package org.djutils.draw.line;
   
   import java.util.ArrayList;
   import java.util.Arrays;
   import java.util.Iterator;
   import java.util.List;
   import java.util.Locale;
   import java.util.function.Function;
   
  import org.djutils.draw.DrawRuntimeException;
  import org.djutils.draw.Drawable3d;
  import org.djutils.draw.bounds.Bounds3d;
  import org.djutils.draw.point.DirectedPoint3d;
  import org.djutils.draw.point.Point2d;
  import org.djutils.draw.point.Point3d;
  import org.djutils.exceptions.Throw;
  import org.djutils.logger.CategoryLogger;
  
  /**
   * Implementation of PolyLine for 3D space.
   * <p>
   * Copyright (c) 2020-2025 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://github.com/peter-knoppers">Peter Knoppers</a>
   * @author <a href="https://github.com/wjschakel">Wouter Schakel</a>
   */
  public class PolyLine3d implements Drawable3d, PolyLine<PolyLine3d, Point3d, Ray3d, DirectedPoint3d, LineSegment3d>
  {
      /** */
      private static final long serialVersionUID = 20200911L;
  
      /** X-coordinates of the points. */
      private final double[] x;
  
      /** Y-coordinates of the points. */
      private final double[] y;
  
      /** Z-coordinates of the points. */
      private final double[] z;
  
      /** The cumulative length of the line at point 'i'. */
      private final double[] lengthIndexedLine;
  
      /** The length. */
      private final double length;
  
      /** Bounding box of this PolyLine3d. */
      private final Bounds3d bounds;
  
      /** Heading at start point (only needed for degenerate PolyLine3d). */
      private final double startDirZ;
  
      /** Complement of the slope at start point (only needed for degenerate PolyLine3d). */
      private final double startDirY;
  
      /**
       * Construct a new PolyLine3d from an array of double x values, an array of double y values and an array of double z values.
       * @param copyNeeded if<code>true</code>; a deep copy of the points array is stored instead of the provided array
       * @param epsilon minimum distance between points to be considered different (these will <b>not</b> be filtered out)
       * @param x the x-coordinates of the points
       * @param y the y-coordinates of the points
       * @param z the z-coordinates of the points
       * @throws NullPointerException when <code>iterator</code> is <code>null</code>
       * @throws IllegalArgumentException when the provided points do not constitute a valid line (too few points or identical
       *             adjacent points, or or <code>x</code> and <code>y</code> and <code>z</code> differ in length)
       */
      private PolyLine3d(final boolean copyNeeded, final double epsilon, final double[] x, final double[] y, final double[] z)
      {
          Throw.when(x.length != y.length || x.length != z.length, IllegalArgumentException.class,
                  "x, y  and z arrays must have same length");
          double[][] filtered = filterNearDuplicates(epsilon, x, y, z);
          Throw.when(x.length < 2, IllegalArgumentException.class, "Need at least two points");
          this.x = copyNeeded && filtered[0].length == x.length ? Arrays.copyOf(x, x.length) : filtered[0];
          this.y = copyNeeded && filtered[0].length == x.length ? Arrays.copyOf(y, y.length) : filtered[1];
          this.z = copyNeeded && filtered[0].length == x.length ? Arrays.copyOf(z, z.length) : filtered[2];
          double minX = this.x[0];
          double minY = this.y[0];
          double minZ = this.z[0];
          double maxX = this.x[0];
          double maxY = this.y[0];
          double maxZ = this.z[0];
          this.lengthIndexedLine = new double[this.x.length];
          this.lengthIndexedLine[0] = 0.0;
          for (int i = 1; i < this.x.length; i++)
          {
              minX = Math.min(minX, this.x[i]);
              minY = Math.min(minY, this.y[i]);
              minZ = Math.min(minZ, this.z[i]);
              maxX = Math.max(maxX, this.x[i]);
              maxY = Math.max(maxY, this.y[i]);
              maxZ = Math.max(maxZ, this.z[i]);
              if (this.x[i - 1] == this.x[i] && this.y[i - 1] == this.y[i] && (this.z[i - 1] == this.z[i]))
              {
                  throw new IllegalArgumentException(
                          "Degenerate PolyLine2d; point " + (i - 1) + " has the same x, y and z as point " + i);
              }
              // There should be a varargs Math.hypot implementation
             this.lengthIndexedLine[i] = this.lengthIndexedLine[i - 1]
                     + Math.hypot(Math.hypot(this.x[i] - this.x[i - 1], this.y[i] - this.y[i - 1]), this.z[i] - this.z[i - 1]);
         }
         this.length = this.lengthIndexedLine[this.lengthIndexedLine.length - 1];
         this.bounds = new Bounds3d(minX, maxX, minY, maxY, minZ, maxZ);
         this.startDirZ = Double.NaN;
         this.startDirY = Double.NaN;
     }
 
     /**
      * Construct a degenerate PolyLine3d (consisting of only one point).
      * @param x the x-coordinate
      * @param y the y-coordinate
      * @param z the z-coordinate
      * @param dirY the angle from the positive Z axis direction in radians
      * @param dirZ the angle from the positive X axis direction in radians.
      * @throws ArithmeticException when <code>x</code>, <code>y</code>, <code>z</code>, or <code>dirY</code>, or
      *             <code>dirZ</code> is <code>NaN</code>
      * @throws IllegalArgumentException when <code>dirY</code>, or <code>dirZ</code> is infinite
      */
     public PolyLine3d(final double x, final double y, final double z, final double dirY, final double dirZ)
     {
         Throw.whenNaN(x, "x");
         Throw.whenNaN(y, "y");
         Throw.whenNaN(z, "z");
         Throw.whenNaN(dirY, "dirY");
         Throw.when(Double.isInfinite(dirY), IllegalArgumentException.class, "dirY must be finite");
         Throw.whenNaN(dirZ, "dirZ");
         Throw.when(Double.isInfinite(dirZ), IllegalArgumentException.class, "dirZ must be finite");
         this.x = new double[] {x};
         this.y = new double[] {y};
         this.z = new double[] {z};
         this.startDirY = dirY;
         this.startDirZ = dirZ;
         this.length = 0;
         this.bounds = new Bounds3d(x, x, y, y, z, z);
         this.lengthIndexedLine = new double[] {0.0};
     }
 
     /**
      * Construct a degenerate PolyLine3d (consisting of only one point).
      * @param p the point of the degenerate PolyLine3d
      * @param dirY the angle from the positive Z axis direction in radians
      * @param dirZ the angle from the positive X axis direction in the XY plane in radians.
      * @throws NullPointerException when <code>p</code> is <code>null</code>
      * @throws ArithmeticException when <code>dirY</code>, or <code>dirZ</code> is <code>NaN</code>
      * @throws IllegalArgumentException when <code>dirY</code>, or <code>dirZ</code> is infinite
      */
     public PolyLine3d(final Point3d p, final double dirY, final double dirZ)
     {
         this(Throw.whenNull(p, "p").x, p.y, p.z, dirY, dirZ);
     }
 
     /**
      * Construct a degenerate PolyLine3d (consisting of only one point).
      * @param directedPoint3d point, <code>dirY</code> and <code>dirZ</code> of the degenerate PolyLine3d
      * @throws NullPointerException when <code>p</code> is <code>null</code>
      * @throws IllegalArgumentException when <code>dirY</code> or <code>dirZ</code> is infinite (should not be possible)
      */
     public PolyLine3d(final DirectedPoint3d directedPoint3d) throws NullPointerException, IllegalArgumentException
     {
         this(Throw.whenNull(directedPoint3d, "r").x, directedPoint3d.y, directedPoint3d.z, directedPoint3d.dirY,
                 directedPoint3d.dirZ);
     }
 
     /**
      * Construct a new PolyLine3d from an array of Point2d. This constructor makes a deep copy of the parameters.
      * @param x the x-coordinates of the points
      * @param y the y-coordinates of the points
      * @param z the z-coordinates of the points
      * @throws NullPointerException when <code>x</code>, <code>y</code>, or <code>z</code> is <code>null</code>
      * @throws IllegalArgumentException when the provided coordinate values do not constitute a valid line (too few points or
      *             identical adjacent points, or the arrays are not the same length)
      */
     public PolyLine3d(final double[] x, final double[] y, final double[] z)
     {
         this(NO_FILTER, x, y, z);
     }
 
     /**
      * Construct a new PolyLine3d from an array of Point2d. This constructor makes a deep copy of the parameters.
      * @param epsilon minimum distance between points to be considered different (these will <b>not</b> be filtered out)
      * @param x the x-coordinates of the points
      * @param y the y-coordinates of the points
      * @param z the z-coordinates of the points
      * @throws NullPointerException when <code>x</code>, <code>y</code>, or <code>z</code> is <code>null</code>
      * @throws IllegalArgumentException when the provided coordinate values do not constitute a valid line (too few points or
      *             identical adjacent points, or the arrays are not the same length)
      */
     public PolyLine3d(final double epsilon, final double[] x, final double[] y, final double[] z)
     {
         this(true, epsilon, x, y, z);
     }
 
     /**
      * Construct a new PolyLine3d from an array of Point3d.
      * @param points the array of points to construct this PolyLine3d from.
      * @throws NullPointerException when the <code>points</code> array is <code>null</code>
      * @throws IllegalArgumentException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine3d(final Point3d[] points)
     {
         this(NO_FILTER, points);
     }
 
     /**
      * Construct a new PolyLine3d from an array of Point3d.
      * @param epsilon minimum distance between points to be considered different (these will <b>not</b> be filtered out)
      * @param points the array of points to construct this PolyLine3d from.
      * @throws NullPointerException when the <code>points</code> array is <code>null</code>
      * @throws IllegalArgumentException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine3d(final double epsilon, final Point3d[] points)
     {
         this(false, epsilon, makeArray(Throw.whenNull(points, "points"), p -> p.x), makeArray(points, p -> p.y),
                 makeArray(points, p -> p.z));
     }
 
     /**
      * Make an array of double an fill it with the appropriate coordinate of points.
      * @param points array of points
      * @param getter function that obtains the intended coordinate
      * @return array of double values filled with the requested coordinate values
      */
     protected static double[] makeArray(final Point3d[] points, final Function<Point3d, 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 PolyLine3d from two or more Point3d arguments.
      * @param point1 starting point of the PolyLine3d
      * @param point2 second point of the PolyLine3d
      * @param otherPoints additional points of the PolyLine3d (may be <code>null</code>, or have zero length)
      * @throws NullPointerException when <code>point1</code>, or <code>point2</code> is <code>null</code>, or
      *             <code>otherPoints</code> contains a <code>null</code> value
      * @throws IllegalArgumentException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine3d(final Point3d point1, final Point3d point2, final Point3d... otherPoints)
     {
         this(NO_FILTER, point1, point2, otherPoints);
     }
 
     /**
      * Construct a new PolyLine3d from two or more Point3d arguments.
      * @param epsilon minimum distance between points to be considered different (these will <b>not</b> be filtered out)
      * @param point1 starting point of the PolyLine3d
      * @param point2 second point of the PolyLine3d
      * @param otherPoints additional points of the PolyLine3d (may be <code>null</code>, or have zero length)
      * @throws NullPointerException when <code>point1</code>, or <code>point2</code> is <code>null</code>, or
      *             <code>otherPoints</code> contains a <code>null</code> value
      * @throws IllegalArgumentException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine3d(final double epsilon, final Point3d point1, final Point3d point2, final Point3d... otherPoints)
     {
         this(epsilon, spliceArray(point1, point2, otherPoints));
     }
 
     /**
      * Construct an array of Point3d from two points plus an array of Point3d.
      * @param point1 the first point (ends up at index 0 of the result)
      * @param point2 the second point (ends up at index 1 of the result)
      * @param otherPoints may be <code>null</code>, may be empty. If non empty, the elements in otherPoints end up
      *            at index 2 and up in the result
      * @return the combined array
      * @throws NullPointerException when <code>point1</code> or <code>point2</code> is <code>null</code>
      */
     private static Point3d[] spliceArray(final Point3d point1, final Point3d point2, final Point3d... otherPoints)
     {
         Point3d[] result = new Point3d[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 PolyLine3d from an iterator that yields Point3d objects.
      * @param iterator iterator that will provide all points that constitute the new PolyLine3d
      * @throws NullPointerException when <code>iterator</code> is <code>null</code>, or yields a <code>null</code> value
      * @throws IllegalArgumentException when the <code>iterator</code> provides too few points, or some adjacent identical
      *             points)
      */
     public PolyLine3d(final Iterator<Point3d> iterator)
     {
         this(NO_FILTER, iterator);
     }
 
     /**
      * Construct a new PolyLine3d from an iterator that yields Point3d objects.
      * @param epsilon minimum distance between points to be considered different (these will <b>not</b> be filtered out)
      * @param iterator iterator that will provide all points that constitute the new PolyLine3d
      * @throws NullPointerException when <code>iterator</code> is <code>null</code>, or yields a <code>null</code> value
      * @throws IllegalArgumentException when the <code>iterator</code> provides too few points, or some adjacent identical
      *             points)
      */
     public PolyLine3d(final double epsilon, final Iterator<Point3d> iterator)
     {
         this(epsilon, iteratorToList(Throw.whenNull(iterator, "iterator")));
     }
 
     /**
      * Construct a new PolyLine3d from a List&lt;Point3d&gt;.
      * @param pointList the list of points to construct the new PolyLine3d from.
      * @throws NullPointerException when <code>pointList</code> is <code>null</code>, or contains a <code>null</code> value
      * @throws IllegalArgumentException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine3d(final List<Point3d> pointList)
     {
         this(NO_FILTER, pointList);
     }
 
     /**
      * Construct a new PolyLine3d from a List&lt;Point3d&gt;.
      * @param epsilon minimum distance between points to be considered different (these will <b>not</b> be filtered out)
      * @param pointList the list of points to construct the new PolyLine3d from.
      * @throws NullPointerException when <code>pointList</code> is <code>null</code>, or contains a <code>null</code> value
      * @throws IllegalArgumentException when the provided points do not constitute a valid line (too few points or identical
      *             adjacent points)
      */
     public PolyLine3d(final double epsilon, final List<Point3d> pointList)
     {
         this(epsilon, pointList.toArray(new Point3d[Throw.whenNull(pointList, "pointList").size()]));
     }
 
     /**
      * Construct a new PolyLine3d from an existing one. This constructor is primarily intended for use in extending classes.
      * @param polyLine the existing PolyLine3d.
      * @throws NullPointerException when <code>polyLine</code> is <code>null</code>
      */
     public PolyLine3d(final PolyLine3d polyLine)
     {
         this.x = polyLine.x;
         this.y = polyLine.y;
         this.z = polyLine.z;
         this.lengthIndexedLine = polyLine.lengthIndexedLine;
         this.length = polyLine.length;
         this.bounds = polyLine.bounds;
         this.startDirY = polyLine.startDirY;
         this.startDirZ = polyLine.startDirZ;
     }
 
     @Override
     public PolyLine3d instantiate(final double epsilon, final List<Point3d> pointList)
     {
         return new PolyLine3d(epsilon, pointList);
     }
 
     /**
      * Build a list from the Point3d objects that an iterator provides.
      * @param iterator the iterator that will provide the points
      * @return a list of the points provided by the iterator
      * @throws NullPointerException when <code>iterator</code> is <code>null</code>
      */
     static List<Point3d> iteratorToList(final Iterator<Point3d> iterator)
     {
         List<Point3d> result = new ArrayList<>();
         iterator.forEachRemaining(result::add);
         return result;
     }
 
     @Override
     public int size()
     {
         return this.x.length;
     }
 
     @Override
     public final Point3d get(final int i) throws IndexOutOfBoundsException
     {
         return new Point3d(this.x[i], this.y[i], this.z[i]);
     }
 
     @Override
     public final double getX(final int i) throws IndexOutOfBoundsException
     {
         return this.x[i];
     }
 
     @Override
     public final double getY(final int i) throws IndexOutOfBoundsException
     {
         return this.y[i];
     }
 
     /**
      * Return the z-coordinate of a point of this PolyLine.
      * @param index the index of the requested z-coordinate
      * @return the z-coordinate of the requested point of this PolyLine
      * @throws IndexOutOfBoundsException when <code>index &lt; 0</code>, or <code>index &ge; size()</code>
      */
     public final double getZ(final int index)
     {
         return this.z[index];
     }
 
     @Override
     public LineSegment3d getSegment(final int index)
     {
         Throw.when(index < 0 || index >= this.x.length - 1, IndexOutOfBoundsException.class,
                 "index must be in range [0, size() - 1) (got %d)", index);
         return new LineSegment3d(this.x[index], this.y[index], this.z[index], this.x[index + 1], this.y[index + 1],
                 this.z[index + 1]);
     }
 
     @Override
     public final double lengthAtIndex(final int index)
     {
         return this.lengthIndexedLine[index];
     }
 
     @Override
     public double getLength()
     {
         return this.length;
     }
 
     @Override
     public Iterator<Point3d> iterator()
     {
         return new Iterator<Point3d>()
         {
             private int nextIndex = 0;
 
             @Override
             public boolean hasNext()
             {
                 return this.nextIndex < size();
             }
 
             @Override
             public Point3d next()
             {
                 return get(this.nextIndex++);
             }
         };
     }
 
     @Override
     public Bounds3d getBounds()
     {
         return this.bounds;
     }
 
     @Override
     public final PolyLine3d noiseFilteredLine(final double noiseLevel)
     {
         if (this.size() <= 2)
         {
             return this; // Except for some cached fields; a PolyLine2d is immutable; so safe to return
         }
         Point3d prevPoint = null;
         List<Point3d> list = new ArrayList<>();
         for (int index = 0; index < this.size(); index++)
         {
             Point3d 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));
         }
         return new PolyLine3d(list);
     }
 
     /**
      * Concatenate several PolyLine3d instances.
      * @param lines one or more PolyLine3d. The last point of the first &lt;strong&gt;must&lt;/strong&gt; match
      *            the first of the second, etc.
      * @return PolyLine3d
      * @throws NullPointerException when <code>lines</code> is <code>null</code>, or contains a <code>null</code> value
      * @throws IllegalArgumentException if zero lines are given, or when there is a gap between consecutive lines
      */
     public static PolyLine3d concatenate(final PolyLine3d... lines)
     {
         return concatenate(0.0, lines);
     }
 
     /**
      * Concatenate two PolyLine3d instances. This method is separate for efficiency reasons.
      * @param tolerance the tolerance between the end point of a line and the first point of the next line
      * @param line1 first line
      * @param line2 second line
      * @return the concatenation of the two lines
      * @throws NullPointerException when <code>line1</code>, or <code>line2</code> is <code>null</code>
      * @throws IllegalArgumentException when there is a gap between the lines
      */
     public static PolyLine3d concatenate(final double tolerance, final PolyLine3d line1, final PolyLine3d line2)
     {
         if (line1.getLast().distance(line2.getFirst()) > tolerance)
         {
             throw new IllegalArgumentException("Lines are not connected: " + line1.getLast() + " to " + line2.getFirst()
                     + " distance is " + line1.getLast().distance(line2.getFirst()) + " > " + tolerance);
         }
         int size = line1.size() + line2.size() - 1;
         Point3d[] points = new Point3d[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 PolyLine3d(points);
     }
 
     /**
      * Concatenate several PolyLine3d instances.
      * @param tolerance the tolerance between the end point of a line and the first point of the next line
      * @param lines one or more PolyLine3d. The last point of the first &lt;strong&gt;must&lt;/strong&gt; match
      *            the first of the second within the provided tolerance value, etc.
      * @return the concatenation of the lines
      * @throws NullPointerException when <code>lines</code> is <code>null</code>, or contains a <code>null</code> value
      * @throws IllegalArgumentException if zero lines are given, or when there is a gap larger than tolerance between
      *             consecutive lines
      */
     public static PolyLine3d concatenate(final double tolerance, final PolyLine3d... lines)
     {
         Throw.when(0 == lines.length, IllegalArgumentException.class, "Empty argument list");
         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 IllegalArgumentException(
                         "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;
         }
         Point3d[] points = new Point3d[size];
         int nextIndex = 0;
         for (int i = 0; i < lines.length; i++)
         {
             PolyLine3d line = lines[i];
             for (int j = 0 == i ? 0 : 1; j < line.size(); j++)
             {
                 points[nextIndex++] = line.get(j);
             }
         }
         return new PolyLine3d(points);
     }
 
     @Override
     public PolyLine2d project()
     {
         for (int i = 1; i < size(); i++)
         {
             if (this.x[i] != this.x[0] || this.y[i] != this.y[0])
             {
                 break;
             }
             Throw.when(i == size() - 1, DrawRuntimeException.class, "all points project onto the same point");
         }
         return new PolyLine2d(false, 0.0, this.x, this.y);
     }
 
     @Override
     public final DirectedPoint3d getLocationExtended(final double position)
     {
         if (position >= 0.0 && position <= this.length)
         {
             return getLocation(position);
         }
 
         // 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 DirectedPoint3d(this.x[0] + fraction * (this.x[1] - this.x[0]),
                     this.y[0] + fraction * (this.y[1] - this.y[0]), this.z[0] + fraction * (this.z[1] - this.z[0]), this.x[1],
                     this.y[1], this.z[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 - this.length;
         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 DirectedPoint3d(this.x[n1], this.y[n1], this.z[n1], 0.0, 0.0); // Bogus direction
             }
             fraction = len / (this.lengthIndexedLine[n1] - this.lengthIndexedLine[n2]);
         }
         return new DirectedPoint3d(this.x[n1] + fraction * (this.x[n1] - this.x[n2]),
                 this.y[n1] + fraction * (this.y[n1] - this.y[n2]), this.z[n1] + fraction * (this.z[n1] - this.z[n2]),
                 Math.atan2(Math.hypot(this.x[n1] - this.x[n2], this.y[n1] - this.y[n2]), this.z[n1] - this.z[n2]),
                 Math.atan2(this.y[n1] - this.y[n2], this.x[n1] - this.x[n2]));
     }
 
     @Override
     public final DirectedPoint3d getLocation(final double position)
     {
         Throw.whenNaN(position, "position");
         Throw.when(position < 0.0 || position > this.length, IllegalArgumentException.class,
                 "illegal position (got %f, should be in range [0.0, %f])", position, this.length);
         // 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 Ray3d(this.x[0], this.y[0], this.z[0], this.startDirZ, this.startDirY);
             }
             return new DirectedPoint3d(this.x[0], this.y[0], this.z[0], this.x[1], this.y[1], this.z[1]);
         }
         if (position == this.length)
         {
             return new DirectedPoint3d(this.x[this.x.length - 1], this.y[this.x.length - 1], this.z[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],
                     2 * this.z[this.x.length - 1] - this.z[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 DirectedPoint3d(this.x[index] + fraction * (this.x[index + 1] - this.x[index]),
                 this.y[index] + fraction * (this.y[index + 1] - this.y[index]),
                 this.z[index] + fraction * (this.z[index + 1] - this.z[index]), 2 * this.x[index + 1] - this.x[index],
                 2 * this.y[index + 1] - this.y[index], 2 * this.z[index + 1] - this.z[index]);
     }
 
     /**
      * Perform the orthogonal projection operation.
      * @param point the point to project
      * @param limitHandling if <code>Null</code>; results outside the interval [0.0, 1.0] are replaced by
      *            <code>NaN</code>, if <code>false</code>, results outside that interval are returned as is; if
      *            <code>true</code> results outside the interval are truncated to the interval and therefore not truly
      *            orthogonal
      * @return the fractional position on this <code>PolyLine3d</code> that is closest to point, or <code>NaN</code>
      * @throws NullPointerException when <code>point</code> is <code>null</code>
      */
     private double projectOrthogonalFractional(final Point3d point, final Boolean limitHandling)
     {
         Throw.whenNull(point, "point");
         double result = Double.NaN;
         if (this.lengthIndexedLine.length == 1)
         {
             // This is a degenerate PolyLine2d
             if (null != limitHandling && limitHandling)
             {
                 return 0.0;
             }
             result = new Ray3d(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.z[index - 1],
                     this.x[index], this.y[index], this.z[index], false, false);
             double distance = Math.hypot(
                     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]))),
                     point.z - (this.z[index - 1] + fraction * (this.z[index] - this.z[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(Math.hypot(point.x - this.x[index - 1], point.y - this.y[index - 1]),
                         point.z - this.z[index - 1]);
                 if (distance < bestDistance)
                 {
                     bestDistance = distance;
                     result = lengthAtIndex(index - 1);
                 }
             }
             else if (index == this.size() - 1 && limitHandling != null && limitHandling)
             {
                 distance = Math.hypot(Math.hypot(point.x - this.x[index], point.y - this.y[index]), point.z - this.z[index]);
                 if (distance < bestDistance)
                 {
                     bestDistance = distance;
                     result = lengthAtIndex(index);
                 }
             }
         }
         if (bestDistance > bestDistanceExtended && (limitHandling == null || !limitHandling))
         {
             return Double.NaN;
         }
         return result / this.length;
     }
 
     @Override
     public Point3d closestPointOnPolyLine(final Point3d point)
     {
         return getLocation(projectOrthogonalFractional(point, true) * this.length);
     }
 
     /**
      * Perform the project orthogonal operation.
      * @param point the point to project
      * @param limitHandling if <code>Null</code>; results outside the interval [0.0, 1.0] are replaced by
      *            <code>NaN</code>, if <code>false</code>, results outside that interval are returned as is; if
      *            <code>true</code> results outside the interval are truncated to the interval and therefore not truly
      *            orthogonal
      * @return the fractional position on this <code>PolyLine3d</code> that is closest to point, or <code>NaN</code>
      * @throws NullPointerException when <code>point</code> is <code>null</code>
      */
     private Point3d projectOrthogonal(final Point3d point, final Boolean limitHandling)
     {
         Throw.whenNull(point, "point");
         if (this.lengthIndexedLine.length == 1) // Handle degenerate case
         {
             // limitHandling == true is not handled because it cannot happen
             Point3d result = new Ray3d(getLocation(0.0)).projectOrthogonalExtended(point);
             if (null == limitHandling)
             {
                 return result.x != this.x[0] || result.y != this.y[0] || result.z != this.z[0] ? null : get(0);
             }
             // limitHandling is false
             return result;
         }
         double fraction = projectOrthogonalFractional(point, limitHandling);
         if (Double.isNaN(fraction))
         {
             return null;
         }
         return getLocationExtended(fraction * this.length);
     }
 
     @Override
     public Point3d projectOrthogonal(final Point3d point)
     {
         return projectOrthogonal(point, null);
     }
 
     @Override
     public Point3d projectOrthogonalExtended(final Point3d point)
     {
         return projectOrthogonal(point, false);
     }
 
     @Override
     public final double projectOrthogonalFractional(final Point3d point)
     {
         return projectOrthogonalFractional(point, null);
     }
 
     @Override
     public double projectOrthogonalFractionalExtended(final Point3d point)
     {
         return projectOrthogonalFractional(point, false);
     }
 
     @Override
     public PolyLine3d extract(final double start, final double end)
     {
         Throw.whenNaN(start, "start");
         Throw.whenNaN(end, "end");
         Throw.when(start < 0 || start >= end || end > this.length, IllegalArgumentException.class,
                 "Bad interval (%f...%f; length of this PolyLine3d is %f)", start, end, this.length);
         double cumulativeLength = 0;
         double nextCumulativeLength = 0;
         double segmentLength = 0;
         int index = 0;
         List<Point3d> pointList = new ArrayList<>();
         while (start > cumulativeLength)
         {
             Point3d fromPoint = get(index);
             index++;
             Point3d 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)
         {
             Point3d fromPoint = get(index);
             index++;
             if (index >= size())
             {
                 break; // rounding error
             }
             Point3d 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)
         {
             Point3d 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
         return instantiate(pointList);
     }
 
     @Override
     public PolyLine3d offsetLine(final double offset, final double circlePrecision, final double offsetMinimumFilterValue,
             final double offsetMaximumFilterValue, final double offsetFilterRatio, final double minimumOffset)
     {
         return restoreElevation(project().offsetLine(offset, circlePrecision, offsetMinimumFilterValue,
                 offsetMaximumFilterValue, offsetFilterRatio, minimumOffset));
     }
 
     @Override
     public PolyLine3d offsetLine(final double[] relativeFractions, final double[] offsets,
             final double offsetMinimumFilterValue)
     {
         return restoreElevation(project().offsetLine(relativeFractions, offsets, offsetMinimumFilterValue));
     }
 
     /**
      * Approximate the z-values of a PolyLine that was made 2d in order to apply some modification.
      * @param flat the modified 2d PolyLine
      * @return the PolyLine with approximately restored z-values
      */
     private PolyLine3d restoreElevation(final PolyLine2d flat)
     {
         List<Point3d> points = new ArrayList<>();
         int start = 0;
         for (int index = 0; index < flat.size(); index++)
         {
             Point2d point2d = flat.get(index);
             // Find the closest point in reference to point2d; starting at start
             int bestIndex = start;
             double bestDistance = Double.POSITIVE_INFINITY;
             Point3d bestInReference = null;
             for (int i = start; i < size(); i++)
             {
                 Point3d pointInReference = get(i);
                 double distance = point2d.distance(pointInReference.project());
                 if (distance < bestDistance)
                 {
                     bestIndex = i;
                     bestDistance = distance;
                     bestInReference = pointInReference;
                 }
             }
             points.add(new Point3d(point2d, bestInReference.z));
             start = bestIndex;
         }
         return new PolyLine3d(points);
     }
 
     @Override
     public PolyLine3d offsetLine(final double offsetAtStart, final double offsetAtEnd, final double circlePrecision,
             final double offsetMinimumFilterValue, final double offsetMaximumFilterValue, final double offsetFilterRatio,
             final double minimumOffset)
     {
         if (offsetAtStart == offsetAtEnd)
         {
             return offsetLine(offsetAtStart, circlePrecision, offsetMinimumFilterValue, offsetMaximumFilterValue,
                     offsetFilterRatio, minimumOffset);
         }
         PolyLine3d atStart = offsetLine(offsetAtStart, circlePrecision, offsetMinimumFilterValue, offsetMaximumFilterValue,
                 offsetFilterRatio, minimumOffset);
         PolyLine3d atEnd = offsetLine(offsetAtEnd, circlePrecision, offsetMinimumFilterValue, offsetMaximumFilterValue,
                 offsetFilterRatio, minimumOffset);
         return atStart.transitionLine(atEnd, new TransitionFunction()
         {
             @Override
             public double function(final double fraction)
             {
                 return fraction;
             }
         });
     }
 
     @Override
     public PolyLine3d transitionLine(final PolyLine3d endLine, final TransitionFunction transition)
     {
         Throw.whenNull(endLine, "endLine");
         Throw.whenNull(transition, "transition");
         List<Point3d> pointList = new ArrayList<>();
         int indexInStart = 0;
         int indexInEnd = 0;
         while (indexInStart < this.size() && indexInEnd < endLine.size())
         {
             double fractionInStart = lengthAtIndex(indexInStart) / this.length;
             double fractionInEnd = endLine.lengthAtIndex(indexInEnd) / endLine.length;
             if (fractionInStart < fractionInEnd)
             {
                 pointList.add(get(indexInStart).interpolate(endLine.getLocation(fractionInStart * endLine.length),
                         transition.function(fractionInStart)));
                 indexInStart++;
             }
             else if (fractionInStart > fractionInEnd)
             {
                 pointList.add(this.getLocation(fractionInEnd * this.length).interpolate(endLine.get(indexInEnd),
                         transition.function(fractionInEnd)));
                 indexInEnd++;
             }
             else
             {
                 pointList.add(this.get(indexInStart).interpolate(endLine.getLocation(fractionInEnd * endLine.length),
                         transition.function(fractionInStart)));
                 indexInStart++;
                 indexInEnd++;
             }
         }
         return new PolyLine3d(0.0, pointList);
     }
 
     @Override
     public PolyLine3d truncate(final double position)
     {
         Throw.when(position <= 0.0 || position > this.length, IllegalArgumentException.class,
                 "illegal position (got %f should be in range (0.0, %f])", position, this.length);
         // handle special case: position == length
         if (position == this.length)
         {
             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));
         Point3d p1 = get(index);
         Point3d lastPoint;
         if (0.0 == fraction)
         {
             lastPoint = p1;
         }
         else
         {
             Point3d p2 = get(index + 1);
             lastPoint = p1.interpolate(p2, fraction);
             index++;
         }
         double[] truncatedX = new double[index + 1];
         double[] truncatedY = new double[index + 1];
         double[] truncatedZ = new double[index + 1];
         for (int i = 0; i < index; i++)
         {
             truncatedX[i] = this.x[i];
             truncatedY[i] = this.y[i];
             truncatedZ[i] = this.z[i];
         }
         truncatedX[index] = lastPoint.x;
         truncatedY[index] = lastPoint.y;
         truncatedZ[index] = lastPoint.z;
         return new PolyLine3d(truncatedX, truncatedY, truncatedZ);
     }
 
     @Override
     public String toString()
     {
         return toString("%f", false);
     }
 
     @Override
     public String toString(final String doubleFormat, final boolean doNotIncludeClassName)
     {
         StringBuilder result = new StringBuilder();
         if (!doNotIncludeClassName)
         {
             result.append("PolyLine3d ");
         }
         String format = String.format("%%sx=%1$s, y=%1$s, z=%1$s", doubleFormat);
         for (int index = 0; index < this.x.length; index++)
         {
             result.append(
                     String.format(Locale.US, format, index == 0 ? "[" : ", ", this.x[index], this.y[index], this.z[index]));
         }
         if (this.lengthIndexedLine.length == 1)
         {
             format = String.format(", startDirY=%1$s, startDirZ=%1$s", doubleFormat);
             result.append(String.format(Locale.US, format, this.startDirY, this.startDirZ));
         }
         result.append("]");
         return result.toString();
     }
 
     @Override
     public int hashCode()
     {
         final int prime = 31;
         int result = 1;
         long temp;
         temp = Double.doubleToLongBits(this.startDirZ);
         result = prime * result + (int) (temp ^ (temp >>> 32));
         temp = Double.doubleToLongBits(this.startDirY);
         result = prime * result + (int) (temp ^ (temp >>> 32));
         result = prime * result + Arrays.hashCode(this.x);
         result = prime * result + Arrays.hashCode(this.y);
         result = prime * result + Arrays.hashCode(this.z);
         return result;
     }
 
     @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;
         PolyLine3d other = (PolyLine3d) obj;
         if (Double.doubleToLongBits(this.startDirZ) != Double.doubleToLongBits(other.startDirZ))
             return false;
         if (Double.doubleToLongBits(this.startDirY) != Double.doubleToLongBits(other.startDirY))
             return false;
         if (!Arrays.equals(this.x, other.x))
             return false;
         if (!Arrays.equals(this.y, other.y))
             return false;
         if (!Arrays.equals(this.z, other.z))
             return false;
         return true;
     }
 
 }