package org.opentrafficsim.kpi.sampling;
   
   import java.util.Arrays;
   import java.util.LinkedHashMap;
   import java.util.Map;
   import java.util.Set;
   
   import org.djunits.unit.AccelerationUnit;
   import org.djunits.unit.DurationUnit;
  import org.djunits.unit.LengthUnit;
  import org.djunits.unit.SpeedUnit;
  import org.djunits.unit.TimeUnit;
  import org.djunits.value.ValueRuntimeException;
  import org.djunits.value.storage.StorageType;
  import org.djunits.value.vdouble.scalar.Acceleration;
  import org.djunits.value.vdouble.scalar.Duration;
  import org.djunits.value.vdouble.scalar.Length;
  import org.djunits.value.vdouble.scalar.Speed;
  import org.djunits.value.vdouble.scalar.Time;
  import org.djunits.value.vfloat.vector.FloatAccelerationVector;
  import org.djunits.value.vfloat.vector.FloatLengthVector;
  import org.djunits.value.vfloat.vector.FloatSpeedVector;
  import org.djunits.value.vfloat.vector.FloatTimeVector;
  import org.djunits.value.vfloat.vector.base.FloatVector;
  import org.djutils.exceptions.Throw;
  import org.opentrafficsim.kpi.interfaces.GtuDataInterface;
  import org.opentrafficsim.kpi.sampling.data.ExtendedDataType;
  import org.opentrafficsim.kpi.sampling.meta.MetaData;
  import org.opentrafficsim.kpi.sampling.meta.FilterDataType;
  
  /**
   * Contains position, speed, acceleration and time data of a GTU, over some section. Position is relative to the start of the
   * lane in the direction of travel, also when trajectories have been truncated at a position x > 0. Note that this regards
   * internal data and output. Input position always refers to the design line of the lane. This class internally flips input
   * positions and boundaries.
   * <p>
   * Copyright (c) 2013-2020 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/current/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 Sep 21, 2016 <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.transport.citg.tudelft.nl">Wouter Schakel</a>
   * @param <G> gtu data type
   */
  // TODO some trajectories have the first time stamp twice, with possibly different values for acceleration (and TTC)
  public final class Trajectory<G extends GtuDataInterface>
  {
  
      /** Default array capacity. */
      private static final int DEFAULT_CAPACITY = 10;
  
      /** Effective length of the underlying data (arrays may be longer). */
      private int size = 0;
  
      /**
       * Position array. Position is relative to the start of the lane in the direction of travel, also when trajectories have
       * been truncated at a position x &gt; 0.
       */
      private float[] x = new float[DEFAULT_CAPACITY];
  
      /** Speed array. */
      private float[] v = new float[DEFAULT_CAPACITY];
  
      /** Acceleration array. */
      private float[] a = new float[DEFAULT_CAPACITY];
  
      /** Time array. */
      private float[] t = new float[DEFAULT_CAPACITY];
  
      /** GTU id. */
      private final String gtuId;
  
      /** Meta data. */
      private final MetaData metaData;
  
      /** Map of array data types and their values. */
      private final Map<ExtendedDataType<?, ?, ?, G>, Object> extendedData = new LinkedHashMap<>();
  
      /** Direction of travel. */
      private final KpiLaneDirection kpiLaneDirection;
  
      /**
       * @param gtu GtuDataInterface; GTU of this trajectory, only the id is stored.
       * @param metaData MetaData; meta data
       * @param extendedData Set&lt;ExtendedDataType&lt;?,?,?,G&gt;&gt;; types of extended data
       * @param kpiLaneDirection KpiLaneDirection; direction of travel
       */
      public Trajectory(final GtuDataInterface gtu, final MetaData metaData, final Set<ExtendedDataType<?, ?, ?, G>> extendedData,
              final KpiLaneDirection kpiLaneDirection)
      {
          this(gtu == null ? null : gtu.getId(), metaData, extendedData, kpiLaneDirection);
      }
  
      /**
       * Private constructor for creating subsets.
       * @param gtuId String; GTU id
       * @param metaData MetaData; meta data
      * @param extendedData Set&lt;ExtendedDataType&lt;?,?,?,G&gt;&gt;; types of extended data
      * @param kpiLaneDirection KpiLaneDirection; direction of travel
      */
     private Trajectory(final String gtuId, final MetaData metaData, final Set<ExtendedDataType<?, ?, ?, G>> extendedData,
             final KpiLaneDirection kpiLaneDirection)
     {
         Throw.whenNull(gtuId, "GTU may not be null.");
         Throw.whenNull(metaData, "Meta data may not be null.");
         Throw.whenNull(extendedData, "Extended data may not be null.");
         Throw.whenNull(kpiLaneDirection, "Lane direction may not be null.");
         this.gtuId = gtuId;
         this.metaData = new MetaData(metaData);
         for (ExtendedDataType<?, ?, ?, G> dataType : extendedData)
         {
             this.extendedData.put(dataType, dataType.initializeStorage());
         }
         this.kpiLaneDirection = kpiLaneDirection;
     }
 
     /**
      * Adds values of position, speed, acceleration and time.
      * @param position Length; position is relative to the start of the lane in the direction of the design line, i.e.
      *            irrespective of the travel direction, also when trajectories have been truncated at a position x &gt; 0
      * @param speed Speed; speed
      * @param acceleration Acceleration; acceleration
      * @param time Time; time
      */
     public void add(final Length position, final Speed speed, final Acceleration acceleration, final Time time)
     {
         add(position, speed, acceleration, time, null);
     }
 
     /**
      * Adds values of position, speed, acceleration and time.
      * @param position Length; position is relative to the start of the lane in the direction of the design line, i.e.
      *            irrespective of the travel direction, also when trajectories have been truncated at a position x &gt; 0
      * @param speed Speed; speed
      * @param acceleration Acceleration; acceleration
      * @param time Time; time
      * @param gtu G; gtu to add extended data for
      */
     public void add(final Length position, final Speed speed, final Acceleration acceleration, final Time time, final G gtu)
     {
         Throw.whenNull(position, "Position may not be null.");
         Throw.whenNull(speed, "Speed may not be null.");
         Throw.whenNull(acceleration, "Acceleration may not be null.");
         Throw.whenNull(time, "Time may not be null.");
         if (!this.extendedData.isEmpty())
         {
             Throw.whenNull(gtu, "GTU may not be null.");
         }
         if (this.size == this.x.length)
         {
             int cap = this.size + (this.size >> 1);
             this.x = Arrays.copyOf(this.x, cap);
             this.v = Arrays.copyOf(this.v, cap);
             this.a = Arrays.copyOf(this.a, cap);
             this.t = Arrays.copyOf(this.t, cap);
         }
         this.x[this.size] = (float) this.kpiLaneDirection.getPositionInDirection(position).si;
         this.v[this.size] = (float) speed.si;
         this.a[this.size] = (float) acceleration.si;
         this.t[this.size] = (float) time.si;
         for (ExtendedDataType<?, ?, ?, G> extendedDataType : this.extendedData.keySet())
         {
             appendValue(extendedDataType, gtu);
         }
         this.size++;
     }
 
     /**
      * @param extendedDataType ExtendedDataType&lt;T,?,S,G&gt;; extended data type
      * @param gtu G; gtu
      */
     @SuppressWarnings("unchecked")
     private <T, S> void appendValue(final ExtendedDataType<T, ?, S, G> extendedDataType, final G gtu)
     {
         S in = (S) this.extendedData.get(extendedDataType);
         S out = extendedDataType.setValue(in, this.size, extendedDataType.getValue(gtu));
         if (in != out)
         {
             this.extendedData.put(extendedDataType, out);
         }
     }
 
     /**
      * @return size of the underlying trajectory data
      */
     public int size()
     {
         return this.size;
     }
 
     /**
      * @return GTU id
      */
     public String getGtuId()
     {
         return this.gtuId;
     }
 
     /**
      * @return si position values, position is relative to the start of the lane, also when trajectories have been truncated at
      *         a position x &gt; 0
      */
     public float[] getX()
     {
         return Arrays.copyOf(this.x, this.size);
     }
 
     /**
      * @return si speed values
      */
     public float[] getV()
     {
         return Arrays.copyOf(this.v, this.size);
     }
 
     /**
      * @return si acceleration values
      */
     public float[] getA()
     {
         return Arrays.copyOf(this.a, this.size);
     }
 
     /**
      * @return si time values
      */
     public float[] getT()
     {
         return Arrays.copyOf(this.t, this.size);
     }
 
     /**
      * Returns the last index with a position smaller than or equal to the given position.
      * @param position float; position
      * @return int; last index with a position smaller than or equal to the given position
      */
     public int binarySearchX(final float position)
     {
         if (this.x[0] >= position)
         {
             return 0;
         }
         int index = Arrays.binarySearch(this.x, 0, this.size, position);
         return index < 0 ? -index - 2 : index;
     }
 
     /**
      * Returns the last index with a time smaller than or equal to the given time.
      * @param time float; time
      * @return int; last index with a time smaller than or equal to the given time
      */
     public int binarySearchT(final float time)
     {
         if (this.t[0] >= time)
         {
             return 0;
         }
         int index = Arrays.binarySearch(this.t, 0, this.size, time);
         return index < 0 ? -index - 2 : index;
     }
 
     /**
      * Returns {@code x} value of a single sample.
      * @param index int; index
      * @return {@code x} value of a single sample
      * @throws SamplingException if the index is out of bounds
      */
     public float getX(final int index) throws SamplingException
     {
         checkSample(index);
         return this.x[index];
     }
 
     /**
      * Returns {@code v} value of a single sample.
      * @param index int; index
      * @return {@code v} value of a single sample
      * @throws SamplingException if the index is out of bounds
      */
     public float getV(final int index) throws SamplingException
     {
         checkSample(index);
         return this.v[index];
     }
 
     /**
      * Returns {@code a} value of a single sample.
      * @param index int; index
      * @return {@code a} value of a single sample
      * @throws SamplingException if the index is out of bounds
      */
     public float getA(final int index) throws SamplingException
     {
         checkSample(index);
         return this.a[index];
     }
 
     /**
      * Returns {@code t} value of a single sample.
      * @param index int; index
      * @return {@code t} value of a single sample
      * @throws SamplingException if the index is out of bounds
      */
     public float getT(final int index) throws SamplingException
     {
         checkSample(index);
         return this.t[index];
     }
 
     /**
      * Returns extended data type value of a single sample.
      * @param extendedDataType ExtendedDataType&lt;T,?,S,?&gt;; data type from which to retrieve the data
      * @param index int; index for which to retrieve the data
      * @param <T> scalar type of extended data type
      * @param <S> storage type of extended data type
      * @return extended data type value of a single sample
      * @throws SamplingException if the index is out of bounds
      */
     @SuppressWarnings("unchecked")
     public <T, S> T getExtendedData(final ExtendedDataType<T, ?, S, ?> extendedDataType, final int index)
             throws SamplingException
     {
         checkSample(index);
         return extendedDataType.getStorageValue((S) this.extendedData.get(extendedDataType), index);
     }
 
     /**
      * Throws an exception if the sample index is out of bounds.
      * @param index int; sample index
      * @throws SamplingException if the sample index is out of bounds
      */
     private void checkSample(final int index) throws SamplingException
     {
         Throw.when(index < 0 || index >= this.size, SamplingException.class, "Index is out of bounds.");
     }
 
     /**
      * @return strongly typed copy of position, position is relative to the start of the lane, also when trajectories have been
      *         truncated at a position x &gt; 0
      */
     public FloatLengthVector getPosition()
     {
         try
         {
             return FloatVector.instantiate(getX(), LengthUnit.SI, StorageType.DENSE);
         }
         catch (ValueRuntimeException exception)
         {
             // should not happen, inputs are not null
             throw new RuntimeException("Could not return trajectory data.", exception);
         }
     }
 
     /**
      * @return strongly typed copy of speed
      */
     public FloatSpeedVector getSpeed()
     {
         try
         {
             return FloatVector.instantiate(getV(), SpeedUnit.SI, StorageType.DENSE);
         }
         catch (ValueRuntimeException exception)
         {
             // should not happen, inputs are not null
             throw new RuntimeException("Could not return trajectory data.", exception);
         }
     }
 
     /**
      * @return strongly typed copy of acceleration
      */
     public FloatAccelerationVector getAcceleration()
     {
         try
         {
             return FloatVector.instantiate(getA(), AccelerationUnit.SI, StorageType.DENSE);
         }
         catch (ValueRuntimeException exception)
         {
             // should not happen, inputs are not null
             throw new RuntimeException("Could not return trajectory data.", exception);
         }
     }
 
     /**
      * @return strongly typed copy of time
      */
     public FloatTimeVector getTime()
     {
         try
         {
             return FloatVector.instantiate(getT(), TimeUnit.BASE_SECOND, StorageType.DENSE);
         }
         catch (ValueRuntimeException exception)
         {
             // should not happen, inputs are not null
             throw new RuntimeException("Could not return trajectory data.", exception);
         }
     }
 
     /**
      * @return total length of this trajectory
      * @throws IllegalStateException if trajectory is empty
      */
     public Length getTotalLength()
     {
         // TODO do not allow empty trajectory
         // Throw.when(this.size == 0, IllegalStateException.class, "Empty trajectory does not have a length.");
         if (this.size == 0)
         {
             return Length.ZERO;
         }
         return new Length(this.x[this.size - 1] - this.x[0], LengthUnit.SI);
     }
 
     /**
      * @return total duration of this trajectory
      * @throws IllegalStateException if trajectory is empty
      */
     public Duration getTotalDuration()
     {
         // TODO do not allow empty trajectory
         // Throw.when(this.size == 0, IllegalStateException.class, "Empty trajectory does not have a duration.");
         if (this.size == 0)
         {
             return Duration.ZERO;
         }
         return new Duration(this.t[this.size - 1] - this.t[0], DurationUnit.SI);
     }
 
     /**
      * @param metaDataType MetaDataType&lt;?&gt;; meta data type
      * @return whether the trajectory contains the meta data of give type
      */
     public boolean contains(final FilterDataType<?> metaDataType)
     {
         return this.metaData.contains(metaDataType);
     }
 
     /**
      * @param metaDataType MetaDataType&lt;T&gt;; meta data type
      * @param <T> class of meta data
      * @return value of meta data
      */
     public <T> T getMetaData(final FilterDataType<T> metaDataType)
     {
         return this.metaData.get(metaDataType);
     }
 
     /**
      * Returns the included meta data types.
      * @return included meta data types
      */
     public Set<FilterDataType<?>> getFilterDataTypes()
     {
         return this.metaData.getMetaDataTypes();
     }
 
     /**
      * @param extendedDataType ExtendedDataType&lt;?,?,?,?&gt;; extended data type
      * @return whether the trajectory contains the extended data of give type
      */
     public boolean contains(final ExtendedDataType<?, ?, ?, ?> extendedDataType)
     {
         return this.extendedData.containsKey(extendedDataType);
     }
 
     /**
      * @param extendedDataType ExtendedDataType&lt;?,O,S,?&gt;; extended data type to return
      * @param <O> output type
      * @param <S> storage type
      * @return values of extended data type
      * @throws SamplingException if the extended data type is not in the trajectory
      */
     @SuppressWarnings("unchecked")
     public <O, S> O getExtendedData(final ExtendedDataType<?, O, S, ?> extendedDataType) throws SamplingException
     {
         Throw.when(!this.extendedData.containsKey(extendedDataType), SamplingException.class,
             "Extended data type %s is not in the trajectory.", extendedDataType);
         return extendedDataType.convert((S) this.extendedData.get(extendedDataType), this.size);
     }
 
     /**
      * Returns the included extended data types.
      * @return included extended data types
      */
     public Set<ExtendedDataType<?, ?, ?, G>> getExtendedDataTypes()
     {
         return this.extendedData.keySet();
     }
 
     /**
      * Returns a space-time view of this trajectory. This is much more efficient than {@code subSet()} as no trajectory is
      * copied. The limitation is that only distance and time (and mean speed) in the space-time view can be obtained.
      * @param startPosition Length; start position
      * @param endPosition Length; end position
      * @param startTime Time; start time
      * @param endTime Time; end time
      * @return space-time view of this trajectory
      */
     @SuppressWarnings("synthetic-access")
     public SpaceTimeView getSpaceTimeView(final Length startPosition, final Length endPosition, final Time startTime,
             final Time endTime)
     {
         if (size() == 0)
         {
             return new SpaceTimeView(Length.ZERO, Duration.ZERO);
         }
         Length length0 = this.kpiLaneDirection.getPositionInDirection(startPosition);
         Length length1 = this.kpiLaneDirection.getPositionInDirection(endPosition);
         Boundaries bounds = spaceBoundaries(length0, length1).intersect(timeBoundaries(startTime, endTime));
         double xFrom;
         double tFrom;
         if (bounds.fFrom > 0.0)
         {
             xFrom = this.x[bounds.from] * (1 - bounds.fFrom) + this.x[bounds.from + 1] * bounds.fFrom;
             tFrom = this.t[bounds.from] * (1 - bounds.fFrom) + this.t[bounds.from + 1] * bounds.fFrom;
         }
         else
         {
             xFrom = this.x[bounds.from];
             tFrom = this.t[bounds.from];
         }
         double xTo;
         double tTo;
         if (bounds.fTo > 0.0)
         {
             xTo = this.x[bounds.to] * (1 - bounds.fTo) + this.x[bounds.to + 1] * bounds.fTo;
             tTo = this.t[bounds.to] * (1 - bounds.fTo) + this.t[bounds.to + 1] * bounds.fTo;
         }
         else
         {
             xTo = this.x[bounds.to];
             tTo = this.t[bounds.to];
         }
         return new SpaceTimeView(Length.instantiateSI(xTo - xFrom), Duration.instantiateSI(tTo - tFrom));
     }
 
     /**
      * Copies the trajectory but with a subset of the data. Longitudinal entry is only true if the original trajectory has true,
      * and the subset is from the start.
      * @param startPosition Length; start position
      * @param endPosition Length; end position
      * @return subset of the trajectory
      * @throws NullPointerException if an input is null
      * @throws IllegalArgumentException of minLength is smaller than maxLength
      */
     public Trajectory<G> subSet(final Length startPosition, final Length endPosition)
     {
         Throw.whenNull(startPosition, "Start position may not be null");
         Throw.whenNull(endPosition, "End position may not be null");
         Length length0 = this.kpiLaneDirection.getPositionInDirection(startPosition);
         Length length1 = this.kpiLaneDirection.getPositionInDirection(endPosition);
         Throw.when(length0.gt(length1), IllegalArgumentException.class,
             "Start position should be smaller than end position in the direction of travel");
         if (this.size == 0)
         {
             return new Trajectory<>(this.gtuId, this.metaData, this.extendedData.keySet(), this.kpiLaneDirection);
         }
         return subSet(spaceBoundaries(length0, length1));
     }
 
     /**
      * Copies the trajectory but with a subset of the data.
      * @param startTime Time; start time
      * @param endTime Time; end time
      * @return subset of the trajectory
      * @throws NullPointerException if an input is null
      * @throws IllegalArgumentException of minTime is smaller than maxTime
      */
     public Trajectory<G> subSet(final Time startTime, final Time endTime)
     {
         Throw.whenNull(startTime, "Start time may not be null");
         Throw.whenNull(endTime, "End time may not be null");
         Throw.when(startTime.gt(endTime), IllegalArgumentException.class, "Start time should be smaller than end time.");
         if (this.size == 0)
         {
             return new Trajectory<>(this.gtuId, this.metaData, this.extendedData.keySet(), this.kpiLaneDirection);
         }
         return subSet(timeBoundaries(startTime, endTime));
     }
 
     /**
      * Copies the trajectory but with a subset of the data.
      * @param startPosition Length; start position
      * @param endPosition Length; end position
      * @param startTime Time; start time
      * @param endTime Time; end time
      * @return subset of the trajectory
      * @throws NullPointerException if an input is null
      * @throws IllegalArgumentException of minLength/Time is smaller than maxLength/Time
      */
     public Trajectory<G> subSet(final Length startPosition, final Length endPosition, final Time startTime, final Time endTime)
     {
         // could use this.subSet(minLength, maxLength).subSet(minTime, maxTime), but that copies twice
         Throw.whenNull(startPosition, "Start position may not be null");
         Throw.whenNull(endPosition, "End position may not be null");
         Length length0 = this.kpiLaneDirection.getPositionInDirection(startPosition);
         Length length1 = this.kpiLaneDirection.getPositionInDirection(endPosition);
         Throw.when(length0.gt(length1), IllegalArgumentException.class,
             "Start position should be smaller than end position in the direction of travel");
         Throw.whenNull(startTime, "Start time may not be null");
         Throw.whenNull(endTime, "End time may not be null");
         Throw.when(startTime.gt(endTime), IllegalArgumentException.class, "Start time should be smaller than end time.");
         if (this.size == 0)
         {
             return new Trajectory<>(this.gtuId, this.metaData, this.extendedData.keySet(), this.kpiLaneDirection);
         }
         return subSet(spaceBoundaries(length0, length1).intersect(timeBoundaries(startTime, endTime)));
     }
 
     /**
      * Determine spatial boundaries.
      * @param startPosition Length; start position
      * @param endPosition Length; end position
      * @return spatial boundaries
      */
     private Boundaries spaceBoundaries(final Length startPosition, final Length endPosition)
     {
         if (startPosition.si > this.x[this.size - 1] || endPosition.si < this.x[0])
         {
             return new Boundaries(0, 0.0, 0, 0.0);
         }
         // to float needed as x is in floats and due to precision fTo > 1 may become true
         float startPos = (float) startPosition.si;
         float endPos = (float) endPosition.si;
         Boundary from = getBoundaryAtPosition(startPos, false);
         Boundary to = getBoundaryAtPosition(endPos, true);
         return new Boundaries(from.index, from.fraction, to.index, to.fraction);
         // int from = binarySearchX(startPos);
         // double fFrom = 0;
         // if (this.x[from] < startPos)
         // {
         // fFrom = (startPos - this.x[from]) / (this.x[from + 1] - this.x[from]);
         // }
         // int to = binarySearchX(endPos);
         // double fTo = 0;
         // if (to < this.size - 1)
         // {
         // fTo = (endPos - this.x[to]) / (this.x[to + 1] - this.x[to]);
         // }
         // return new Boundaries(from, fFrom, to, fTo);
     }
 
     /**
      * Determine temporal boundaries.
      * @param startTime Time; start time
      * @param endTime Time; end time
      * @return spatial boundaries
      */
     private Boundaries timeBoundaries(final Time startTime, final Time endTime)
     {
         if (startTime.si > this.t[this.size - 1] || endTime.si < this.t[0])
         {
             return new Boundaries(0, 0.0, 0, 0.0);
         }
         // to float needed as x is in floats and due to precision fTo > 1 may become true
         float startTim = (float) startTime.si;
         float endTim = (float) endTime.si;
         Boundary from = getBoundaryAtTime(startTim, false);
         Boundary to = getBoundaryAtTime(endTim, true);
         return new Boundaries(from.index, from.fraction, to.index, to.fraction);
         // int from = binarySearchT(startTim);
         // double fFrom = 0;
         // if (this.t[from] < startTim)
         // {
         // fFrom = (startTim - this.t[from]) / (this.t[from + 1] - this.t[from]);
         // }
         // int to = binarySearchT(endTim);
         // double fTo = 0;
         // if (to < this.size - 1)
         // {
         // fTo = (endTim - this.t[to]) / (this.t[to + 1] - this.t[to]);
         // }
         // return new Boundaries(from, fFrom, to, fTo);
     }
 
     /**
      * Returns the boundary at the given position.
      * @param position float; position
      * @param end boolean; whether the end of a range is searched
      * @return Boundary; boundary at the given position
      */
     private Boundary getBoundaryAtPosition(final float position, final boolean end)
     {
         int index = binarySearchX(position);
         double fraction = 0;
         if (end ? index < this.size - 1 : this.x[index] < position)
         {
             fraction = (position - this.x[index]) / (this.x[index + 1] - this.x[index]);
         }
         return new Boundary(index, fraction);
     }
 
     /**
      * Returns the boundary at the given time.
      * @param time float; time
      * @param end boolean; whether the end of a range is searched
      * @return Boundary; boundary at the given time
      */
     private Boundary getBoundaryAtTime(final float time, final boolean end)
     {
         int index = binarySearchT(time);
         double fraction = 0;
         if (end ? index < this.size - 1 : this.t[index] < time)
         {
             fraction = (time - this.t[index]) / (this.t[index + 1] - this.t[index]);
         }
         return new Boundary(index, fraction);
     }
 
     /**
      * Returns an interpolated time at the given position.
      * @param position Length; position
      * @return Time; interpolated time at the given position
      */
     public Time getTimeAtPosition(final Length position)
     {
         return Time.instantiateSI(getBoundaryAtPosition((float) position.si, false).getValue(this.t));
     }
 
     /**
      * Returns an interpolated speed at the given position.
      * @param position Length; position
      * @return Speed; interpolated speed at the given position
      */
     public Speed getSpeedAtPosition(final Length position)
     {
         return Speed.instantiateSI(getBoundaryAtPosition((float) position.si, false).getValue(this.v));
     }
 
     /**
      * Returns an interpolated acceleration at the given position.
      * @param position Length; position
      * @return Acceleration; interpolated acceleration at the given position
      */
     public Acceleration getAccelerationAtPosition(final Length position)
     {
         return Acceleration.instantiateSI(getBoundaryAtPosition((float) position.si, false).getValue(this.a));
     }
 
     /**
      * Returns an interpolated position at the given time.
      * @param time Time; time
      * @return Length; interpolated position at the given time
      */
     public Length getPositionAtTime(final Time time)
     {
         return Length.instantiateSI(getBoundaryAtTime((float) time.si, false).getValue(this.x));
     }
 
     /**
      * Returns an interpolated speed at the given time.
      * @param time Time; time
      * @return Speed; interpolated speed at the given time
      */
     public Speed getSpeedAtTime(final Time time)
     {
         return Speed.instantiateSI(getBoundaryAtTime((float) time.si, false).getValue(this.v));
     }
 
     /**
      * Returns an interpolated acceleration at the given time.
      * @param time Time; time
      * @return Acceleration; interpolated acceleration at the given time
      */
     public Acceleration getAccelerationAtTime(final Time time)
     {
         return Acceleration.instantiateSI(getBoundaryAtTime((float) time.si, false).getValue(this.a));
     }
 
     /**
      * Copies the trajectory but with a subset of the data. Data is taken from position (from + fFrom) to (to + fTo).
      * @param bounds Boundaries; boundaries
      * @param <T> type of underlying extended data value
      * @param <S> storage type
      * @return subset of the trajectory
      */
     @SuppressWarnings("unchecked")
     private <T, S> Trajectory<G> subSet(final Boundaries bounds)
     {
         Trajectory<G> out = new Trajectory<>(this.gtuId, this.metaData, this.extendedData.keySet(), this.kpiLaneDirection);
         if (bounds.from < bounds.to) // otherwise empty, no data in the subset
         {
             int nBefore = bounds.fFrom < 1.0 ? 1 : 0;
             int nAfter = bounds.fTo > 0.0 ? 1 : 0;
             int n = bounds.to - bounds.from + nBefore + nAfter;
             out.x = new float[n];
             out.v = new float[n];
             out.a = new float[n];
             out.t = new float[n];
             System.arraycopy(this.x, bounds.from + 1, out.x, nBefore, bounds.to - bounds.from);
             System.arraycopy(this.v, bounds.from + 1, out.v, nBefore, bounds.to - bounds.from);
             System.arraycopy(this.a, bounds.from + 1, out.a, nBefore, bounds.to - bounds.from);
             System.arraycopy(this.t, bounds.from + 1, out.t, nBefore, bounds.to - bounds.from);
             if (nBefore == 1)
             {
                 out.x[0] = (float) (this.x[bounds.from] * (1 - bounds.fFrom) + this.x[bounds.from + 1] * bounds.fFrom);
                 out.v[0] = (float) (this.v[bounds.from] * (1 - bounds.fFrom) + this.v[bounds.from + 1] * bounds.fFrom);
                 out.a[0] = (float) (this.a[bounds.from] * (1 - bounds.fFrom) + this.a[bounds.from + 1] * bounds.fFrom);
                 out.t[0] = (float) (this.t[bounds.from] * (1 - bounds.fFrom) + this.t[bounds.from + 1] * bounds.fFrom);
             }
             if (nAfter == 1)
             {
                 out.x[n - 1] = (float) (this.x[bounds.to] * (1 - bounds.fTo) + this.x[bounds.to + 1] * bounds.fTo);
                 out.v[n - 1] = (float) (this.v[bounds.to] * (1 - bounds.fTo) + this.v[bounds.to + 1] * bounds.fTo);
                 out.a[n - 1] = (float) (this.a[bounds.to] * (1 - bounds.fTo) + this.a[bounds.to + 1] * bounds.fTo);
                 out.t[n - 1] = (float) (this.t[bounds.to] * (1 - bounds.fTo) + this.t[bounds.to + 1] * bounds.fTo);
             }
             out.size = n;
             for (ExtendedDataType<?, ?, ?, G> extendedDataType : this.extendedData.keySet())
             {
                 int j = 0;
                 ExtendedDataType<T, ?, S, G> edt = (ExtendedDataType<T, ?, S, G>) extendedDataType;
                 S fromList = (S) this.extendedData.get(extendedDataType);
                 S toList = edt.initializeStorage();
                 try
                 {
                     if (nBefore == 1)
                     {
                         toList = edt.setValue(toList, j, ((ExtendedDataType<T, ?, ?, G>) extendedDataType).interpolate(edt
                             .getStorageValue(fromList, bounds.from), edt.getStorageValue(fromList, bounds.from + 1),
                             bounds.fFrom));
                         j++;
                     }
                     for (int i = bounds.from + 1; i <= bounds.to; i++)
                     {
                         toList = edt.setValue(toList, j, edt.getStorageValue(fromList, i));
                         j++;
                     }
                     if (nAfter == 1)
                     {
                         toList = edt.setValue(toList, j, ((ExtendedDataType<T, ?, ?, G>) extendedDataType).interpolate(edt
                             .getStorageValue(fromList, bounds.to), edt.getStorageValue(fromList, bounds.to + 1), bounds.fTo));
                     }
                 }
                 catch (SamplingException se)
                 {
                     // should not happen as bounds are determined internally
                     throw new RuntimeException("Error while obtaining subset of trajectory.", se);
                 }
                 out.extendedData.put(extendedDataType, toList);
             }
         }
         return out;
     }
 
     /** {@inheritDoc} */
     @Override
     public int hashCode()
     {
         final int prime = 31;
         int result = 1;
         result = prime * result + ((this.gtuId == null) ? 0 : this.gtuId.hashCode());
         result = prime * result + this.size;
         if (this.size > 0)
         {
             result = prime * result + Float.floatToIntBits(this.t[0]);
         }
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean equals(final Object obj)
     {
         if (this == obj)
         {
             return true;
         }
         if (obj == null)
         {
             return false;
         }
         if (getClass() != obj.getClass())
         {
             return false;
         }
         Trajectory<?> other = (Trajectory<?>) obj;
         if (this.size != other.size)
         {
             return false;
         }
         if (this.gtuId == null)
         {
             if (other.gtuId != null)
             {
                 return false;
             }
         }
         else if (!this.gtuId.equals(other.gtuId))
         {
             return false;
         }
         if (this.size > 0)
         {
             if (this.t[0] != other.t[0])
             {
                 return false;
             }
         }
         return true;
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString()
     {
         if (this.size > 0)
         {
             return "Trajectory [size=" + this.size + ", x={" + this.x[0] + "..." + this.x[this.size - 1] + "}, t={" + this.t[0]
                 + "..." + this.t[this.size - 1] + "}, metaData=" + this.metaData + ", gtuId=" + this.gtuId + "]";
         }
         return "Trajectory [size=" + this.size + ", x={}, t={}, metaData=" + this.metaData + ", gtuId=" + this.gtuId + "]";
     }
 
     /**
      * <p>
      * Copyright (c) 2013-2020 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/node/13">OpenTrafficSim License</a>.
      * <p>
      * @version $Revision$, $LastChangedDate$, by $Author$, initial version 15 okt. 2018 <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.transport.citg.tudelft.nl">Wouter Schakel</a>
      */
     public class Boundary
     {
         /** Rounded-down index. */
         @SuppressWarnings("checkstyle:visibilitymodifier")
         public final int index;
 
         /** Fraction. */
         @SuppressWarnings("checkstyle:visibilitymodifier")
         public final double fraction;
 
         /**
          * @param index int; rounded down index
          * @param fraction double; fraction
          */
         Boundary(final int index, final double fraction)
         {
             this.index = index;
             this.fraction = fraction;
         }
 
         /** {@inheritDoc} */
         @Override
         public final String toString()
         {
             return "Boundary [index=" + this.index + ", fraction=" + this.fraction + "]";
         }
 
         /**
          * Returns the value at the boundary in the array.
          * @param array float[]; float[] array
          * @return double; value at the boundary in the array
          */
         public double getValue(final float[] array)
         {
             if (this.fraction == 0.0)
             {
                 return array[this.index];
             }
             if (this.fraction == 1.0)
             {
                 return array[this.index + 1];
             }
             return (1 - this.fraction) * array[this.index] + this.fraction * array[this.index + 1];
         }
     }
 
     /**
      * <p>
      * Copyright (c) 2013-2020 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/node/13">OpenTrafficSim License</a>.
      * <p>
      * @version $Revision$, $LastChangedDate$, by $Author$, initial version 12 okt. 2016 <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.transport.citg.tudelft.nl">Wouter Schakel</a>
      */
     private class Boundaries
     {
         /** Rounded-down from-index. */
         @SuppressWarnings("checkstyle:visibilitymodifier")
         public final int from;
 
         /** Fraction of to-index. */
         @SuppressWarnings("checkstyle:visibilitymodifier")
         public final double fFrom;
 
         /** Rounded-down to-index. */
         @SuppressWarnings("checkstyle:visibilitymodifier")
         public final int to;
 
         /** Fraction of to-index. */
         @SuppressWarnings("checkstyle:visibilitymodifier")
         public final double fTo;
 
         /**
          * @param from int; from index, rounded down
          * @param fFrom double; from index, fraction
          * @param to int; to index, rounded down
          * @param fTo double; to index, fraction
          */
         Boundaries(final int from, final double fFrom, final int to, final double fTo)
         {
             Throw.when(from < 0 || from > Trajectory.this.size() - 1, IllegalArgumentException.class,
                 "Argument from (%d) is out of bounds.", from);
             Throw.when(fFrom < 0 || fFrom > 1, IllegalArgumentException.class, "Argument fFrom (%f) is out of bounds.", fFrom);
             Throw.when(from == Trajectory.this.size() && fFrom > 0, IllegalArgumentException.class,
                 "Arguments from (%d) and fFrom (%f) are out of bounds.", from, fFrom);
             Throw.when(to < 0 || to >= Trajectory.this.size(), IllegalArgumentException.class,
                 "Argument to (%d) is out of bounds.", to);
             Throw.when(fTo < 0 || fTo > 1, IllegalArgumentException.class, "Argument fTo (%f) is out of bounds.", fTo);
             Throw.when(to == Trajectory.this.size() && fTo > 0, IllegalArgumentException.class,
                 "Arguments to (%d) and fTo (%f) are out of bounds.", to, fTo);
             this.from = from;
             this.fFrom = fFrom;
             this.to = to;
             this.fTo = fTo;
         }
 
         /**
          * @param boundaries Boundaries; boundaries
          * @return intersection of both boundaries
          */
         public Boundaries intersect(final Boundaries boundaries)
         {
             if (this.to < boundaries.from || boundaries.to < this.from || this.to == boundaries.from
                 && this.fTo < boundaries.fFrom || boundaries.to == this.from && boundaries.fTo < this.fFrom)
             {
                 return new Boundaries(0, 0.0, 0, 0.0); // no overlap
             }
             int newFrom;
             double newFFrom;
             if (this.from > boundaries.from || this.from == boundaries.from && this.fFrom > boundaries.fFrom)
             {
                 newFrom = this.from;
                 newFFrom = this.fFrom;
             }
             else
             {
                 newFrom = boundaries.from;
                 newFFrom = boundaries.fFrom;
             }
             int newTo;
             double newFTo;
             if (this.to < boundaries.to || this.to == boundaries.to && this.fTo < boundaries.fTo)
             {
                 newTo = this.to;
                 newFTo = this.fTo;
             }
             else
             {
                 newTo = boundaries.to;
                 newFTo = boundaries.fTo;
             }
             return new Boundaries(newFrom, newFFrom, newTo, newFTo);
         }
 
         /** {@inheritDoc} */
         @Override
         public final String toString()
         {
             return "Boundaries [from=" + this.from + ", fFrom=" + this.fFrom + ", to=" + this.to + ", fTo=" + this.fTo + "]";
         }
 
     }
 
     /**
      * Space-time view of a trajectory. This supplies distance and time (and mean speed) in a space-time box.
      * <p>
      * Copyright (c) 2013-2020 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/node/13">OpenTrafficSim License</a>.
      * <p>
      * @version $Revision$, $LastChangedDate$, by $Author$, initial version 5 okt. 2018 <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.transport.citg.tudelft.nl">Wouter Schakel</a>
      */
     public static class SpaceTimeView
     {
 
         /** Distance. */
         final Length distance;
 
         /** Time. */
         final Duration time;
 
         /**
          * Constructor.
          * @param distance Length; distance
          * @param time Duration; time
          */
         private SpaceTimeView(final Length distance, final Duration time)
         {
             this.distance = distance;
             this.time = time;
         }
 
         /**
          * Returns the distance.
          * @return Length; distance
          */
         public final Length getDistance()
         {
             return this.distance;
         }
 
         /**
          * Returns the time.
          * @return Duration; time
          */
         public final Duration getTime()
         {
             return this.time;
         }
 
         /** {@inheritDoc} */
         @Override
         public String toString()
         {
             return "SpaceTimeView [distance=" + this.distance + ", time=" + this.time + "]";
         }
     }
 
 }