package org.opentrafficsim.road.gtu.lane.perception;
   
   import java.util.ArrayList;
   import java.util.Collection;
   import java.util.HashMap;
   import java.util.HashSet;
   import java.util.LinkedHashSet;
   import java.util.List;
   import java.util.Map;
  import java.util.Set;
  
  import org.djunits.unit.LengthUnit;
  import org.djunits.unit.SpeedUnit;
  import org.djunits.value.vdouble.scalar.Length;
  import org.djunits.value.vdouble.scalar.Speed;
  import org.djunits.value.vdouble.scalar.Time;
  import org.opentrafficsim.core.Throw;
  import org.opentrafficsim.core.gtu.GTUDirectionality;
  import org.opentrafficsim.core.gtu.GTUException;
  import org.opentrafficsim.core.gtu.RelativePosition;
  import org.opentrafficsim.core.gtu.behavioralcharacteristics.ParameterException;
  import org.opentrafficsim.core.gtu.behavioralcharacteristics.ParameterTypes;
  import org.opentrafficsim.core.gtu.perception.TimeStampedObject;
  import org.opentrafficsim.core.network.LateralDirectionality;
  import org.opentrafficsim.core.network.NetworkException;
  import org.opentrafficsim.core.perception.PerceivedObject;
  import org.opentrafficsim.road.gtu.lane.LaneBasedGTU;
  import org.opentrafficsim.road.gtu.lane.tactical.AbstractLaneBasedTacticalPlanner;
  import org.opentrafficsim.road.gtu.lane.tactical.LanePathInfo;
  import org.opentrafficsim.road.network.lane.Lane;
  import org.opentrafficsim.road.network.lane.LaneDirection;
  
  /**
   * The perception module of a GTU based on lanes. It is responsible for perceiving (sensing) the environment of the GTU, which
   * includes the locations of other GTUs. Perception is done at a certain time, and the perceived information might have a
   * limited validity. In that sense, Perception is stateful. Information can be requested as often as needed, but will only be
   * recalculated when asked explicitly. This abstract class provides the building blocks for lane-based perception. <br>
   * Perception for lane-based GTUs involves information about GTUs in front of the owner GTU on the same lane (the 'leader' GTU),
   * parallel vehicles (important if we want to change lanes), distance to other vehicles on parallel lanes, as well in front as
   * to the back (important if we want to change lanes), and information about obstacles, traffic lights, speed signs, and ending
   * lanes.
   * <p>
   * Copyright (c) 2013-2015 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: 2015-07-24 02:58:59 +0200 (Fri, 24 Jul 2015) $, @version $Revision: 1147 $, by $Author: averbraeck $,
   * initial version Nov 15, 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>
   */
  public abstract class AbstractLanePerception implements LanePerception
  {
      /** */
      private static final long serialVersionUID = 20151128L;
  
      /** The lane based GTU for which this perception module stores information. */
      private LaneBasedGTU gtu;
  
      /** The forward headway and (leader) object. */
      private TimeStampedObject<Headway> forwardHeadway;
  
      /** The backward headway and (follower) object. */
      private TimeStampedObject<Headway> backwardHeadway;
  
      /** The minimum speed limit of all lanes where the GTU is registered. */
      private TimeStampedObject<Speed> speedLimit;
  
      /** The adjacent lanes that are accessible for the GTU at the left side. */
      private TimeStampedObject<Map<Lane, Set<Lane>>> accessibleAdjacentLanesLeft;
  
      /** The adjacent lanes that are accessible for the GTU at the right side. */
      private TimeStampedObject<Map<Lane, Set<Lane>>> accessibleAdjacentLanesRight;
  
      /** The objects parallel to us on the left side. */
      private TimeStampedObject<Collection<Headway>> parallelHeadwaysLeft;
  
      /** The objects parallel to us on the right side. */
      private TimeStampedObject<Collection<Headway>> parallelHeadwaysRight;
  
      /** The GTUs on the left side. */
      private TimeStampedObject<Collection<Headway>> neighboringHeadwaysLeft;
  
      /** The GTUs on the right side. */
      private TimeStampedObject<Collection<Headway>> neighboringHeadwaysRight;
  
      /** The lanes and path we expect to take if we do not change lanes. */
      private TimeStampedObject<LanePathInfo> lanePathInfo;
  
      /** The structure of the lanes in front of the GTU. */
      // TODO private LaneStructure laneStructure;
  
      /**
       * Create a new LanePerception module. Because the constructor is often called inside the constructor of a GTU, this
       * constructor does not ask for the pointer to the GTU, as it is often impossible to provide at the time of construction.
       * Use the setter of the GTU instead.
       */
      public AbstractLanePerception()
      {
          super();
     }
 
     /** {@inheritDoc} */
     @Override
     public final void setGTU(final LaneBasedGTU laneBasedGtu)
     {
         this.gtu = laneBasedGtu;
     }
 
     /**
      * Check whether the GTU has been initialized, and returns the current time.
      * @return the current time according to the simulator.
      * @throws GTUException when the GTU was not initialized yet.
      */
     private Time getTimestamp() throws GTUException
     {
         if (this.gtu == null)
         {
             throw new GTUException("gtu value has not been initialized for LanePerception when perceiving.");
         }
         return this.gtu.getSimulator().getSimulatorTime().getTime();
     }
 
     /**
      * @throws GTUException when the GTU was not initialized yet.
      * @throws NetworkException when the speed limit for a GTU type cannot be retrieved from the network.
      * @throws ParameterException in case of not being able to retrieve parameter ParameterTypes.LOOKAHEAD
      */
     public final void updateLanePathInfo() throws GTUException, NetworkException, ParameterException
     {
         Time timestamp = getTimestamp();
         this.lanePathInfo =
                 new TimeStampedObject<LanePathInfo>(AbstractLaneBasedTacticalPlanner.buildLanePathInfo(this.gtu, this.gtu
                         .getBehavioralCharacteristics().getParameter(ParameterTypes.LOOKAHEAD)), timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateSpeedLimit() throws GTUException, NetworkException
     {
         Time timestamp = getTimestamp();
         // assess the speed limit where we are right now
         this.speedLimit = new TimeStampedObject<>(new Speed(Double.MAX_VALUE, SpeedUnit.SI), timestamp);
         for (Lane lane : this.gtu.getLanes().keySet())
         {
             if (lane.getSpeedLimit(this.gtu.getGTUType()).lt(this.speedLimit.getObject()))
             {
                 this.speedLimit = new TimeStampedObject<>(lane.getSpeedLimit(this.gtu.getGTUType()), timestamp);
             }
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateForwardHeadway() throws GTUException, NetworkException, ParameterException
     {
         Time timestamp = getTimestamp();
         if (this.lanePathInfo == null || this.lanePathInfo.getTimestamp().ne(timestamp))
         {
             updateLanePathInfo();
         }
         Length maximumForwardHeadway = this.gtu.getBehavioralCharacteristics().getParameter(ParameterTypes.LOOKAHEAD);
         this.forwardHeadway = new TimeStampedObject<>(forwardHeadway(maximumForwardHeadway), timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateBackwardHeadway() throws GTUException, NetworkException, ParameterException
     {
         Time timestamp = getTimestamp();
         Length maximumReverseHeadway = this.gtu.getBehavioralCharacteristics().getParameter(ParameterTypes.LOOKBACKOLD);
         this.backwardHeadway = new TimeStampedObject<>(backwardHeadway(maximumReverseHeadway), timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateAccessibleAdjacentLanesLeft() throws GTUException
     {
         Time timestamp = getTimestamp();
         Map<Lane, Set<Lane>> accessibleAdjacentLanesMap = new HashMap<>();
         for (Lane lane : this.gtu.getLanes().keySet())
         {
             Set<Lane> adjacentLanes = new HashSet<Lane>(1);
             adjacentLanes.addAll(lane.accessibleAdjacentLanes(LateralDirectionality.LEFT, this.gtu.getGTUType()));
             accessibleAdjacentLanesMap.put(lane, adjacentLanes);
         }
         this.accessibleAdjacentLanesLeft = new TimeStampedObject<>(accessibleAdjacentLanesMap, timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateAccessibleAdjacentLanesRight() throws GTUException
     {
         Time timestamp = getTimestamp();
         Map<Lane, Set<Lane>> accessibleAdjacentLanesMap = new HashMap<>();
         for (Lane lane : this.gtu.getLanes().keySet())
         {
             Set<Lane> adjacentLanes = new HashSet<Lane>(1);
             adjacentLanes.addAll(lane.accessibleAdjacentLanes(LateralDirectionality.RIGHT, this.gtu.getGTUType()));
             accessibleAdjacentLanesMap.put(lane, adjacentLanes);
         }
         this.accessibleAdjacentLanesRight = new TimeStampedObject<>(accessibleAdjacentLanesMap, timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateParallelHeadwaysLeft() throws GTUException
     {
         Time timestamp = getTimestamp();
         if (this.accessibleAdjacentLanesLeft == null || !timestamp.equals(this.accessibleAdjacentLanesLeft.getTimestamp()))
         {
             updateAccessibleAdjacentLanesLeft();
         }
         Set<Headway> parallelHeadwaySet = new HashSet<>();
         for (Lane lane : this.accessibleAdjacentLanesLeft.getObject().keySet())
         {
             for (Lane adjacentLane : this.accessibleAdjacentLanesLeft.getObject().get(lane))
             {
                 parallelHeadwaySet.addAll(parallel(adjacentLane, timestamp));
             }
         }
         this.parallelHeadwaysLeft = new TimeStampedObject<>(parallelHeadwaySet, timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateParallelHeadwaysRight() throws GTUException
     {
         Time timestamp = getTimestamp();
         if (this.accessibleAdjacentLanesRight == null || !timestamp.equals(this.accessibleAdjacentLanesRight.getTimestamp()))
         {
             updateAccessibleAdjacentLanesRight();
         }
         Set<Headway> parallelHeadwaySet = new HashSet<>();
         for (Lane lane : this.accessibleAdjacentLanesRight.getObject().keySet())
         {
             for (Lane adjacentLane : this.accessibleAdjacentLanesRight.getObject().get(lane))
             {
                 parallelHeadwaySet.addAll(parallel(adjacentLane, timestamp));
             }
         }
         this.parallelHeadwaysRight = new TimeStampedObject<>(parallelHeadwaySet, timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateLaneTrafficLeft() throws GTUException, NetworkException, ParameterException
     {
         Time timestamp = getTimestamp();
         if (this.accessibleAdjacentLanesLeft == null || !timestamp.equals(this.accessibleAdjacentLanesLeft.getTimestamp()))
         {
             updateAccessibleAdjacentLanesLeft();
         }
 
         if (this.parallelHeadwaysLeft == null || !timestamp.equals(this.parallelHeadwaysLeft.getTimestamp()))
         {
             updateParallelHeadwaysLeft();
         }
 
         // for the accessible lanes, see who is ahead of us and in front of us
         Length maximumForwardHeadway = this.gtu.getBehavioralCharacteristics().getParameter(ParameterTypes.LOOKAHEAD);
         Length maximumReverseHeadway = this.gtu.getBehavioralCharacteristics().getParameter(ParameterTypes.LOOKBACKOLD);
         this.neighboringHeadwaysLeft =
                 new TimeStampedObject<>(collectNeighborLaneTraffic(LateralDirectionality.LEFT, timestamp,
                         maximumForwardHeadway, maximumReverseHeadway), timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final void updateLaneTrafficRight() throws GTUException, NetworkException, ParameterException
     {
         Time timestamp = getTimestamp();
         if (this.accessibleAdjacentLanesRight == null || !timestamp.equals(this.accessibleAdjacentLanesRight.getTimestamp()))
         {
             updateAccessibleAdjacentLanesRight();
         }
 
         if (this.parallelHeadwaysRight == null || !timestamp.equals(this.parallelHeadwaysRight.getTimestamp()))
         {
             updateParallelHeadwaysRight();
         }
 
         // for the accessible lanes, see who is ahead of us and in front of us
         Length maximumForwardHeadway = this.gtu.getBehavioralCharacteristics().getParameter(ParameterTypes.LOOKAHEAD);
         Length maximumReverseHeadway = this.gtu.getBehavioralCharacteristics().getParameter(ParameterTypes.LOOKBACKOLD);
         this.neighboringHeadwaysRight =
                 new TimeStampedObject<>(collectNeighborLaneTraffic(LateralDirectionality.RIGHT, timestamp,
                         maximumForwardHeadway, maximumReverseHeadway), timestamp);
     }
 
     /** {@inheritDoc} */
     @Override
     public final Map<Lane, Set<Lane>> accessibleAdjacentLaneMap(final LateralDirectionality lateralDirection)
     {
         return lateralDirection.equals(LateralDirectionality.LEFT) ? this.accessibleAdjacentLanesLeft.getObject()
                 : this.accessibleAdjacentLanesRight.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Collection<Headway> getNeighboringHeadways(final LateralDirectionality lateralDirection)
     {
         return lateralDirection.equals(LateralDirectionality.LEFT) ? this.parallelHeadwaysLeft.getObject()
                 : this.parallelHeadwaysRight.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Collection<Headway> getParallelHeadways(final LateralDirectionality lateralDirection)
     {
         return lateralDirection.equals(LateralDirectionality.LEFT) ? this.neighboringHeadwaysLeft.getObject()
                 : this.neighboringHeadwaysRight.getObject();
     }
 
     /**************************************************************************************************************************/
     /**************************************************** HEADWAY ALGORITHMS **************************************************/
     /**************************************************************************************************************************/
 
     /**
      * Determine which GTU is in front of this GTU. This method looks in all lanes where this GTU is registered, and not further
      * than the value of the given maxDistance. The minimum headway is returned of all Lanes where the GTU is registered. When
      * no GTU is found within the given maxDistance, a HeadwayGTU with <b>null</b> as the gtuId and maxDistance as the distance
      * is returned. The search will extend into successive lanes if the maxDistance is larger than the remaining length on the
      * lane. When Lanes (or underlying CrossSectionLinks) diverge, a route planner may be used to determine which kinks and
      * lanes to take into account and which ones not. When the Lanes (or underlying CrossSectionLinks) converge, "parallel"
      * traffic is not taken into account in the headway calculation. Instead, gap acceptance algorithms or their equivalent
      * should guide the merging behavior.<br>
      * <b>Note:</b> Headway is the net headway and calculated on a front-to-back basis.
      * @param maxDistance the maximum distance to look for the nearest GTU; positive values search forwards; negative values
      *            search backwards
      * @return HeadwayGTU; the headway and the GTU information
      * @throws GTUException when there is an error with the next lanes in the network.
      * @throws NetworkException when there is a problem with the route planner
      */
     private Headway forwardHeadway(final Length maxDistance) throws GTUException, NetworkException
     {
         LanePathInfo lpi = getLanePathInfo();
         return forwardHeadway(lpi, maxDistance);
     }
 
     /**
      * Determine which GTU is in front of this GTU. This method uses a given lanePathInfo to look forward, but not further than
      * the value of the given maxDistance. The minimum headway is returned of all Lanes where the GTU is registered. When no GTU
      * is found within the given maxDistance, a HeadwayGTU with <b>null</b> as the gtuId and maxDistance as the distance is
      * returned. The search will extend into successive lanes if the maxDistance is larger than the remaining length on the
      * lane. When Lanes (or underlying CrossSectionLinks) diverge, a route planner may be used to determine which kinks and
      * lanes to take into account and which ones not. When the Lanes (or underlying CrossSectionLinks) converge, "parallel"
      * traffic is not taken into account in the headway calculation. Instead, gap acceptance algorithms or their equivalent
      * should guide the merging behavior.<br>
      * <b>Note:</b> Headway is the net headway and calculated on a front-to-back basis.
      * @param lpi the lanePathInfo object that informs the headway algorithm in which lanes to look, and from which position on
      *            the first lane.
      * @param maxDistance the maximum distance to look for the nearest GTU; positive values search forwards; negative values
      *            search backwards
      * @return HeadwayGTU; the headway and the GTU information
      * @throws GTUException when there is an error with the next lanes in the network.
      * @throws NetworkException when there is a problem with the route planner
      */
     private Headway forwardHeadway(final LanePathInfo lpi, final Length maxDistance) throws GTUException, NetworkException
     {
         Throw.when(maxDistance.le(Length.ZERO), GTUException.class, "forwardHeadway: maxDistance should be positive");
 
         int ldIndex = 0;
         LaneDirection ld = lpi.getReferenceLaneDirection();
         double gtuPosFrontSI = lpi.getReferencePosition().si;
         if (lpi.getReferenceLaneDirection().getDirection().isPlus())
         {
             gtuPosFrontSI += this.gtu.getFront().getDx().si;
         }
         else
         {
             gtuPosFrontSI -= this.gtu.getFront().getDx().si;
         }
 
         // TODO end of lanepath
 
         while ((gtuPosFrontSI > ld.getLane().getLength().si || gtuPosFrontSI < 0.0)
                 && ldIndex < lpi.getLaneDirectionList().size() - 1)
         {
             ldIndex++;
             if (ld.getDirection().isPlus()) // e.g. 1005 on length of lane = 1000
             {
                 if (lpi.getLaneDirectionList().get(ldIndex).getDirection().isPlus())
                 {
                     gtuPosFrontSI -= ld.getLane().getLength().si;
                 }
                 else
                 {
                     gtuPosFrontSI = lpi.getLaneDirectionList().get(ldIndex).getLane().getLength().si - gtuPosFrontSI;
                 }
                 ld = lpi.getLaneDirectionList().get(ldIndex);
             }
             else
             // e.g. -5 on lane of whatever length
             {
                 if (lpi.getLaneDirectionList().get(ldIndex).getDirection().isPlus())
                 {
                     gtuPosFrontSI += ld.getLane().getLength().si;
                 }
                 else
                 {
                     gtuPosFrontSI += lpi.getLaneDirectionList().get(ldIndex).getLane().getLength().si;
                 }
                 ld = lpi.getLaneDirectionList().get(ldIndex);
             }
         }
 
         double maxDistanceSI = maxDistance.si;
         Time time = this.gtu.getSimulator().getSimulatorTime().getTime();
 
         // look forward based on the provided lanePathInfo.
         Headway closest = headwayLane(ld, gtuPosFrontSI, 0.0, time);
         if (closest != null)
         {
             if (closest.getDistance().si > maxDistanceSI)
             {
                 return new HeadwayDistance(maxDistanceSI);
             }
             return closest;
         }
         double cumDistSI = ld.getDirection().isPlus() ? ld.getLane().getLength().si - gtuPosFrontSI : gtuPosFrontSI;
         for (int i = ldIndex + 1; i < lpi.getLaneDirectionList().size(); i++)
         {
             ld = lpi.getLaneDirectionList().get(i);
             closest = headwayLane(ld, ld.getDirection().isPlus() ? 0.0 : ld.getLane().getLength().si, cumDistSI, time);
             if (closest != null)
             {
                 if (closest.getDistance().si > maxDistanceSI)
                 {
                     return new HeadwayDistance(maxDistanceSI);
                 }
                 return closest;
             }
             cumDistSI += ld.getLane().getLength().si;
         }
         return new HeadwayDistance(maxDistanceSI);
     }
 
     /**
      * Determine the positive headway on a lane, or null if no GTU can be found on this lane.
      * @param laneDirection the lane and direction to look
      * @param startPosSI the start position to look from in meters
      * @param cumDistSI the cumulative distance that has already been observed on other lanes
      * @param now the current time to determine the GTU positions on the lane
      * @return the HeadwayGTU, containing information on a GTU that is ahead of the given start position, or null if no GTU can
      *         be found on this lane
      * @throws GTUException when the GTUs ahead on the lane cannot be determined
      */
     private Headway headwayLane(final LaneDirection laneDirection, final double startPosSI, final double cumDistSI,
             final Time now) throws GTUException
     {
         Lane lane = laneDirection.getLane();
         LaneBasedGTU laneBasedGTU =
                 lane.getGtuAhead(new Length(startPosSI, LengthUnit.SI), laneDirection.getDirection(),
                         RelativePosition.REAR, now);
         if (laneBasedGTU == null)
         {
             return null;
         }
         double distanceSI = Math.abs(laneBasedGTU.position(lane, laneBasedGTU.getRear()).si - startPosSI);
         return new HeadwayGTU(laneBasedGTU.getId(), laneBasedGTU.getGTUType(), new Length(cumDistSI + distanceSI,
                 LengthUnit.SI), laneBasedGTU.getSpeed(), laneBasedGTU.getAcceleration());
     }
 
     /**
      * Determine which GTU is behind this GTU. This method looks in all lanes where this GTU is registered, and not further back
      * than the absolute value of the given maxDistance. The minimum net headway is returned of all Lanes where the GTU is
      * registered. When no GTU is found within the given maxDistance, <b>null</b> is returned. The search will extend into
      * successive lanes if the maxDistance is larger than the remaining length on the lane. When Lanes (or underlying
      * CrossSectionLinks) diverge, the headway algorithms have to look at multiple Lanes and return the minimum headway in each
      * of the Lanes. When the Lanes (or underlying CrossSectionLinks) converge, "parallel" traffic is not taken into account in
      * the headway calculation. Instead, gap acceptance algorithms or their equivalent should guide the merging behavior.<br>
      * <b>Note:</b> Headway is the net headway and calculated on a back-to-front basis.
      * @param maxDistance the maximum distance to look for the nearest GTU; it should have a negative value to search backwards
      * @return HeadwayGTU; the headway and the GTU information
      * @throws GTUException when there is an error with the next lanes in the network.
      * @throws NetworkException when there is a problem with the route planner
      */
     private Headway backwardHeadway(final Length maxDistance) throws GTUException, NetworkException
     {
         Throw.when(maxDistance.ge(Length.ZERO), GTUException.class, "backwardHeadway: maxDistance should be negative");
         Time time = this.gtu.getSimulator().getSimulatorTime().getTime();
         double maxDistanceSI = maxDistance.si;
         Headway foundHeadway = new HeadwayDistance(-maxDistanceSI);
         for (Lane lane : this.gtu.positions(this.gtu.getRear()).keySet())
         {
             Headway closest =
                     headwayRecursiveBackwardSI(lane, this.gtu.getLanes().get(lane),
                             this.gtu.position(lane, this.gtu.getRear(), time).getSI(), 0.0, -maxDistanceSI, time);
             if (closest.getDistance().si < -maxDistanceSI && closest.getDistance().si < -foundHeadway.getDistance().si)
             {
                 foundHeadway = closest;
             }
         }
         if (foundHeadway instanceof HeadwayGTU)
         {
             return new HeadwayGTU(foundHeadway.getId(), ((HeadwayGTU) foundHeadway).getGtuType(), foundHeadway.getDistance()
                     .multiplyBy(-1.0), foundHeadway.getSpeed(), null);
         }
         if (foundHeadway instanceof HeadwayDistance)
         {
             return new HeadwayDistance(foundHeadway.getDistance().multiplyBy(-1.0));
         }
         // TODO allow observation of other objects as well.
         throw new GTUException("backwardHeadway not implemented yet for other object types than GTU");
     }
 
     /**
      * Calculate the minimum headway, possibly on subsequent lanes, in backward direction (so between our back, and the other
      * GTU's front). Note: this method returns a POSITIVE number.
      * @param lane the lane where we are looking right now
      * @param direction the direction we are driving on that lane
      * @param lanePositionSI from which position on this lane do we start measuring? This is the current position of the rear of
      *            the GTU when we measure in the lane where the original GTU is positioned, and lane.getLength() for each
      *            subsequent lane.
      * @param cumDistanceSI the distance we have already covered searching on previous lanes. Note: This is a POSITIVE number.
      * @param maxDistanceSI the maximum distance to look for in SI units; stays the same in subsequent calls. Note: this is a
      *            POSITIVE number.
      * @param when the current or future time for which to calculate the headway
      * @return the headway in SI units when we have found the GTU, or a null GTU with a distance of Double.MAX_VALUE meters when
      *         no other GTU could not be found within maxDistanceSI meters
      * @throws GTUException when there is a problem with the geometry of the network
      */
     private Headway headwayRecursiveBackwardSI(final Lane lane, final GTUDirectionality direction, final double lanePositionSI,
             final double cumDistanceSI, final double maxDistanceSI, final Time when) throws GTUException
     {
         LaneBasedGTU otherGTU =
                 lane.getGtuBehind(new Length(lanePositionSI, LengthUnit.SI), direction, RelativePosition.FRONT, when);
         if (otherGTU != null)
         {
             double distanceM = cumDistanceSI + lanePositionSI - otherGTU.position(lane, otherGTU.getFront(), when).getSI();
             if (distanceM > 0 && distanceM <= maxDistanceSI)
             {
                 return new HeadwayGTU(otherGTU.getId(), otherGTU.getGTUType(), new Length(distanceM, LengthUnit.SI),
                         otherGTU.getSpeed(), null);
             }
             return new HeadwayDistance(Double.MAX_VALUE);
         }
 
         // Continue search on predecessor lanes.
         if (cumDistanceSI + lanePositionSI < maxDistanceSI)
         {
             // is there a predecessor link?
             if (lane.prevLanes(this.gtu.getGTUType()).size() > 0)
             {
                 Headway foundMaxGTUDistanceSI = new HeadwayDistance(Double.MAX_VALUE);
                 for (Lane prevLane : lane.prevLanes(this.gtu.getGTUType()).keySet())
                 {
                     // What is behind us is INDEPENDENT of the followed route!
                     double traveledDistanceSI = cumDistanceSI + lanePositionSI;
                     // WRONG - adapt method to forward perception method!
                     Headway closest =
                             headwayRecursiveBackwardSI(prevLane, direction, prevLane.getLength().getSI(), traveledDistanceSI,
                                     maxDistanceSI, when);
                     if (closest.getDistance().si < maxDistanceSI
                             && closest.getDistance().si < foundMaxGTUDistanceSI.getDistance().si)
                     {
                         foundMaxGTUDistanceSI = closest;
                     }
                 }
                 return foundMaxGTUDistanceSI;
             }
         }
 
         // No other GTU was not on one of the current lanes or their successors.
         return new HeadwayDistance(Double.MAX_VALUE);
     }
 
     /**************************************************************************************************************************/
     /************************************************ ADJACENT LANE TRAFFIC ***************************************************/
     /**************************************************************************************************************************/
 
     /**
      * Determine which GTUs are parallel with us on another lane, based on fractional positions. <br>
      * Note: When the GTU that calls the method is also registered on the given lane, it is excluded from the return set.
      * @param lane the lane to look for parallel (partial or full overlapping) GTUs.
      * @param when the future time for which to calculate the headway
      * @return the set of GTUs parallel to us on the other lane (partial overlap counts as parallel), based on fractional
      *         positions, or an empty set when no GTUs were found.
      * @throws GTUException when the vehicle's route is inconclusive, when vehicles are not registered correctly on their lanes,
      *             or when the given lane is not parallel to one of the lanes where we are registered.
      */
     private Collection<Headway> parallel(final Lane lane, final Time when) throws GTUException
     {
         Collection<Headway> headwayCollection = new LinkedHashSet<Headway>();
         for (Lane l : this.gtu.getLanes().keySet())
         {
             // only take lanes that we can compare based on a shared design line
             if (l.getParentLink().equals(lane.getParentLink()))
             {
                 // compare based on fractional positions.
                 double posFractionRef = this.gtu.fractionalPosition(l, this.gtu.getReference(), when);
                 double posFractionFront = Math.max(0.0, posFractionRef + this.gtu.getFront().getDx().si / lane.getLength().si);
                 double posFractionRear = Math.min(1.0, posFractionRef + this.gtu.getRear().getDx().si / lane.getLength().si);
                 // double posFractionFront = Math.max(0.0, this.gtu.fractionalPosition(l, this.gtu.getFront(), when));
                 // double posFractionRear = Math.min(1.0, this.gtu.fractionalPosition(l, this.gtu.getRear(), when));
                 double posMin = Math.min(posFractionFront, posFractionRear);
                 double posMax = Math.max(posFractionFront, posFractionRear);
                 for (LaneBasedGTU otherGTU : lane.getGtuList())
                 {
                     if (!otherGTU.equals(this)) // TODO
                     {
                         /*- cater for: *-----*         *-----*       *-----*       *----------*
                          *                *-----*    *----*      *------------*       *-----*
                          * where the GTUs can each drive in two directions (!)
                          */
                         double gtuFractionRef = otherGTU.fractionalPosition(lane, otherGTU.getReference(), when);
                         double gtuFractionFront =
                                 Math.max(0.0, gtuFractionRef + otherGTU.getFront().getDx().si / lane.getLength().si);
                         double gtuFractionRear =
                                 Math.min(1.0, gtuFractionRef + otherGTU.getRear().getDx().si / lane.getLength().si);
                         double gtuMin = Math.min(gtuFractionFront, gtuFractionRear);
                         double gtuMax = Math.max(gtuFractionFront, gtuFractionRear);
                         // TODO calculate real overlaps
                         Length overlapFront = new Length(1.0, LengthUnit.SI);
                         Length overlap = new Length(1.0, LengthUnit.SI);
                         Length overlapRear = new Length(1.0, LengthUnit.SI);
                         if ((gtuMin >= posMin && gtuMin <= posMax) || (gtuMax >= posMin && gtuMax <= posMax)
                                 || (posMin >= gtuMin && posMin <= gtuMax) || (posMax >= gtuMin && posMax <= gtuMax))
                         {
                             headwayCollection.add(new HeadwayGTU(otherGTU.getId(), otherGTU.getGTUType(), overlapFront,
                                     overlap, overlapRear, otherGTU.getSpeed(), otherGTU.getAcceleration()));
                         }
                     }
                 }
             }
         }
         return headwayCollection;
     }
 
     /**
      * Determine which GTUs are parallel with us in a certain lateral direction, based on fractional positions. <br>
      * Note 1: This method will look to the adjacent lanes of all lanes where the vehicle has been registered.<br>
      * Note 2: When the GTU that calls the method is also registered on the given lane, it is excluded from the return set.
      * @param lateralDirection the direction of the adjacent lane(s) to look for parallel (partial or full overlapping) GTUs.
      * @param when the future time for which to calculate the headway
      * @return the set of GTUs parallel to us on other lane(s) in the given direction (partial overlap counts as parallel),
      *         based on fractional positions, or an empty set when no GTUs were found.
      * @throws GTUException when the vehicle's route is inconclusive, when vehicles are not registered correctly on their lanes,
      *             or when there are no lanes parallel to one of the lanes where we are registered in the given direction.
      */
     private Collection<Headway> parallel(final LateralDirectionality lateralDirection, final Time when) throws GTUException
     {
         Collection<Headway> gtuSet = new LinkedHashSet<Headway>();
         for (Lane lane : this.gtu.getLanes().keySet())
         {
             for (Lane adjacentLane : accessibleAdjacentLaneMap(lateralDirection).get(lane))
             {
                 gtuSet.addAll(parallel(adjacentLane, when));
             }
         }
         return gtuSet;
     }
 
     /**
      * Determine whether there is a lane to the left or to the right of this lane, which is accessible from this lane, or null
      * if no lane could be found. The method takes the LongitidinalDirectionality of the lane into account. In other words, if
      * we drive FORWARD and look for a lane on the LEFT, and there is a lane but the Directionality of that lane is not FORWARD
      * or BOTH, null will be returned.<br>
      * A lane is called adjacent to another lane if the lateral edges are not more than a delta distance apart. This means that
      * a lane that <i>overlaps</i> with another lane is <b>not</b> returned as an adjacent lane. <br>
      * The algorithm also looks for RoadMarkerAcross elements between the lanes to determine the lateral permeability for a GTU.
      * A RoadMarkerAcross is seen as being between two lanes if its center line is not more than delta distance from the
      * relevant lateral edges of the two adjacent lanes. <br>
      * When there are multiple lanes that are adjacent, which could e.g. be the case if an overlapping tram lane and a car lane
      * are adjacent to the current lane, the widest lane that best matches the GTU accessibility of the provided GTUType is
      * returned. <br>
      * <b>Note:</b> LEFT is seen as a negative lateral direction, RIGHT as a positive lateral direction. <br>
      * FIXME In other places in OTS LEFT is positive (and RIGHT is negative). This should be made more consistent.
      * @param currentLane the lane to look for the best accessible adjacent lane
      * @param lateralDirection the direction (LEFT, RIGHT) to look at
      * @param longitudinalPosition Length; the position of the GTU along <cite>currentLane</cite>
      * @return the lane if it is accessible, or null if there is no lane, it is not accessible, or the driving direction does
      *         not match.
      */
     public final Lane bestAccessibleAdjacentLane(final Lane currentLane, final LateralDirectionality lateralDirection,
             final Length longitudinalPosition)
     {
         Set<Lane> candidates = accessibleAdjacentLaneMap(lateralDirection).get(currentLane);
         if (candidates.isEmpty())
         {
             return null; // There is no adjacent Lane that this GTU type can cross into
         }
         if (candidates.size() == 1)
         {
             return candidates.iterator().next(); // There is exactly one adjacent Lane that this GTU type can cross into
         }
         // There are several candidates; find the one that is widest at the beginning.
         Lane bestLane = null;
         double widestSeen = Double.NEGATIVE_INFINITY;
         for (Lane lane : candidates)
         {
             if (lane.getWidth(longitudinalPosition).getSI() > widestSeen)
             {
                 widestSeen = lane.getWidth(longitudinalPosition).getSI();
                 bestLane = lane;
             }
         }
         return bestLane;
     }
 
     /**
      * Collect relevant traffic in adjacent lanes. Parallel traffic is included with headway equal to Double.NaN.
      * @param directionality LateralDirectionality; either <cite>LateralDirectionality.LEFT</cite>, or
      *            <cite>LateralDirectionality.RIGHT</cite>
      * @param when DoubleScalar.Abs&lt;TimeUnit&gt;; the (current) time
      * @param maximumForwardHeadway DoubleScalar.Rel&lt;LengthUnit&gt;; the maximum forward search distance
      * @param maximumReverseHeadway DoubleScalar.Rel&lt;LengthUnit&gt;; the maximum reverse search distance
      * @return Collection&lt;LaneBasedGTU&gt;;
      * @throws NetworkException on network inconsistency
      * @throws GTUException on problems with the GTU state (e.g., position)
      * @throws ParameterException in case of a parameter problem
      */
     private Collection<Headway> collectNeighborLaneTraffic(final LateralDirectionality directionality, final Time when,
             final Length maximumForwardHeadway, final Length maximumReverseHeadway) throws NetworkException,
             GTUException, ParameterException
     {
         Collection<Headway> result = new HashSet<Headway>();
         for (Headway p : parallel(directionality, when))
         {
             // TODO expand for other types of Headways
             result.add(new HeadwayGTU(p.getId(), ((HeadwayGTU) p).getGtuType(), new Length(Double.NaN, LengthUnit.SI), p
                     .getSpeed(), p.getAcceleration()));
         }
 
         // forward
         for (Lane adjacentLane : accessibleAdjacentLaneMap(directionality).get(getLanePathInfo().getReferenceLane()))
         {
             LanePathInfo lpiAdjacent = buildLanePathInfoAdjacent(adjacentLane, directionality, when);
             Headway leader = forwardHeadway(lpiAdjacent, maximumForwardHeadway);
             if (null != leader.getId() && !result.contains(leader))
             {
                 result.add(leader);
             }
         }
 
         // backward
         for (Lane lane : this.gtu.getLanes().keySet())
         {
             for (Lane adjacentLane : accessibleAdjacentLaneMap(directionality).get(lane))
             {
                 Headway follower =
                         headwayRecursiveBackwardSI(adjacentLane, this.gtu.getLanes().get(lane),
                                 this.gtu.projectedPosition(adjacentLane, this.gtu.getRear(), when).getSI(), 0.0,
                                 -maximumReverseHeadway.getSI(), when);
                 if (follower instanceof HeadwayGTU)
                 {
                     boolean found = false;
                     for (Headway headway : result)
                     {
                         if (headway.getId().equals(follower.getId()))
                         {
                             found = true;
                         }
                     }
                     if (!found)
                     {
                         result.add(new HeadwayGTU(follower.getId(), ((HeadwayGTU) follower).getGtuType(), follower
                                 .getDistance().multiplyBy(-1.0), follower.getSpeed(), null));
                     }
                 }
                 else if (follower instanceof HeadwayDistance) // always add for potential lane drop
                 {
                     result.add(new HeadwayDistance(follower.getDistance().multiplyBy(-1.0)));
                 }
                 else
                 {
                     throw new GTUException(
                             "collectNeighborLaneTraffic not yet suited to observe obstacles on neighboring lanes");
                 }
             }
         }
         return result;
     }
 
     /**
      * Find a lanePathInfo left or right of the current LanePath.
      * @param adjacentLane the start adjacent lane for which we calculate the LanePathInfo
      * @param direction LateralDirectionality; either <cite>LateralDirectionality.LEFT</cite>, or
      *            <cite>LateralDirectionality.RIGHT</cite>
      * @param when DoubleScalar.Abs&lt;TimeUnit&gt;; the (current) time
      * @return the adjacent LanePathInfo
      * @throws GTUException when the GTU was not initialized yet.
      * @throws NetworkException when the speed limit for a GTU type cannot be retrieved from the network.
      * @throws ParameterException in case of a parameter problem
      */
     private LanePathInfo buildLanePathInfoAdjacent(final Lane adjacentLane, final LateralDirectionality direction,
             final Time when) throws GTUException, NetworkException, ParameterException
     {
         if (this.lanePathInfo == null || this.lanePathInfo.getTimestamp().ne(when))
         {
             updateLanePathInfo();
         }
         LanePathInfo lpi = getLanePathInfo();
         List<LaneDirection> laneDirectionList = new ArrayList<>();
         laneDirectionList.add(new LaneDirection(adjacentLane, lpi.getReferenceLaneDirection().getDirection()));
         Length referencePosition = this.gtu.projectedPosition(adjacentLane, this.gtu.getReference(), when);
         for (int i = 1; i < lpi.getLaneDirectionList().size(); i++)
         {
             LaneDirection ld = lpi.getLaneDirectionList().get(i);
             Set<Lane> accessibleLanes = ld.getLane().accessibleAdjacentLanes(direction, this.gtu.getGTUType());
             Lane adjLane = null;
             for (Lane lane : accessibleLanes)
             {
                 if (lane.getParentLink().equals(ld.getLane().getParentLink()))
                 {
                     adjLane = lane;
                 }
             }
             if (adjLane == null)
             {
                 break;
             }
             laneDirectionList.add(new LaneDirection(adjLane, ld.getDirection()));
         }
         return new LanePathInfo(null, laneDirectionList, referencePosition);
     }
 
     /**************************************************************************************************************************/
     /*************************************************** GETTERS FOR THE INFORMATION ******************************************/
     /**************************************************************************************************************************/
 
     /** {@inheritDoc} */
     @Override
     public final LaneBasedGTU getGTU()
     {
         return this.gtu;
     }
 
     /**
      * Retrieve the last perceived lane path info.
      * @return LanePathInfo
      */
     public final LanePathInfo getLanePathInfo()
     {
         return this.lanePathInfo.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Headway getForwardHeadway()
     {
         return this.forwardHeadway.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Headway getBackwardHeadway()
     {
         return this.backwardHeadway.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Map<Lane, Set<Lane>> getAccessibleAdjacentLanesLeft()
     {
         return this.accessibleAdjacentLanesLeft.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Map<Lane, Set<Lane>> getAccessibleAdjacentLanesRight()
     {
         return this.accessibleAdjacentLanesRight.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Collection<Headway> getNeighboringHeadwaysLeft()
     {
         return this.neighboringHeadwaysLeft.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Collection<Headway> getNeighboringHeadwaysRight()
     {
         return this.neighboringHeadwaysRight.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Collection<Headway> getParallelHeadwaysLeft()
     {
         return this.parallelHeadwaysLeft.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Collection<Headway> getParallelHeadwaysRight()
     {
         return this.parallelHeadwaysRight.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Speed getSpeedLimit()
     {
         return this.speedLimit.getObject();
     }
 
     /** {@inheritDoc} */
     @Override
     public final Set<PerceivedObject> getPerceivedObjects()
     {
         // TODO getPerceivedObjects() in LanePerception
         return new HashSet<PerceivedObject>();
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Headway> getTimeStampedForwardHeadway()
     {
         return this.forwardHeadway;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Headway> getTimeStampedBackwardHeadway()
     {
         return this.backwardHeadway;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Map<Lane, Set<Lane>>> getTimeStampedAccessibleAdjacentLanesLeft()
     {
         return this.accessibleAdjacentLanesLeft;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Map<Lane, Set<Lane>>> getTimeStampedAccessibleAdjacentLanesRight()
     {
         return this.accessibleAdjacentLanesRight;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Collection<Headway>> getTimeStampedNeighboringHeadwaysLeft()
     {
         return this.neighboringHeadwaysLeft;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Collection<Headway>> getTimeStampedNeighboringHeadwaysRight()
     {
         return this.neighboringHeadwaysRight;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Collection<Headway>> getTimeStampedParallelHeadwaysLeft()
     {
         return this.parallelHeadwaysLeft;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Collection<Headway>> getTimeStampedParallelHeadwaysRight()
     {
         return this.parallelHeadwaysRight;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Speed> getTimeStampedSpeedLimit()
     {
         return this.speedLimit;
     }
 
     /** {@inheritDoc} */
     @Override
     public final TimeStampedObject<Collection<PerceivedObject>> getTimeStampedPerceivedObjects() throws GTUException
     {
         // TODO getPerceivedObjects() in LanePerception
         return new TimeStampedObject<Collection<PerceivedObject>>(new HashSet<PerceivedObject>(), getTimestamp());
     }
 
 }