedLine[0] = 0.0;
          for (int i = 1; i < points.length; i++)
          {
              Point2d point = points[i];
              minX = Math.min(minX, point.x);
              minY = Math.min(minY, point.y);
              maxX = Math.max(maxX, point.x);
              maxY = Math.max(maxY, point.y);
              if (prevPoint.x == point.x && prevPoint.y == point.y)
              {
                  throw new DrawRuntimeException("Degenerate Line2d; point " + (i - 1) + " has the same x and y as point " + i);
              }
              this.lengthIndexedLine[i] = this.lengthIndexedLine[i - 1] + prevPoint.distance(point);
              prevPoint = point;
          }
          this.length = this.lengthIndexedLine[this.lengthIndexedLine.length - 1];
          this.bounds = new Bounds2d(minX, maxX, minY, maxY);
      }
  
      /**
       * 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
       * @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.html#Point2d">Point2d point1, final Point2d point2, final Point2d... otherPoints)
              throws NullPointerException, DrawRuntimeException
      {
          this(false, spliceArray(point1, point2, 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.html#Point2d">Point2dPoint2d">Point2d[] spliceArray(final Point2d.html#Point2d">Point2d point1, final Point2d point2, final Point2d... otherPoints)
     {
         Point2dhtml#Point2d">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 array of Point2d.
      * @param points Point2d[]; points of the PolyLine2d
      * @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[] points) throws NullPointerException, DrawRuntimeException
     {
         this(true, checkLengthIsTwoOrMore(Throw.whenNull(points, "points may not be null")));
     }
 
     /**
      * Check that the length of an array of Point2d is at least two.
      * @param points Point2d[]; the array of points to check
      * @return Point2d[]; points
      * @throws DrawRuntimeException when the length of points is less than two
      */
     private static Point2dint2d[] checkLengthIsTwoOrMore(final Point2d[] points) throws DrawRuntimeException
     {
         Throw.when(points.length < 2, DrawRuntimeException.class, "Need at least two points");
         return points;
     }
 
     /**
      * Construct a new Line2d and initialize its length indexed line, bounds, centroid and length.
      * @param iterator Iterator&lt;Point2d&gt;; iterator that will provide all points that constitute the new Line2d
      * @throws NullPointerException when iterator is null
      * @throws DrawException when the iterator provides too few points, or some adjacent identical points)
      */
     public PolyLine2d(final Iterator<Point2d> iterator) throws NullPointerException, DrawException
     {
         this(iteratorToList(Throw.whenNull(iterator, "iterator cannot be null")));
     }
 
     /**
      * Construct a new Line2d from a List&lt;Point2d&gt;.
      * @param pointList List&lt;Point2d&gt;; the list of points to construct this Line2d from.
      * @throws DrawRuntimeException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine2d(final List<Point2d> pointList) throws DrawRuntimeException
     {
         this(false, pointList.toArray(new Point2d[pointList.size()]));
     }
 
     /** {@inheritDoc} */
     @Override
     public PolyLine2d instantiate(final List<Point2d> pointList) throws NullPointerException, DrawRuntimeException
     {
         return new PolyLine2d(pointList);
     }
 
     /**
      * Construct a new Line2d (closed shape) from a Path2D.
      * @param path Path2D; the Path2D to construct this Line2d from.
      * @throws DrawException when the provided points do not constitute a valid line (too few points or identical adjacent
      *             points)
      */
     public PolyLine2d(final Path2D path) throws DrawException
     {
         this(false, path2DtoArray(path));
     }
 
     /**
      * 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 DrawException when the pathIterator of the path returns an unsupported command
      */
     private static Point2d[] path2DtoArray(final Path2D path) throws DrawException
     {
         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 DrawException("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
      */
     private static List<Point2d> iteratorToList(final Iterator<Point2d> iterator)
     {
         List<Point2d> result = new ArrayList<>();
         iterator.forEachRemaining(result::add);
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     public int size()
     {
         return this.points.length;
     }
 
     /** {@inheritDoc} */
     @Override
     public final Point2d get(final int i) throws IndexOutOfBoundsException
     {
         return this.points[i];
     }
 
     /** {@inheritDoc} */
     @Override
     public final double lengthAtIndex(final int index)
     {
         return this.lengthIndexedLine[index];
     }
 
     /** {@inheritDoc} */
     @Override
     public final double getLength()
     {
         return this.length;
     }
 
     /** {@inheritDoc} */
     @Override
     public Iterator<Point2d> getPoints()
     {
         return Arrays.stream(this.points).iterator();
     }
 
     /** {@inheritDoc} */
     @Override
     public Bounds2d getBounds()
     {
         return this.bounds;
     }
 
     /**
      * Construct a new Line2d that is equal to this line except for segments that are shorter than the <cite>noiseLevel</cite>.
      * The result is guaranteed to start with the first point of this line and end with the last point of this line.
      * @param noiseLevel double; the minimum segment length that is <b>not</b> removed
      * @return Line2d; the filtered line
      */
     public final PolyLine2d noiseFilteredLine(final double noiseLevel)
     {
         if (this.size() <= 2)
         {
             return this; // Except for some cached fields; an Line2d is immutable; so safe to return
         }
         Point2d prevPoint = null;
         List<Point2d> list = null;
         for (int index = 0; index < this.size(); index++)
         {
             Point2d currentPoint = this.points[index];
             if (null != prevPoint && prevPoint.distance(currentPoint) < noiseLevel)
             {
                 if (null == list)
                 {
                     // Found something to filter; copy this up to (and including) prevPoint
                     list = new ArrayList<>();
                     for (int i = 0; i < index; i++)
                     {
                         list.add(this.points[i]);
                     }
                 }
                 if (index == this.size() - 1)
                 {
                     if (list.size() > 1)
                     {
                         // Replace the last point of the result by the last point of this Line2d
                         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
             }
             else if (null != list)
             {
                 list.add(currentPoint);
             }
             prevPoint = currentPoint;
         }
         if (null == list)
         {
             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, this.points[1]);
         }
         try
         {
             return new PolyLine2d(list);
         }
         catch (DrawRuntimeException exception)
         {
             // Cannot happen
             CategoryLogger.always().error(exception);
             throw new Error(exception);
         }
     }
 
     /**
      * Concatenate several Line2d instances.
      * @param lines PolyLine2d...; Line2d... one or more Line2d. The last point of the first &lt;strong&gt;must&lt;/strong&gt;
      *            match the first of the second, etc.
      * @return Line2d
      * @throws DrawException if zero lines are given, or when there is a gap between consecutive lines
      */
     public static PolyLine2d concatenate(final PolyLine2d... lines) throws DrawException
     {
         return concatenate(0.0, lines);
     }
 
     /**
      * Concatenate two Line2d 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 Line2d; the concatenation of the two lines
      * @throws DrawException if zero lines are given, or when there is a gap between consecutive lines
      */
     public static PolyLine2d concatenate(final PolyLine2d.html#PolyLine2d">PolyLine2djxr_keyword">double tolerance, final PolyLine2d.html#PolyLine2d">PolyLine2d line1, final PolyLine2d line2)
             throws DrawException
     {
         if (line1.getLast().distance(line2.getFirst()) > tolerance)
         {
             throw new DrawException("Lines are not connected: " + line1.getLast() + " to " + line2.getFirst() + " distance is "
                     + line1.getLast().distance(line2.getFirst()) + " > " + tolerance);
         }
         int size = line1.size() + line2.size() - 1;
         Point2dhtml#Point2d">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(false, points);
     }
 
     /**
      * Concatenate several Line2d instances.
      * @param tolerance double; the tolerance between the end point of a line and the first point of the next line
      * @param lines PolyLine2d...; Line2d... one or more Line2d. The last point of the first &lt;strong&gt;must&lt;/strong&gt;
      *            match the first of the second, etc.
      * @return Line2d; the concatenation of the lines
      * @throws DrawException 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 DrawException
     {
         if (0 == lines.length)
         {
             throw new DrawException("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 DrawException("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;
         }
         Point2dhtml#Point2d">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(false, points);
     }
 
     /**
      * Create a new Line2d, filtering out repeating successive points.
      * @param points Point2d...; the coordinates of the line as Point2d
      * @return the line
      * @throws DrawException when number of points &lt; 2
      */
     public static PolyLine2d createAndCleanPolyLine2d(final Point2d... points) throws DrawException
     {
         if (points.length < 2)
         {
             throw new DrawException("Degenerate Line2d; has " + points.length + " point" + (points.length != 1 ? "s" : ""));
         }
         return createAndCleanPolyLine2d(new ArrayList<>(Arrays.asList(points)));
     }
 
     /**
      * Create an Line2d, while filtering out repeating successive points.
      * @param pointList List&lt;Point2d&gt;; list of the coordinates of the line as Point2d; any duplicate points in this list
      *            are removed (this method may modify the provided list)
      * @return Line2d; the line
      * @throws DrawException when number of non-equal points &lt; 2
      */
     public static PolyLine2d createAndCleanPolyLine2d(final List<Point2d> pointList) throws DrawException
     {
         // TODO avoid modifying the input list.
         // clean successive equal points
         int i = 1;
         while (i < pointList.size())
         {
             if (pointList.get(i - 1).equals(pointList.get(i)))
             {
                 pointList.remove(i);
             }
             else
             {
                 i++;
             }
         }
         return new PolyLine2d(pointList);
     }
 
     /** {@inheritDoc} */
     @Override
     public final Ray2d getLocationExtended(final double position)
     {
         if (position >= 0.0 && position <= getLength())
         {
             try
             {
                 return getLocation(position);
             }
             catch (DrawException exception)
             {
                 // cannot happen
             }
         }
 
         // position before start point -- extrapolate using direction from first point to second point of this Line2d
         if (position < 0.0)
         {
             double len = position;
             double fraction = len / (this.lengthIndexedLine[1] - this.lengthIndexedLine[0]);
             Point2d p1 = this.points[0];
             Point2d p2 = this.points[1];
             return new Ray2d(p1.x + fraction * (p2.x - p1.x), p1.y + fraction * (p2.y - p1.y), p2);
         }
 
         // position beyond end point -- extrapolate using the direction from the before last point to the last point of this
         // Line2d
         int n1 = this.lengthIndexedLine.length - 1;
         int n2 = this.lengthIndexedLine.length - 2;
         double len = position - getLength();
         double fraction = len / (this.lengthIndexedLine[n1] - this.lengthIndexedLine[n2]);
         while (Double.isInfinite(fraction))
         {
             if (--n2 < 0)
             {
                 CategoryLogger.always().error("lengthIndexedLine of {} is invalid", this);
                 Point2d p = this.points[n1];
                 return new Ray2d(p.x, p.y, 0.0); // Bogus direction
             }
             fraction = len / (this.lengthIndexedLine[n1] - this.lengthIndexedLine[n2]);
         }
         Point2d p1 = this.points[n2];
         Point2d p2 = this.points[n1];
         return new Ray2d(p2.x + fraction * (p2.x - p1.x), p2.y + fraction * (p2.y - p1.y), p1.directionTo(p2));
     }
 
     /** {@inheritDoc} */
     @Override
     public final Ray2d getLocation(final double position) throws DrawException
     {
         if (position < 0.0 || position > getLength())
         {
             throw new DrawException("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)
         {
             Point2d p1 = this.points[0];
             Point2d p2 = this.points[1];
             return new Ray2d(p1.x, p1.y, p2);
         }
         if (position == getLength())
         {
             Point2d p1 = this.points[this.points.length - 2];
             Point2d p2 = this.points[this.points.length - 1];
             return new Ray2d(p2.x, p2.y, p1.directionTo(p2));
         }
 
         // 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]);
         Point2d p1 = this.points[index];
         Point2d p2 = this.points[index + 1];
         return new Ray2d(p1.x + fraction * (p2.x - p1.x), p1.y + fraction * (p2.y - p1.y), p1.directionTo(p2));
     }
 
     /**
      * Returns the fractional position along this line of the orthogonal projection of a point on this line. If the point is not
      * orthogonal to the closest line segment, the nearest point is selected.
      * @param point Point2d; the point to project
      * @return fractional position along this line of the orthogonal projection on this line of a point
      */
     public final double projectOrthogonal(final Point2d point)
     {
         return projectOrthogonal(point.x, point.y);
     }
 
     /**
      * Returns the fractional position along this line of the orthogonal projection of point (x, y) on this line. If the point
      * is not orthogonal to the closest line segment, the nearest point is selected.
      * @param x double; x-coordinate of point to project
      * @param y double; y-coordinate of point to project
      * @return fractional position along this line of the orthogonal projection on this line of a point
      */
     public final double projectOrthogonal(final double x, final double y)
     {
         // prepare
         double minDistance = Double.POSITIVE_INFINITY;
         double minSegmentFraction = 0;
         int minSegment = -1;
 
         // code based on Line2D.ptSegDistSq(...)
         for (int i = 0; i < size() - 1; i++)
         {
             double dx = this.points[i + 1].x - this.points[i].x;
             double dy = this.points[i + 1].y - this.points[i].y;
             // vector relative to (x(i), y(i))
             double px = x - this.points[i].x;
             double py = y - this.points[i].y;
             // dot product
             double dot1 = px * dx + py * dy;
             double f;
             double distance;
             if (dot1 > 0)
             {
                 // vector relative to (x(i+1), y(i+1))
                 px = dx - px;
                 py = dy - py;
                 // dot product
                 double dot2 = px * dx + py * dy;
                 if (dot2 > 0)
                 {
                     // projection on line segment
                     double len2 = dx * dx + dy * dy;
                     double proj = dot2 * dot2 / len2;
                     f = dot1 / len2;
                     distance = px * px + py * py - proj;
                 }
                 else
                 {
                     // dot<=0 projection 'after' line segment
                     f = 1;
                     distance = px * px + py * py;
                 }
             }
             else
             {
                 // dot<=0 projection 'before' line segment
                 f = 0;
                 distance = px * px + py * py;
             }
             // check if closer than previous
             if (distance < minDistance)
             {
                 minDistance = distance;
                 minSegmentFraction = f;
                 minSegment = i;
             }
         }
 
         // return
         double segLen = this.lengthIndexedLine[minSegment + 1] - this.lengthIndexedLine[minSegment];
         return (this.lengthIndexedLine[minSegment] + segLen * minSegmentFraction) / getLength();
     }
 
     /** {@inheritDoc} */
     @Override
     public PolyLine2d extract(final double start, final double end) throws DrawException
     {
         if (Double.isNaN(start) || Double.isNaN(end) || start < 0 || start >= end || end > getLength())
         {
             throw new DrawException(
                     "Bad interval (" + start + ".." + end + "; length of this Line2d 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
         {
             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);
             }
         }
         try
         {
             return instantiate(pointList);
         }
         catch (DrawRuntimeException exception)
         {
             CategoryLogger.always().error(exception, "interval " + start + ".." + end + " too short");
             throw new DrawException("interval " + start + ".." + end + "too short");
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public PolyLine2d truncate(final double position) throws DrawException
     {
         if (position <= 0.0 || position > getLength())
         {
             throw new DrawException("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)
         {
             index--;
             lastPoint = p1;
         }
         else
         {
             Point2d p2 = get(index + 1);
             lastPoint = p1.interpolate(p2, fraction);
 
         }
         // FIXME: Cannot create a P[]; will have to do it with a List<P>
         List<Point2d> coords = new ArrayList<>(index + 2);
         for (int i = 0; i <= index; i++)
         {
             coords.add(get(i));
         }
         coords.add(lastPoint);
         return instantiate(coords);
     }
 
     /** Default precision of approximation of arcs in the offsetLine method. */
     public static final double DEFAULT_CIRCLE_PRECISION = 0.001;
 
     /** By default, noise in the reference line of the offsetLine method less than this value is always filtered. */
     public static final double DEFAULT_OFFSET_MINIMUM_FILTER_VALUE = 0.001;
 
     /** By default, noise in the reference line of the offsetLineMethod greater than this value is never filtered. */
     public static final double DEFAULT_OFFSET_MAXIMUM_FILTER_VALUE = 0.1;
 
     /**
      * By default, noise in the reference line of the offsetLineMethod less than <cite>offset / offsetFilterRatio</cite> is
      * filtered except when the resulting value exceeds <cite>offsetMaximumFilterValue</cite>.
      */
     public static final double DEFAULT_OFFSET_FILTER_RATIO = 10;
 
     /** By default, the offsetLineMethod uses this offset precision. */
     public static final double DEFAULT_OFFSET_PRECISION = 0.00001;
 
     /**
      * Construct an offset line. This is similar to what geographical specialists call buffering, except that this method only
      * construct a new line on one side of the reference line and does not add half disks around the end points. This method
      * tries to strike a delicate balance between generating too few and too many points to approximate arcs. Noise in
      * <cite>this</cite> (the reference line) can cause major artifacts in the offset line. This method calls the underlying
      * method with default values for circlePrecision (<cite>DEFAULT_OFFSET</cite>), offsetMinimumFilterValue
      * (<cite>DEFAULT_OFFSET_MINIMUM_FILTER_VALUE</cite>), offsetMaximumFilterValue
      * (<cite>DEFAULT_OFFSET_MAXIMUM_FILTER_VALUE</cite>), offsetFilterRatio (<cite>DEFAULT_OFFSET_FILTER_RATIO</cite>),
      * minimumOffset (<cite>DEFAULT_OFFSET_PRECISION</cite>).
      * @param offset double; the offset; positive values indicate left of the reference line, negative values indicate right of
      *            the reference line
      * @return PolyLine2d; a line at the specified offset from the reference line
      */
     public PolyLine2d offsetLine(final double offset)
     {
         return offsetLine(offset, DEFAULT_CIRCLE_PRECISION, DEFAULT_OFFSET_MINIMUM_FILTER_VALUE,
                 DEFAULT_OFFSET_MAXIMUM_FILTER_VALUE, DEFAULT_OFFSET_FILTER_RATIO, DEFAULT_OFFSET_PRECISION);
     }
 
     /**
      * Construct an offset line. This is similar to what geographical specialists call buffering, except that this method only
      * construct a new line on one side of the reference line and does not add half disks around the end points. This method
      * tries to strike a delicate balance between generating too few and too many points to approximate arcs. Noise in
      * <cite>this</cite> (the reference line) can cause major artifacts in the offset line.
      * @param offset double; the offset; positive values indicate left of the reference line, negative values indicate right of
      *            the reference line
      * @param circlePrecision double; precision of approximation of arcs; the line segments that are used to approximate an arc
      *            will not deviate from the exact arc by more than this value
      * @param offsetMinimumFilterValue double; noise in the reference line less than this value is always filtered
      * @param offsetMaximumFilterValue double; noise in the reference line greater than this value is never filtered
      * @param offsetFilterRatio double; noise in the reference line less than <cite>offset / offsetFilterRatio</cite> is
      *            filtered except when the resulting value exceeds <cite>offsetMaximumFilterValue</cite>
      * @param minimumOffset double; an offset value less than this value is treated as 0.0
      * @return PolyLine2d; a line at the specified offset from the reference line
      * @throws IllegalArgumentException when offset is NaN, or circlePrecision, offsetMinimumFilterValue,
      *             offsetMaximumfilterValue, offsetFilterRatio, or minimumOffset is not positive, or NaN, or
      *             offsetMinimumFilterValue &gt;= offsetMaximumFilterValue
      */
     @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 an OTSLine3D 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);
             Point2dl#Point2d">Point2d segmentFrom = new Point2d(prevPoint.x - Math.sin(angle) * offset, prevPoint.y + Math.cos(angle) * offset);
             Point2dtml#Point2d">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;
                         }
                         Point2dt2d">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 PolyLine2d.createAndCleanPolyLine2d(tempPoints);
         }
         catch (DrawException exception)
         {
             exception.printStackTrace();
         }
         return null;
     }
 
     /**
      * Find a location on this PolyLine2d that is a reasonable projection of a DirectedPoint on this line. The result (if not
      * NaN) lies on a line perpendicular to the direction of the DirectedPoint and on some segment of this PolyLine. This method
      * attempts to give continuous results for continuous changes of the DirectedPoint 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 orientedPoint Ray2d; the DirectedPoint
      * @return double; length along this PolyLine (some value between 0 and the length of this PolyLine) where directedPoint
      *         projects, or NaN if there is no solution
      * @throws NullPointerException when directedPoint is null
      */
     public double projectRay(final Ray2d orientedPoint) throws NullPointerException
     {
         Throw.whenNull(orientedPoint, "directedPoint 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
         Point2d perpendicular = orientedPoint.translate(-Math.sin(orientedPoint.phi), Math.cos(orientedPoint.phi));
         double cumulativeDistance = 0;
         for (Point2d nextPoint : this.points)
         {
             if (null != prevPoint)
             {
                 double segmentLength = prevPoint.distance(nextPoint);
                 Point2d intersection = Point2d.intersectionOfLines(orientedPoint, perpendicular, prevPoint, nextPoint);
                 double distanceToPrevPoint = intersection.distance(prevPoint);
                 if (distanceToPrevPoint <= segmentLength && intersection.distance(nextPoint) <= segmentLength)
                 {
                     // Intersection is on the segment
                     double thisDistance = intersection.distance(orientedPoint);
                     if (thisDistance < bestDistance)
                     {
                         positionAtBestDistance = cumulativeDistance + distanceToPrevPoint;
                         bestDistance = thisDistance;
                     }
                 }
                 cumulativeDistance += segmentLength;
             }
             prevPoint = nextPoint;
         }
         return positionAtBestDistance;
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString()
     {
         return "PolyLine2d [points=" + Arrays.toString(this.points) + "]";
     }
 
     /**
      * Convert this PolyLine2d to something that MS-Excel can plot.
      * @return excel XY plottable output
      */
     public final String toExcel()
     {
         StringBuffer s = new StringBuffer();
         for (Point2d p : this.points)
         {
             s.append(p.x + "\t" + p.y + "\n");
         }
         return s.toString();
     }
 
     /**
      * Convert this PolyLine3D to Peter's plot format.
      * @return Peter's format plot output
      */
     public final String toPlot()
     {
         StringBuffer result = new StringBuffer();
         for (Point2d p : this.points)
         {
             result.append(String.format(Locale.US, "%s%.3f,%.3f", 0 == result.length() ? "M" : " L", p.x, p.y));
         }
         result.append("\n");
         return result.toString();
     }
 
     /** {@inheritDoc} */
     @Override
     public int hashCode()
     {
         final int prime = 31;
         int result = 1;
         result = prime * result + Arrays.hashCode(this.points);
         return result;
     }
 
     /** {@inheritDoc} */
     @SuppressWarnings({"checkstyle:designforextension", "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../../../org/djutils/draw/line/PolyLine2d.html#PolyLine2d">PolyLine2d other = (PolyLine2d) obj;
         if (!Arrays.equals(this.points, other.points))
             return false;
         return true;
     }
 
 }