package org.opentrafficsim.core.geometry;
   
   import java.awt.geom.Point2D;
   import java.io.Serializable;
   import java.util.ArrayList;
   import java.util.List;
   
   import org.djunits.unit.DirectionUnit;
   import org.djunits.unit.LengthUnit;
  import org.djunits.unit.Unit;
  import org.djunits.value.storage.StorageType;
  import org.djunits.value.vdouble.scalar.Direction;
  import org.djunits.value.vdouble.scalar.Length;
  import org.djunits.value.vdouble.scalar.base.DoubleScalarInterface;
  import org.djunits.value.vdouble.vector.base.DoubleVector;
  import org.djunits.value.vdouble.vector.base.DoubleVectorInterface;
  import org.djutils.draw.point.Point3d;
  import org.locationtech.jts.geom.Coordinate;
  import org.locationtech.jts.geom.Point;
  
  import nl.tudelft.simulation.dsol.animation.Locatable;
  import nl.tudelft.simulation.language.d3.CartesianPoint;
  
  /**
   * An OTSPoint3D implements a 3D-coordinate for OTS. X, y and z are stored as doubles, but it is assumed that the scale is in SI
   * units, i.e. in meters. A distance between two points is therefore also in meters.
   * <p>
   * Copyright (c) 2013-2022 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved. <br>
   * BSD-style license. See <a href="http://opentrafficsim.org/docs/license.html">OpenTrafficSim License</a>.
   * <p>
   * $LastChangedDate: 2015-07-16 10:20:53 +0200 (Thu, 16 Jul 2015) $, @version $Revision: 1124 $, by $Author: pknoppers $,
   * initial version Jul 22, 2015 <br>
   * @author <a href="http://www.tbm.tudelft.nl/averbraeck">Alexander Verbraeck</a>
   * @author <a href="http://www.tudelft.nl/pknoppers">Peter Knoppers</a>
   * @author <a href="http://www.citg.tudelft.nl">Guus Tamminga</a>
   */
  public class OTSPoint3D implements Locatable, Serializable
  {
      /** */
      private static final long serialVersionUID = 20150722L;
  
      /** The internal representation of the point; x-coordinate. */
      @SuppressWarnings("checkstyle:visibilitymodifier")
      public final double x;
  
      /** The internal representation of the point; y-coordinate. */
      @SuppressWarnings("checkstyle:visibilitymodifier")
      public final double y;
  
      /** The internal representation of the point; z-coordinate. */
      @SuppressWarnings("checkstyle:visibilitymodifier")
      public final double z;
  
      /**
       * The x, y and z in the point are assumed to be in meters relative to an origin.
       * @param x double; x-coordinate
       * @param y double; y-coordinate
       * @param z double; z-coordinate
       */
      public OTSPoint3D(final double x, final double y, final double z)
      {
          this.x = x;
          this.y = y;
          this.z = z;
      }
  
      /**
       * @param xyz array with three elements; x, y and z are assumed to be in meters relative to an origin.
       */
      public OTSPoint3D(final double[] xyz)
      {
          this(xyz[0], xyz[1], (xyz.length > 2) ? xyz[2] : 0.0);
      }
  
      /**
       * @param point OTSPoint3D; a point to "clone".
       */
      public OTSPoint3Deometry/OTSPoint3D.html#OTSPoint3D">OTSPoint3D(final OTSPoint3D point)
      {
          this(point.x, point.y, point.z);
      }
  
      /**
       * @param point javax.vecmath 3D double point; the x, y and z in the point are assumed to be in meters relative to an
       *            origin.
       */
      public OTSPoint3D(final Point3d point)
      {
          this(point.x, point.y, point.z);
      }
  
      /**
       * @param point javax.vecmath 3D double point; the x, y and z in the point are assumed to be in meters relative to an
       *            origin.
       */
      public OTSPoint3D(final CartesianPoint point)
      {
          this(point.x, point.y, point.z);
      }
 
     /**
      * @param point javax.vecmath 3D double point; the x, y and z in the point are assumed to be in meters relative to an
      *            origin.
      */
     public OTSPoint3D(final DirectedPoint point)
     {
         this(point.x, point.y, point.z);
     }
 
     /**
      * @param point2d java.awt 2D point, z-coordinate will be zero; the x and y in the point are assumed to be in meters
      *            relative to an origin.
      */
     public OTSPoint3D(final Point2D point2d)
     {
         this(point2d.getX(), point2d.getY(), 0.0);
     }
 
     /**
      * @param coordinate geotools coordinate; the x, y and z in the coordinate are assumed to be in meters relative to an
      *            origin.
      */
     public OTSPoint3D(final Coordinate coordinate)
     {
         this(coordinate.x, coordinate.y, Double.isNaN(coordinate.getZ()) ? 0.0 : coordinate.getZ());
     }
 
     /**
      * @param point geotools point; z-coordinate will be zero; the x and y in the point are assumed to be in meters relative to
      *            an origin.
      */
     public OTSPoint3D(final Point point)
     {
         this(point.getX(), point.getY(), 0.0);
     }
 
     /**
      * The x and y in the point are assumed to be in meters relative to an origin. z will be set to 0.
      * @param x double; x-coordinate
      * @param y double; y-coordinate
      */
     public OTSPoint3D(final double x, final double y)
     {
         this(x, y, 0.0);
     }
 
     /**
      * Interpolate (or extrapolate) between (outside) two given points.
      * @param ratio double; 0 selects the zeroValue point, 1 selects the oneValue point, 0.5 selects a point halfway, etc.
      * @param zeroValue OTSPoint3D; the point that is returned when ratio equals 0
      * @param oneValue OTSPoint3D; the point that is returned when ratio equals 1
      * @return OTSPoint3D
      */
     public static OTSPoint3D interpolate(finalOTSPoint3DPoint3D.html#OTSPoint3D">OTSPoint3Ddouble ratio, final OTSPoint3DPoint3D.html#OTSPoint3D">OTSPoint3D zeroValue, final OTSPoint3D oneValue)
     {
         double complement = 1 - ratio;
         return new OTSPoint3D(complement * zeroValue.x + ratio * oneValue.x, complement * zeroValue.y + ratio * oneValue.y,
                 complement * zeroValue.z + ratio * oneValue.z);
     }
 
     /**
      * Compute the 2D intersection of two line segments. The Z-component of the lines is ignored. Both line segments are defined
      * by two points (that should be distinct). This version suffers loss of precision when called with very large coordinate
      * values.
      * @param line1P1 OTSPoint3D; first point of line segment 1
      * @param line1P2 OTSPoint3D; second point of line segment 1
      * @param line2P1 OTSPoint3D; first point of line segment 2
      * @param line2P2 OTSPoint3D; second point of line segment 2
      * @return OTSPoint3D; the intersection of the two lines, or null if the lines are (almost) parallel, or do not intersect
      */
     @Deprecated
     public static OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3Dt3D">OTSPoint3D intersectionOfLineSegmentsDumb(final OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3D line1P1, final OTSPoint3D line1P2,
             final OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3D line2P1, final OTSPoint3D line2P2)
     {
         double denominator =
                 (line2P2.y - line2P1.y) * (line1P2.x - line1P1.x) - (line2P2.x - line2P1.x) * (line1P2.y - line1P1.y);
         if (denominator == 0f)
         {
             return null; // lines are parallel (they might even be on top of each other, but we don't check that)
         }
         double uA = ((line2P2.x - line2P1.x) * (line1P1.y - line2P1.y) - (line2P2.y - line2P1.y) * (line1P1.x - line2P1.x))
                 / denominator;
         if ((uA < 0f) || (uA > 1f))
         {
             return null; // intersection outside line 1
         }
         double uB = ((line1P2.x - line1P1.x) * (line1P1.y - line2P1.y) - (line1P2.y - line1P1.y) * (line1P1.x - line2P1.x))
                 / denominator;
         if (uB < 0 || uB > 1)
         {
             return null; // intersection outside line 2
         }
         return new OTSPoint3D(line1P1.x + uA * (line1P2.x - line1P1.x), line1P1.y + uA * (line1P2.y - line1P1.y), 0);
     }
 
     /**
      * Compute the 2D intersection of two line segments. The Z-component of the lines is ignored. Both line segments are defined
      * by two points (that should be distinct).
      * @param line1P1 OTSPoint3D; first point of line segment 1
      * @param line1P2 OTSPoint3D; second point of line segment 1
      * @param line2P1 OTSPoint3D; first point of line segment 2
      * @param line2P2 OTSPoint3D; second point of line segment 2
      * @return OTSPoint3D; the intersection of the two lines, or null if the lines are (almost) parallel, or do not intersect
      */
     public static OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3DPoint3D">OTSPoint3D intersectionOfLineSegments(final OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3D line1P1, final OTSPoint3D line1P2,
             final OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3D line2P1, final OTSPoint3D line2P2)
     {
         double l1p1x = line1P1.x;
         double l1p1y = line1P1.y;
         double l1p2x = line1P2.x - l1p1x;
         double l1p2y = line1P2.y - l1p1y;
         double l2p1x = line2P1.x - l1p1x;
         double l2p1y = line2P1.y - l1p1y;
         double l2p2x = line2P2.x - l1p1x;
         double l2p2y = line2P2.y - l1p1y;
         double denominator = (l2p2y - l2p1y) * l1p2x - (l2p2x - l2p1x) * l1p2y;
         if (denominator == 0.0)
         {
             return null; // lines are parallel (they might even be on top of each other, but we don't check that)
         }
         double uA = ((l2p2x - l2p1x) * (-l2p1y) - (l2p2y - l2p1y) * (-l2p1x)) / denominator;
         // System.out.println("uA is " + uA);
         if ((uA < 0.0) || (uA > 1.0))
         {
             return null; // intersection outside line 1
         }
         double uB = (l1p2y * l2p1x - l1p2x * l2p1y) / denominator;
         // System.out.println("uB is " + uB);
         if (uB < 0.0 || uB > 1.0)
         {
             return null; // intersection outside line 2
         }
         return new OTSPoint3D(line1P1.x + uA * l1p2x, line1P1.y + uA * l1p2y, 0);
     }
 
     /**
      * Compute the 2D intersection of two infinite lines. The Z-component of the lines is ignored. Both lines are defined by two
      * points (that should be distinct). This version suffers loss of precision when called with very large coordinate values.
      * @param line1P1 OTSPoint3D; first point of line 1
      * @param line1P2 OTSPoint3D; second point of line 1
      * @param line2P1 OTSPoint3D; first point of line 2
      * @param line2P2 OTSPoint3D; second point of line 2
      * @return OTSPoint3D; the intersection of the two lines, or null if the lines are (almost) parallel
      */
     @Deprecated
     public static OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3DOTSPoint3D">OTSPoint3D intersectionOfLinesDumb(final OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3D line1P1, final OTSPoint3D line1P2,
             final OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3D line2P1, final OTSPoint3D line2P2)
     {
         double determinant =
                 (line1P1.x - line1P2.x) * (line2P1.y - line2P2.y) - (line1P1.y - line1P2.y) * (line2P1.x - line2P2.x);
         if (Math.abs(determinant) < 0.0000001)
         {
             return null;
         }
         return new OTSPoint3D(
                 ((line1P1.x * line1P2.y - line1P1.y * line1P2.x) * (line2P1.x - line2P2.x)
                         - (line1P1.x - line1P2.x) * (line2P1.x * line2P2.y - line2P1.y * line2P2.x)) / determinant,
                 ((line1P1.x * line1P2.y - line1P1.y * line1P2.x) * (line2P1.y - line2P2.y)
                         - (line1P1.y - line1P2.y) * (line2P1.x * line2P2.y - line2P1.y * line2P2.x)) / determinant);
     }
 
     /**
      * Compute the 2D intersection of two infinite lines. The Z-component of the lines is ignored. Both lines are defined by two
      * points (that should be distinct).
      * @param line1P1 OTSPoint3D; first point of line 1
      * @param line1P2 OTSPoint3D; second point of line 1
      * @param line2P1 OTSPoint3D; first point of line 2
      * @param line2P2 OTSPoint3D; second point of line 2
      * @return OTSPoint3D; the intersection of the two lines, or null if the lines are (almost) parallel
      */
     public static OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3Dtml#OTSPoint3D">OTSPoint3D intersectionOfLines(final OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3D line1P1, final OTSPoint3DTSPoint3D.html#OTSPoint3D">OTSPoint3D line1P2, final OTSPoint3D line2P1,
             final OTSPoint3D line2P2)
     {
         double l1p1x = line1P1.x;
         double l1p1y = line1P1.y;
         double l1p2x = line1P2.x - l1p1x;
         double l1p2y = line1P2.y - l1p1y;
         double l2p1x = line2P1.x - l1p1x;
         double l2p1y = line2P1.y - l1p1y;
         double l2p2x = line2P2.x - l1p1x;
         double l2p2y = line2P2.y - l1p1y;
         double determinant = (0 - l1p2x) * (l2p1y - l2p2y) - (0 - l1p2y) * (l2p1x - l2p2x);
         if (Math.abs(determinant) < 0.0000001)
         {
             return null;
         }
         return new OTSPoint3D(l1p1x + (l1p2x * (l2p1x * l2p2y - l2p1y * l2p2x)) / determinant,
                 l1p1y + (l1p2y * (l2p1x * l2p2y - l2p1y * l2p2x)) / determinant);
     }
 
     /**
      * Project a point on a line segment (2D - Z-component is ignored). If the the projected points lies outside the line
      * segment, the nearest end point of the line segment is returned. Otherwise the returned point lies between the end points
      * of the line segment. <br>
      * Adapted from <a href="http://paulbourke.net/geometry/pointlineplane/DistancePoint.java">example code provided by Paul
      * Bourke</a>.
      * @param segmentPoint1 OTSPoint3D; start of line segment
      * @param segmentPoint2 OTSPoint3D; end of line segment
      * @return Point2D.Double; either <cite>lineP1</cite>, or <cite>lineP2</cite> or a new OTSPoint3D that lies somewhere in
      *         between those two. The Z-component of the result matches the Z-component of the line segment at that point
      */
     public final OTSPoint3Dt3D.html#OTSPoint3D">OTSPoint3Dl#OTSPoint3D">OTSPoint3D closestPointOnSegment(final OTSPoint3Dt3D.html#OTSPoint3D">OTSPoint3D segmentPoint1, final OTSPoint3D segmentPoint2)
     {
         double dX = segmentPoint2.x - segmentPoint1.x;
         double dY = segmentPoint2.y - segmentPoint1.y;
         if ((0 == dX) && (0 == dY))
         {
             return segmentPoint1;
         }
         final double u = ((this.x - segmentPoint1.x) * dX + (this.y - segmentPoint1.y) * dY) / (dX * dX + dY * dY);
         if (u < 0)
         {
             return segmentPoint1;
         }
         else if (u > 1)
         {
             return segmentPoint2;
         }
         else
         {
             return interpolate(u, segmentPoint1, segmentPoint2);
         }
     }
 
     /**
      * Return the closest point on an OTSLine3D.
      * @param line OTSLine3D; the line
      * @param useHorizontalDistance boolean; if true; the horizontal distance is used to determine the closest point; if false;
      *            the 3D distance is used to determine the closest point
      * @return OTSPoint3D; the Z component of the returned point matches the Z-component of the line at that point
      */
     private OTSPoint3D internalClosestPointOnLine(final OTSLine3D line, final boolean useHorizontalDistance)
     {
         OTSPoint3D prevPoint = null;
         double distance = Double.MAX_VALUE;
         OTSPoint3D result = null;
         for (OTSPoint3D nextPoint : line.getPoints())
         {
             if (null != prevPoint)
             {
                 OTSPoint3D closest = closestPointOnSegment(prevPoint, nextPoint);
                 double thisDistance = useHorizontalDistance ? horizontalDistanceSI(closest) : distanceSI(closest);
                 if (thisDistance < distance)
                 {
                     result = closest;
                     distance = thisDistance;
                 }
             }
             prevPoint = nextPoint;
         }
         return result;
     }
 
     /**
      * Return the closest point on an OTSLine3D. This method takes the Z-component of this point and the line into account.
      * @param line OTSLine3D; the line
      * @return OTSPoint3D; the Z-component of the returned point matches the Z-component of the line at that point
      */
     public final OTSPoint3D closestPointOnLine(final OTSLine3D line)
     {
         return internalClosestPointOnLine(line, false);
     }
 
     /**
      * Return the closest point on an OTSLine3D. This method ignores the Z-component of this point and the line when computing
      * the distance.
      * @param line OTSLine3D; the line
      * @return OTSPoint3D; the Z-component of the returned point matches the Z-component of the line at that point
      */
     public final OTSPoint3D closestPointOnLine2D(final OTSLine3D line)
     {
         return internalClosestPointOnLine(line, true);
     }
 
     /**
      * Return the point with a length of 1 to the origin.
      * @return OTSPoint3D; the normalized point
      */
     public final OTSPoint3D normalize()
     {
         double length = Math.sqrt(this.x * this.x + this.y * this.y + this.z * this.z);
         return this.translate(length);
     }
 
     /**
      * Return this point translated by a factor from the origin.
      * @param factor double; the translation factor
      * @return OTSPoint3D; the translated point
      */
     public final OTSPoint3D translate(final double factor)
     {
         return new OTSPoint3D(this.x / factor, this.y / factor, this.z / factor);
     }
 
     /**
      * Return the possible center points of a circle (sphere), given two points and a radius. Only points with Z-coordinate
      * equal to the mean of the given points are returned. (Without this restriction on the Z-coordinate, the result set would
      * be either empty, a single point, or all points on a circle.)
      * @param point1 OTSPoint3D; the first point
      * @param point2 OTSPoint3D; the second point
      * @param radius double; the radius
      * @return List&lt;OTSPoint3D&gt; a list of zero, one or two points
      */
     public static final List<OTSPoint3D> circleCenter(final OTSPoint3DOTSPoint3D.html#OTSPoint3D">OTSPoint3D point1, final OTSPoint3D point2, final double radius)
     {
         List<OTSPoint3D> result = new ArrayList<>();
         OTSPoint3D m = interpolate(0.5, point1, point2);
         double h = point1.distanceSI(m);
         if (radius < h) // no intersection
         {
             return result;
         }
         if (radius == h) // intersection at m
         {
             result.add(m);
             return result;
         }
         OTSPoint3Dmetry/OTSPoint3D.html#OTSPoint3D">OTSPoint3D p = new OTSPoint3D(point2.y - point1.y, point1.x - point2.x).normalize();
         double d = Math.sqrt(radius * radius - h * h); // distance of center from m
         d = Math.sqrt(radius * radius - h * h);
         result.add(new OTSPoint3D(m.x + d * p.x, m.y + d * p.y, m.z));
         result.add(new OTSPoint3D(m.x - d * p.x, m.y - d * p.y, m.z));
         return result;
     }
 
     /**
      * Return the possible intersections between two circles.
      * @param center1 OTSPoint3D; the center of circle 1
      * @param radius1 double; the radius of circle 1
      * @param center2 OTSPoint3D; the center of circle 2
      * @param radius2 double; the radius of circle 2
      * @return List&lt;OTSPoint3D&gt; a list of zero, one or two points
      */
     public static final List<OTSPoint3D> circleIntersections(final OTSPoint3D center1, final double radius1,
             final OTSPoint3D center2, final double radius2)
     {
         List<OTSPoint3D> center = new ArrayList<>();
         OTSPoint3D m = interpolate(radius1 / (radius1 + radius2), center1, center2);
         double h = center1.distanceSI(m);
         if (radius1 < h) // no intersection
         {
             return center;
         }
         if (radius1 == h) // intersection at m
         {
             center.add(m);
             return center;
         }
         OTSPoint3Dmetry/OTSPoint3D.html#OTSPoint3D">OTSPoint3D p = new OTSPoint3D(center2.y - center1.y, center1.x - center2.x).normalize();
         double d = Math.sqrt(radius1 * radius1 - h * h); // distance of center from m
         center.add(new OTSPoint3D(m.x + d * p.x, m.y + d * p.y, m.z));
         center.add(new OTSPoint3D(m.x - d * p.x, m.y - d * p.y, m.z));
         return center;
     }
 
     /**
      * @param point OTSPoint3D; the point to which the distance has to be calculated.
      * @return the distance in 3D according to Pythagoras, expressed in the SI unit for length (meter)
      */
     public final double distanceSI(final OTSPoint3D point)
     {
         double dx = point.x - this.x;
         double dy = point.y - this.y;
         double dz = point.z - this.z;
 
         return Math.sqrt(dx * dx + dy * dy + dz * dz);
     }
 
     /**
      * @param point OTSPoint3D; the point to which the distance has to be calculated.
      * @return the distance in 3D according to Pythagoras, expressed in the SI unit for length (meter)
      */
     public final double horizontalDistanceSI(final OTSPoint3D point)
     {
         double dx = point.x - this.x;
         double dy = point.y - this.y;
 
         return Math.sqrt(dx * dx + dy * dy);
     }
 
     /**
      * @param point OTSPoint3D; the point to which the distance has to be calculated.
      * @return the distance in 3D according to Pythagoras
      */
     public final Length horizontalDistance(final OTSPoint3D point)
     {
         return new Length(horizontalDistanceSI(point), LengthUnit.SI);
     }
 
     /**
      * Compute the distance to another point.
      * @param point OTSPoint3D; the point to which the distance has to be calculated.
      * @return the distance in 3D according to Pythagoras
      */
     public final Length distance(final OTSPoint3D point)
     {
         return new Length(distanceSI(point), LengthUnit.SI);
     }
 
     /**
      * Compute the horizontal direction to another point.
      * @param point OTSPoint3D; the other point
      * @return double; the direction in radians
      */
     public final double horizontalDirectionSI(final OTSPoint3D point)
     {
         return Math.atan2(point.y - this.y, point.x - this.x);
     }
 
     /**
      * Compute the horizontal direction to another point.
      * @param point OTSPoint3D; the other point
      * @return double; the direction in radians
      */
     public final Direction horizontalDirection(final OTSPoint3D point)
     {
         return Direction.instantiateSI(Math.atan2(point.y - this.y, point.x - this.x));
     }
 
     /**
      * @return the equivalent geotools Coordinate of this point.
      */
     public final Coordinate getCoordinate()
     {
         return new Coordinate(this.x, this.y, this.z);
     }
 
     /**
      * @return the equivalent DSOL DirectedPoint of this point. Should the result be cached?
      */
     public final DirectedPoint getDirectedPoint()
     {
         return new DirectedPoint(this.x, this.y, this.z);
     }
 
     /**
      * @return a Point2D with the x and y structure.
      */
     public final Point2D getPoint2D()
     {
         return new Point2D.Double(this.x, this.y);
     }
 
     /** {@inheritDoc} */
     @Override
     public final DirectedPoint getLocation()
     {
         return getDirectedPoint();
     }
 
     /**
      * This method returns a sphere with a diameter of half a meter as the default bounds for a point. {@inheritDoc}
      */
     @Override
     public final Bounds getBounds()
     {
         return new Bounds();
     }
 
     /**
      * Create a DENSE DoubleVector with the x, y and z values of this OTSPoint3D.
      * @param unit U; unit of the values in this OTSPoint3D (and also the display unit of the returned DoubleVector)
      * @return DoubleVector; the constructed DoubleVector, size is 3; first value is x, second is y, third is z
      * @param <U> the unit type
      * @param <S> the corresponding scalar type
      * @param <V> the corresponding vector type
      */
     public <U extends Unit<U>, S extends DoubleScalarInterface<U, S>,
             V extends DoubleVectorInterface<U, S, V>> V doubleVector(final U unit)
     {
         return DoubleVector.instantiate(new double[] { this.x, this.y, this.z }, unit, StorageType.DENSE);
     }
     
     /**
      * Construct a Direction from the rotZ component of a DirectedPoint.
      * @param directedPoint DirectedPoint; the DirectedPoint
      * @param directionUnit DirectionUnit; the unit in which the rotZ of <code>directedPoint</code> is expressed and which is
      *            also the display unit of the returned Direction
      * @return Direction; the horizontal direction (rotZ) of the <code>directedPoint</code> with display unit
      *         <code>directionUnit</code>
      */
     public static Direction direction(final DirectedPoint directedPoint, final DirectionUnit directionUnit)
     {
         return new Direction(directedPoint.getRotZ(), directionUnit);
     }
 
     /** {@inheritDoc} */
     @Override
     @SuppressWarnings("checkstyle:designforextension")
     public String toString()
     {
         return String.format("(%.3f,%.3f,%.3f)", this.x, this.y, this.z);
     }
 
     /** {@inheritDoc} */
     @Override
     @SuppressWarnings("checkstyle:designforextension")
     public int hashCode()
     {
         final int prime = 31;
         int result = 1;
         long temp;
         temp = Double.doubleToLongBits(this.x);
         result = prime * result + (int) (temp ^ (temp >>> 32));
         temp = Double.doubleToLongBits(this.y);
         result = prime * result + (int) (temp ^ (temp >>> 32));
         temp = Double.doubleToLongBits(this.z);
         result = prime * result + (int) (temp ^ (temp >>> 32));
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     @SuppressWarnings({ "checkstyle:designforextension", "checkstyle:needbraces" })
     public boolean equals(final Object obj)
     {
         if (this == obj)
             return true;
         if (obj == null)
             return false;
         if (getClass() != obj.getClass())
             return false;
         OTSPoint3D../../../org/opentrafficsim/core/geometry/OTSPoint3D.html#OTSPoint3D">OTSPoint3D other = (OTSPoint3D) obj;
         if (Double.doubleToLongBits(this.x) != Double.doubleToLongBits(other.x))
             return false;
         if (Double.doubleToLongBits(this.y) != Double.doubleToLongBits(other.y))
             return false;
         if (Double.doubleToLongBits(this.z) != Double.doubleToLongBits(other.z))
             return false;
         return true;
     }
 
 }