package org.opentrafficsim.draw.graphs;
   
   import java.awt.Color;
   import java.time.Period;
   import java.util.ArrayList;
   import java.util.EnumSet;
   import java.util.Iterator;
   import java.util.LinkedHashMap;
   import java.util.LinkedHashSet;
  import java.util.List;
  import java.util.Map;
  import java.util.Map.Entry;
  import java.util.Set;
  import java.util.SortedSet;
  import java.util.TreeSet;
  
  import org.djunits.value.vdouble.scalar.Duration;
  import org.djunits.value.vdouble.scalar.Length;
  import org.djunits.value.vdouble.scalar.Time;
  import org.djutils.exceptions.Throw;
  import org.djutils.immutablecollections.ImmutableLinkedHashSet;
  import org.djutils.immutablecollections.ImmutableSet;
  import org.jfree.chart.JFreeChart;
  import org.jfree.chart.LegendItem;
  import org.jfree.chart.LegendItemCollection;
  import org.jfree.chart.axis.NumberAxis;
  import org.jfree.chart.plot.XYPlot;
  import org.jfree.chart.renderer.xy.XYLineAndShapeRenderer;
  import org.jfree.data.DomainOrder;
  import org.jfree.data.xy.XYDataset;
  import org.opentrafficsim.core.dsol.OTSSimulatorInterface;
  import org.opentrafficsim.kpi.sampling.KpiLaneDirection;
  import org.opentrafficsim.kpi.sampling.Sampler;
  import org.opentrafficsim.kpi.sampling.SamplingException;
  import org.opentrafficsim.kpi.sampling.SpaceTimeRegion;
  import org.opentrafficsim.kpi.sampling.Trajectory;
  import org.opentrafficsim.kpi.sampling.Trajectory.SpaceTimeView;
  import org.opentrafficsim.kpi.sampling.TrajectoryGroup;
  
  /**
   * Fundamental diagram from various sources.
   * <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 14 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 FundamentalDiagram extends AbstractBoundedPlot implements XYDataset
  {
  
      /** Aggregation periods. */
      public static final double[] DEFAULT_PERIODS = new double[] {5.0, 10.0, 30.0, 60.0, 120.0, 300.0, 900.0};
  
      /** Update frequencies (n * 1/period). */
      public static final int[] DEFAULT_UPDATE_FREQUENCIES = new int[] {1, 2, 3, 5, 10};
  
      /** Source providing the data. */
      private final FdSource source;
  
      /** Fundamental diagram line. */
      private final FdLine fdLine;
  
      /** Quantity on domain axis. */
      private Quantity domainQuantity;
  
      /** Quantity on range axis. */
      private Quantity rangeQuantity;
  
      /** The other, 3rd quantity. */
      private Quantity otherQuantity;
  
      /** Labels of series. */
      private final List<String> seriesLabels = new ArrayList<>();
  
      /** Updater for update times. */
      private final GraphUpdater<Time> graphUpdater;
  
      /** Property for chart listener to provide time info for status label. */
      private String timeInfo = "";
  
      /** Legend to change text color to indicate visibility. */
      private LegendItemCollection legend;
  
      /** Whether each lane is visible or not. */
      private final List<Boolean> laneVisible = new ArrayList<>();
  
      /**
       * Constructor.
       * @param caption String; caption
       * @param domainQuantity Quantity; initial quantity on the domain axis
       * @param rangeQuantity Quantity; initial quantity on the range axis
       * @param simulator OTSSimulatorInterface; simulator
       * @param source FdSource; source providing the data
       * @param fdLine fundamental diagram line, may be {@code null}
       */
      public FundamentalDiagram(final String caption, final Quantity domainQuantity, final Quantity rangeQuantity,
             final OTSSimulatorInterface simulator, final FdSource source, final FdLine fdLine)
     {
         super(simulator, caption, source.getUpdateInterval(), source.getDelay());
         Throw.when(domainQuantity.equals(rangeQuantity), IllegalArgumentException.class,
             "Domain and range quantity should not be equal.");
         this.fdLine = fdLine;
         this.setDomainQuantity(domainQuantity);
         this.setRangeQuantity(rangeQuantity);
         Set<Quantity> quantities = EnumSet.allOf(Quantity.class);
         quantities.remove(domainQuantity);
         quantities.remove(rangeQuantity);
         this.setOtherQuantity(quantities.iterator().next());
         this.source = source;
         int d = 0;
         if (fdLine != null)
         {
             d = 1;
             this.seriesLabels.add(fdLine.getName());
             this.laneVisible.add(true);
         }
         for (int series = 0; series < source.getNumberOfSeries(); series++)
         {
             this.seriesLabels.add(series + d, source.getName(series));
             this.laneVisible.add(true);
         }
         setChart(createChart());
         setLowerDomainBound(0.0);
         setLowerRangeBound(0.0);
 
         // setup updater to do the actual work in another thread
         this.graphUpdater = new GraphUpdater<>("Fundamental diagram worker", Thread.currentThread(), (t) ->
         {
             if (this.getSource() != null)
             {
                 this.getSource().increaseTime(t);
                 notifyPlotChange();
             }
         });
 
         // let this diagram be notified by the source
         source.addFundamentalDiagram(this);
     }
 
     /**
      * Create a chart.
      * @return JFreeChart; chart
      */
     private JFreeChart createChart()
     {
         NumberAxis xAxis = new NumberAxis(this.getDomainQuantity().label());
         NumberAxis yAxis = new NumberAxis(this.getRangeQuantity().label());
         XYLineAndShapeRenderer renderer = new XYLineAndShapeRenderer()
         {
             /** */
             private static final long serialVersionUID = 20181022L;
 
             /** {@inheritDoc} */
             @SuppressWarnings("synthetic-access")
             @Override
             public boolean isSeriesVisible(final int series)
             {
                 return FundamentalDiagram.this.laneVisible.get(series);
             }
         }; // XYDotRenderer doesn't support different markers
         renderer.setDefaultLinesVisible(false);
         if (hasLineFD())
         {
             int series = this.getSource().getNumberOfSeries();
             renderer.setSeriesLinesVisible(series, true);
             renderer.setSeriesPaint(series, Color.BLACK);
             renderer.setSeriesShapesVisible(series, false);
         }
         XYPlot plot = new XYPlot(this, xAxis, yAxis, renderer);
         boolean showLegend = true;
         if (!hasLineFD() && this.getSource().getNumberOfSeries() < 2)
         {
             plot.setFixedLegendItems(null);
             showLegend = false;
         }
         else
         {
             this.legend = new LegendItemCollection();
             for (int i = 0; i < this.getSource().getNumberOfSeries(); i++)
             {
                 LegendItem li = new LegendItem(this.getSource().getName(i));
                 li.setSeriesKey(i); // lane series, not curve series
                 li.setShape(renderer.lookupLegendShape(i));
                 li.setFillPaint(renderer.lookupSeriesPaint(i));
                 this.legend.add(li);
             }
             if (hasLineFD())
             {
                 LegendItem li = new LegendItem(this.fdLine.getName());
                 li.setSeriesKey(-1);
                 this.legend.add(li);
             }
             plot.setFixedLegendItems(this.legend);
             showLegend = true;
         }
         return new JFreeChart(getCaption(), JFreeChart.DEFAULT_TITLE_FONT, plot, showLegend);
     }
 
     /** {@inheritDoc} */
     @Override
     protected void increaseTime(final Time time)
     {
         if (this.graphUpdater != null && time.si >= this.getSource().getAggregationPeriod().si) // null during construction
         {
             this.graphUpdater.offer(time);
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public int getSeriesCount()
     {
         if (this.getSource() == null)
         {
             return 0;
         }
         return this.getSource().getNumberOfSeries() + (hasLineFD() ? 1 : 0);
     }
 
     /** {@inheritDoc} */
     @Override
     public Comparable<String> getSeriesKey(final int series)
     {
         return this.seriesLabels.get(series);
     }
 
     /** {@inheritDoc} */
     @SuppressWarnings("rawtypes")
     @Override
     public int indexOf(final Comparable seriesKey)
     {
         int index = this.seriesLabels.indexOf(seriesKey);
         return index < 0 ? 0 : index;
     }
 
     /** {@inheritDoc} */
     @Override
     public DomainOrder getDomainOrder()
     {
         return DomainOrder.NONE;
     }
 
     /** {@inheritDoc} */
     @Override
     public int getItemCount(final int series)
     {
         if (hasLineFD() && series == getSeriesCount() - 1)
         {
             return this.fdLine.getValues(this.domainQuantity).length;
         }
         return this.getSource().getItemCount(series);
     }
 
     /** {@inheritDoc} */
     @Override
     public Number getX(final int series, final int item)
     {
         return getXValue(series, item);
     }
 
     /** {@inheritDoc} */
     @Override
     public double getXValue(final int series, final int item)
     {
         if (hasLineFD() && series == getSeriesCount() - 1)
         {
             return this.fdLine.getValues(this.domainQuantity)[item];
         }
         return this.getDomainQuantity().getValue(this.getSource(), series, item);
     }
 
     /** {@inheritDoc} */
     @Override
     public Number getY(final int series, final int item)
     {
         return getYValue(series, item);
     }
 
     /** {@inheritDoc} */
     @Override
     public double getYValue(final int series, final int item)
     {
         if (hasLineFD() && series == getSeriesCount() - 1)
         {
             return this.fdLine.getValues(this.rangeQuantity)[item];
         }
         return this.getRangeQuantity().getValue(this.getSource(), series, item);
     }
 
     /** {@inheritDoc} */
     @Override
     public GraphType getGraphType()
     {
         return GraphType.FUNDAMENTAL_DIAGRAM;
     }
 
     /** {@inheritDoc} */
     @Override
     public String getStatusLabel(final double domainValue, final double rangeValue)
     {
         return this.getDomainQuantity().format(domainValue) + ", " + this.getRangeQuantity().format(rangeValue) + ", " + this
             .getOtherQuantity().format(this.getDomainQuantity().computeOther(this.getRangeQuantity(), domainValue, rangeValue))
             + this.getTimeInfo();
     }
 
     /**
      * Quantity enum defining density, flow and speed.
      * <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 16 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 enum Quantity
     {
         /** Density. */
         DENSITY
         {
             /** {@inheritDoc} */
             @Override
             public String label()
             {
                 return "Density [veh/km] \u2192";
             }
 
             /** {@inheritDoc} */
             @Override
             public String format(final double value)
             {
                 return String.format("%.0f veh/km", value);
             }
 
             /** {@inheritDoc} */
             @Override
             public double getValue(final FdSource src, final int series, final int item)
             {
                 return 1000 * src.getDensity(series, item);
             }
 
             /** {@inheritDoc} */
             @Override
             public double computeOther(final Quantity pairing, final double thisValue, final double pairedValue)
             {
                 // .......................... speed = flow / density .. flow = density * speed
                 return pairing.equals(FLOW) ? pairedValue / thisValue : thisValue * pairedValue;
             }
         },
 
         /** Flow. */
         FLOW
         {
             /** {@inheritDoc} */
             @Override
             public String label()
             {
                 return "Flow [veh/h] \u2192";
             }
 
             /** {@inheritDoc} */
             @Override
             public String format(final double value)
             {
                 return String.format("%.0f veh/h", value);
             }
 
             /** {@inheritDoc} */
             @Override
             public double getValue(final FdSource src, final int series, final int item)
             {
                 return 3600 * src.getFlow(series, item);
             }
 
             /** {@inheritDoc} */
             @Override
             public double computeOther(final Quantity pairing, final double thisValue, final double pairedValue)
             {
                 // speed = flow * density ... density = flow / speed
                 return thisValue / pairedValue;
             }
         },
 
         /** Speed. */
         SPEED
         {
             /** {@inheritDoc} */
             @Override
             public String label()
             {
                 return "Speed [km/h] \u2192";
             }
 
             /** {@inheritDoc} */
             @Override
             public String format(final double value)
             {
                 return String.format("%.1f km/h", value);
             }
 
             /** {@inheritDoc} */
             @Override
             public double getValue(final FdSource src, final int series, final int item)
             {
                 return 3.6 * src.getSpeed(series, item);
             }
 
             /** {@inheritDoc} */
             @Override
             public double computeOther(final Quantity pairing, final double thisValue, final double pairedValue)
             {
                 // ............................. flow = speed * density .. density = flow / speed
                 return pairing.equals(DENSITY) ? thisValue * pairedValue : pairedValue / thisValue;
             }
         };
 
         /**
          * Returns an axis label of the quantity.
          * @return String; axis label of the quantity
          */
         public abstract String label();
 
         /**
          * Formats a value for status display.
          * @param value double; value
          * @return String; formatted string including quantity
          */
         public abstract String format(double value);
 
         /**
          * Get scaled value in presentation unit.
          * @param src FdSource; the data source
          * @param series int; series number
          * @param item int; item number in series
          * @return double; scaled value in presentation unit
          */
         public abstract double getValue(FdSource src, int series, int item);
 
         /**
          * Compute the value of the 3rd quantity.
          * @param pairing Quantity; quantity on other axis
          * @param thisValue double; value of this quantity
          * @param pairedValue double; value of the paired quantity on the other axis
          * @return double; value of the 3rd quantity
          */
         public abstract double computeOther(Quantity pairing, double thisValue, double pairedValue);
 
     }
 
     /**
      * Data source for a fundamental diagram.
      * <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 16 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 interface FdSource
     {
         /**
          * Returns the possible intervals.
          * @return double[]; possible intervals
          */
         default double[] getPossibleAggregationPeriods()
         {
             return DEFAULT_PERIODS;
         }
 
         /**
          * Returns the possible frequencies, as a factor on 1 / 'aggregation interval'.
          * @return int[]; possible frequencies
          */
         default int[] getPossibleUpdateFrequencies()
         {
             return DEFAULT_UPDATE_FREQUENCIES;
         }
 
         /**
          * Add fundamental diagram. Used to notify diagrams when data has changed.
          * @param fundamentalDiagram FundamentalDiagram; fundamental diagram
          */
         void addFundamentalDiagram(FundamentalDiagram fundamentalDiagram);
 
         /**
          * Clears all connected fundamental diagrams.
          */
         void clearFundamentalDiagrams();
 
         /**
          * Returns the diagrams.
          * @return ImmutableSet&lt;FundamentalDiagram&gt; diagrams
          */
         ImmutableSet<FundamentalDiagram> getDiagrams();
 
         /**
          * The update interval.
          * @return Duration; update interval
          */
         Duration getUpdateInterval();
 
         /**
          * Changes the update interval.
          * @param interval Duration; update interval
          * @param time Time; time until which data has to be recalculated
          */
         void setUpdateInterval(Duration interval, Time time);
 
         /**
          * The aggregation period.
          * @return Duration; aggregation period
          */
         Duration getAggregationPeriod();
 
         /**
          * Changes the aggregation period.
          * @param period Duration; aggregation period
          */
         void setAggregationPeriod(Duration period);
 
         /**
          * Recalculates the data after the aggregation or update time was changed.
          * @param time Time; time up to which recalculation is required
          */
         void recalculate(Time time);
 
         /**
          * Return the delay for graph updates so future influencing events have occurred, e.d. GTU move's.
          * @return Duration; graph delay
          */
         Duration getDelay();
 
         /**
          * Increase the time span.
          * @param time Time; time to increase to
          */
         void increaseTime(Time time);
 
         /**
          * Returns the number of series (i.e. lanes or 1 for aggregated).
          * @return int; number of series
          */
         int getNumberOfSeries();
 
         /**
          * Returns a name of the series.
          * @param series int; series number
          * @return String; name of the series
          */
         String getName(int series);
 
         /**
          * Returns the number of items in the series.
          * @param series int; series number
          * @return int; number of items in the series
          */
         int getItemCount(int series);
 
         /**
          * Return the SI flow value of item in series.
          * @param series int; series number
          * @param item int; item number in the series
          * @return double; SI flow value of item in series
          */
         double getFlow(int series, int item);
 
         /**
          * Return the SI density value of item in series.
          * @param series int; series number
          * @param item int; item number in the series
          * @return double; SI density value of item in series
          */
         double getDensity(int series, int item);
 
         /**
          * Return the SI speed value of item in series.
          * @param series int; series number
          * @param item int; item number in the series
          * @return double; SI speed value of item in series
          */
         double getSpeed(int series, int item);
 
         /**
          * Returns whether this source aggregates lanes.
          * @return boolean; whether this source aggregates lanes
          */
         boolean isAggregate();
 
         /**
          * Sets the name of the series when aggregated, e.g. for legend. Default is "Aggregate".
          * @param aggregateName String; name of the series when aggregated
          */
         void setAggregateName(String aggregateName);
     }
 
     /**
      * Abstract implementation to link to fundamental diagrams.
      */
     abstract static class AbstractFdSource implements FdSource
     {
 
         /** Fundamental diagrams. */
         private Set<FundamentalDiagram> fundamentalDiagrams = new LinkedHashSet<>();
 
         /** {@inheritDoc} */
         @Override
         public void addFundamentalDiagram(final FundamentalDiagram fundamentalDiagram)
         {
             this.fundamentalDiagrams.add(fundamentalDiagram);
         }
 
         /** {@inheritDoc} */
         @Override
         public void clearFundamentalDiagrams()
         {
             this.fundamentalDiagrams.clear();
         }
 
         /** {@inheritDoc} */
         @Override
         public ImmutableSet<FundamentalDiagram> getDiagrams()
         {
             return new ImmutableLinkedHashSet<>(this.fundamentalDiagrams);
         }
 
     }
 
     /**
      * Creates a {@code Source} from a sampler and positions.
      * @param sampler Sampler&lt;?&gt;; sampler
      * @param crossSection GraphCrossSection&lt;KpiLaneDirection&gt;; cross section
      * @param aggregateLanes boolean; whether to aggregate the positions
      * @param aggregationTime Duration; aggregation time (and update time)
      * @param harmonic boolean; harmonic mean
      * @return Source; source for a fundamental diagram from a sampler and positions
      */
     @SuppressWarnings("methodlength")
     public static FdSource sourceFromSampler(final Sampler<?> sampler, final GraphCrossSection<KpiLaneDirection> crossSection,
             final boolean aggregateLanes, final Duration aggregationTime, final boolean harmonic)
     {
         return new CrossSectionSamplerFdSource<>(sampler, crossSection, aggregateLanes, aggregationTime, harmonic);
     }
 
     /**
      * Creates a {@code Source} from a sampler and positions.
      * @param sampler Sampler&lt;?&gt;; sampler
      * @param path GraphPath&lt;KpiLaneDirection&gt;; cross section
      * @param aggregateLanes boolean; whether to aggregate the positions
      * @param aggregationTime Duration; aggregation time (and update time)
      * @return Source; source for a fundamental diagram from a sampler and positions
      */
     public static FdSource sourceFromSampler(final Sampler<?> sampler, final GraphPath<KpiLaneDirection> path,
             final boolean aggregateLanes, final Duration aggregationTime)
     {
         return new PathSamplerFdSource<>(sampler, path, aggregateLanes, aggregationTime);
     }
 
     /**
      * Combines multiple sources in to one source.
      * @param sources Map&lt;String, FdSource&gt;; sources coupled to their names for in the legend
      * @return FdSource; combined source
      */
     public static FdSource combinedSource(final Map<String, FdSource> sources)
     {
         return new MultiFdSource(sources);
     }
 
     /**
      * Fundamental diagram source based on a cross section.
      * @param <S> underlying source type
      */
     private static class CrossSectionSamplerFdSource<S extends GraphCrossSection<? extends KpiLaneDirection>> extends
         AbstractSpaceSamplerFdSource<S>
     {
         /** Harmonic mean. */
         private final boolean harmonic;
 
         /**
          * Constructor.
          * @param sampler Sampler&lt;?&gt;; sampler
          * @param crossSection S; cross section
          * @param aggregateLanes boolean; whether to aggregate the lanes
          * @param aggregationPeriod Duration; initial aggregation {@link Period}
          * @param harmonic boolean; harmonic mean
          */
         CrossSectionSamplerFdSource(final Sampler<?> sampler, final S crossSection, final boolean aggregateLanes,
                 final Duration aggregationPeriod, final boolean harmonic)
         {
             super(sampler, crossSection, aggregateLanes, aggregationPeriod);
             this.harmonic = harmonic;
         }
 
         /** {@inheritDoc} */
         @Override
         protected void getMeasurements(final Trajectory<?> trajectory, final Time startTime, final Time endTime,
                 final Length length, final int series, final double[] measurements)
         {
             Length x = getSpace().position(series);
             if (GraphUtil.considerTrajectory(trajectory, x, x))
             {
                 // detailed check
                 Time t = trajectory.getTimeAtPosition(x);
                 if (t.si >= startTime.si && t.si < endTime.si)
                 {
                     measurements[0] = 1; // first = count
                     measurements[1] = // second = sum of (inverted) speeds
                             this.harmonic ? 1.0 / trajectory.getSpeedAtPosition(x).si : trajectory.getSpeedAtPosition(x).si;
                 }
             }
         }
 
         /** {@inheritDoc} */
         @Override
         protected double getVehicleCount(final double first, final double second)
         {
             return first; // is divided by aggregation period by caller
         }
 
         /** {@inheritDoc} */
         @Override
         protected double getSpeed(final double first, final double second)
         {
             return this.harmonic ? first / second : second / first;
         }
 
         /** {@inheritDoc} */
         @Override
         public String toString()
         {
             return "CrossSectionSamplerFdSource [harmonic=" + this.harmonic + "]";
         }
 
     }
 
     /**
      * Fundamental diagram source based on a path. Density, speed and flow over the entire path are calculated per lane.
      * @param <S> underlying source type
      */
     private static class PathSamplerFdSource<S extends GraphPath<? extends KpiLaneDirection>> extends
         AbstractSpaceSamplerFdSource<S>
     {
         /**
          * Constructor.
          * @param sampler Sampler&lt;?&gt;; sampler
          * @param path S; path
          * @param aggregateLanes boolean; whether to aggregate the lanes
          * @param aggregationPeriod Duration; initial aggregation period
          */
         PathSamplerFdSource(final Sampler<?> sampler, final S path, final boolean aggregateLanes,
                 final Duration aggregationPeriod)
         {
             super(sampler, path, aggregateLanes, aggregationPeriod);
         }
 
         /** {@inheritDoc} */
         @Override
         protected void getMeasurements(final Trajectory<?> trajectory, final Time startTime, final Time endTime,
                 final Length length, final int sereies, final double[] measurements)
         {
             SpaceTimeView stv = trajectory.getSpaceTimeView(Length.ZERO, length, startTime, endTime);
             measurements[0] = stv.getDistance().si; // first = total traveled distance
             measurements[1] = stv.getTime().si; // second = total traveled time
         }
 
         /** {@inheritDoc} */
         @Override
         protected double getVehicleCount(final double first, final double second)
         {
             return first / getSpace().getTotalLength().si; // is divided by aggregation period by caller
         }
 
         /** {@inheritDoc} */
         @Override
         protected double getSpeed(final double first, final double second)
         {
             return first / second;
         }
 
         /** {@inheritDoc} */
         @Override
         public String toString()
         {
             return "PathSamplerFdSource []";
         }
 
     }
 
     /**
      * Abstract class that deals with updating and recalculating the fundamental diagram.
      * @param <S> underlying source type
      */
     private abstract static class AbstractSpaceSamplerFdSource<S extends AbstractGraphSpace<? extends KpiLaneDirection>> extends
         AbstractFdSource
     {
         /** Period number of last calculated period. */
         private int periodNumber = -1;
 
         /** Update interval. */
         private Duration updateInterval;
 
         /** Aggregation period. */
         private Duration aggregationPeriod;
 
         /** Last update time. */
         private Time lastUpdateTime;
 
         /** Number of series. */
         private final int nSeries;
 
         /** First data. */
         private double[][] firstMeasurement;
 
         /** Second data. */
         private double[][] secondMeasurement;
 
         /** Whether the plot is in a process such that the data is invalid for the current draw of the plot. */
         private boolean invalid = false;
 
         /** The sampler. */
         private final Sampler<?> sampler;
 
         /** Space. */
         private final S space;
 
         /** Whether to aggregate the lanes. */
         private final boolean aggregateLanes;
 
         /** Name of the series when aggregated. */
         private String aggregateName = "Aggregate";
 
         /** For each series (lane), the highest trajectory number (n) below which all trajectories were also handled (0:n). */
         private Map<KpiLaneDirection, Integer> lastConsecutivelyAssignedTrajectories = new LinkedHashMap<>();
 
         /** For each series (lane), a list of handled trajectories above n, excluding n+1. */
         private Map<KpiLaneDirection, SortedSet<Integer>> assignedTrajectories = new LinkedHashMap<>();
 
         /**
          * Constructor.
          * @param sampler Sampler&lt;?&gt;; sampler
          * @param space S; space
          * @param aggregateLanes boolean; whether to aggregate the lanes
          * @param aggregationPeriod Duration; initial aggregation period
          */
         AbstractSpaceSamplerFdSource(final Sampler<?> sampler, final S space, final boolean aggregateLanes,
                 final Duration aggregationPeriod)
         {
             this.sampler = sampler;
             this.space = space;
             this.aggregateLanes = aggregateLanes;
             this.nSeries = aggregateLanes ? 1 : space.getNumberOfSeries();
             // create and register kpi lane directions
             for (KpiLaneDirection laneDirection : space)
             {
                 sampler.registerSpaceTimeRegion(new SpaceTimeRegion(laneDirection, Length.ZERO, laneDirection.getLaneData()
                     .getLength(), sampler.now(), Time.instantiateSI(Double.MAX_VALUE)));
 
                 // info per kpi lane direction
                 this.lastConsecutivelyAssignedTrajectories.put(laneDirection, -1);
                 this.assignedTrajectories.put(laneDirection, new TreeSet<>());
             }
 
             this.updateInterval = aggregationPeriod;
             this.aggregationPeriod = aggregationPeriod;
             this.firstMeasurement = new double[this.nSeries][10];
             this.secondMeasurement = new double[this.nSeries][10];
         }
 
         /**
          * Returns the space.
          * @return S; space
          */
         protected S getSpace()
         {
             return this.space;
         }
 
         /** {@inheritDoc} */
         @Override
         public Duration getUpdateInterval()
         {
             return this.updateInterval;
         }
 
         /** {@inheritDoc} */
         @Override
         public void setUpdateInterval(final Duration interval, final Time time)
         {
             if (this.updateInterval != interval)
             {
                 this.updateInterval = interval;
                 recalculate(time);
             }
         }
 
         /** {@inheritDoc} */
         @Override
         public Duration getAggregationPeriod()
         {
             return this.aggregationPeriod;
         }
 
         /** {@inheritDoc} */
         @Override
         public void setAggregationPeriod(final Duration period)
         {
             if (this.aggregationPeriod != period)
             {
                 this.aggregationPeriod = period;
             }
         }
 
         /** {@inheritDoc} */
         @Override
         public void recalculate(final Time time)
         {
             new Thread(new Runnable()
             {
                 @Override
                 @SuppressWarnings("synthetic-access")
                 public void run()
                 {
                     synchronized (AbstractSpaceSamplerFdSource.this)
                     {
                         // an active plot draw will now request data on invalid items
                         AbstractSpaceSamplerFdSource.this.invalid = true;
                         AbstractSpaceSamplerFdSource.this.periodNumber = -1;
                         AbstractSpaceSamplerFdSource.this.updateInterval = getUpdateInterval();
                         AbstractSpaceSamplerFdSource.this.firstMeasurement =
                                 new double[AbstractSpaceSamplerFdSource.this.nSeries][10];
                         AbstractSpaceSamplerFdSource.this.secondMeasurement =
                                 new double[AbstractSpaceSamplerFdSource.this.nSeries][10];
                         AbstractSpaceSamplerFdSource.this.lastConsecutivelyAssignedTrajectories.clear();
                         AbstractSpaceSamplerFdSource.this.assignedTrajectories.clear();
                         for (KpiLaneDirection lane : AbstractSpaceSamplerFdSource.this.space)
                         {
                             AbstractSpaceSamplerFdSource.this.lastConsecutivelyAssignedTrajectories.put(lane, -1);
                             AbstractSpaceSamplerFdSource.this.assignedTrajectories.put(lane, new TreeSet<>());
                         }
                         AbstractSpaceSamplerFdSource.this.lastUpdateTime = null; // so the increaseTime call is not skipped
                         while ((AbstractSpaceSamplerFdSource.this.periodNumber + 1) * getUpdateInterval().si
                             + AbstractSpaceSamplerFdSource.this.aggregationPeriod.si <= time.si)
                         {
                             increaseTime(Time.instantiateSI((AbstractSpaceSamplerFdSource.this.periodNumber + 1)
                                 * getUpdateInterval().si + AbstractSpaceSamplerFdSource.this.aggregationPeriod.si));
                             // TODO: if multiple plots are coupled to the same source, other plots are not invalidated
                             // TODO: change of aggregation period / update freq, is not updated in the GUI on other plots
                             // for (FundamentalDiagram diagram : getDiagrams())
                             // {
                             // }
                         }
                         AbstractSpaceSamplerFdSource.this.invalid = false;
                     }
                 }
             }, "Fundamental diagram recalculation").start();
         }
 
         /** {@inheritDoc} */
         @Override
         public Duration getDelay()
         {
             return Duration.instantiateSI(1.0);
         }
 
         /** {@inheritDoc} */
         @Override
         public synchronized void increaseTime(final Time time)
         {
             if (time.si < this.aggregationPeriod.si)
             {
                 // skip periods that fall below 0.0 time
                 return;
             }
 
             if (this.lastUpdateTime != null && time.le(this.lastUpdateTime))
             {
                 // skip updates from different graphs at the same time
                 return;
             }
             this.lastUpdateTime = time;
 
             // ensure capacity
             int nextPeriod = this.periodNumber + 1;
             if (nextPeriod >= this.firstMeasurement[0].length - 1)
             {
                 for (int i = 0; i < this.nSeries; i++)
                 {
                     this.firstMeasurement[i] = GraphUtil.ensureCapacity(this.firstMeasurement[i], nextPeriod + 1);
                     this.secondMeasurement[i] = GraphUtil.ensureCapacity(this.secondMeasurement[i], nextPeriod + 1);
                 }
             }
 
             // loop positions and trajectories
             Time startTime = time.minus(this.aggregationPeriod);
             double first = 0;
             double second = 0.0;
             for (int series = 0; series < this.space.getNumberOfSeries(); series++)
             {
                 Iterator<? extends KpiLaneDirection> it = this.space.iterator(series);
                 while (it.hasNext())
                 {
                     KpiLaneDirection lane = it.next();
                     if (!this.sampler.getSamplerData().contains(lane))
                     {
                         // sampler has not yet started to record on this lane
                         continue;
                     }
                     TrajectoryGroup<?> trajectoryGroup = this.sampler.getSamplerData().getTrajectoryGroup(lane);
                     int last = this.lastConsecutivelyAssignedTrajectories.get(lane);
                     SortedSet<Integer> assigned = this.assignedTrajectories.get(lane);
                     if (!this.aggregateLanes)
                     {
                         first = 0.0;
                         second = 0.0;
                     }
 
                     // Length x = this.crossSection.position(series);
                     int i = 0;
                     for (Trajectory<?> trajectory : trajectoryGroup.getTrajectories())
                     {
                         // we can skip all assigned trajectories, which are all up to and including 'last' and all in 'assigned'
                         try
                         {
                             if (i > last && !assigned.contains(i))
                             {
                                 // quickly filter
                                 if (GraphUtil.considerTrajectory(trajectory, startTime, time))
                                 {
                                     double[] measurements = new double[2];
                                     getMeasurements(trajectory, startTime, time, lane.getLaneData().getLength(), series,
                                         measurements);
                                     first += measurements[0];
                                     second += measurements[1];
                                 }
                                 if (trajectory.getT(trajectory.size() - 1) < startTime.si - getDelay().si)
                                 {
                                     assigned.add(i);
                                 }
                             }
                             i++;
                         }
                         catch (SamplingException exception)
                         {
                             throw new RuntimeException("Unexpected exception while counting trajectories.", exception);
                         }
                     }
                     if (!this.aggregateLanes)
                     {
                         this.firstMeasurement[series][nextPeriod] = first;
                         this.secondMeasurement[series][nextPeriod] = second;
                     }
 
                     // consolidate list of assigned trajectories in 'all up to n' and 'these specific ones beyond n'
                     if (!assigned.isEmpty())
                     {
                         int possibleNextLastAssigned = assigned.first();
                         while (possibleNextLastAssigned == last + 1) // consecutive or very first
                         {
                             last = possibleNextLastAssigned;
                             assigned.remove(possibleNextLastAssigned);
                             possibleNextLastAssigned = assigned.isEmpty() ? -1 : assigned.first();
                         }
                         this.lastConsecutivelyAssignedTrajectories.put(lane, last);
                     }
                 }
             }
             if (this.aggregateLanes)
             {
                 // whatever we measured, it was summed and can be normalized per line like this
                 this.firstMeasurement[0][nextPeriod] = first / this.space.getNumberOfSeries();
                 this.secondMeasurement[0][nextPeriod] = second / this.space.getNumberOfSeries();
             }
             this.periodNumber = nextPeriod;
         }
 
         /** {@inheritDoc} */
         @Override
         public int getNumberOfSeries()
         {
             // if there is an active plot draw as the data is being recalculated, data on invalid items is requested
             // a call to getSeriesCount() indicates a new draw, and during a recalculation the data is limited but valid
             this.invalid = false;
             return this.nSeries;
         }
 
         /** {@inheritDoc} */
         @Override
         public void setAggregateName(final String aggregateName)
         {
             this.aggregateName = aggregateName;
         }
 
         /** {@inheritDoc} */
         @Override
         public String getName(final int series)
         {
             if (this.aggregateLanes)
             {
                 return this.aggregateName;
             }
             return this.space.getName(series);
         }
 
         /** {@inheritDoc} */
         @Override
         public int getItemCount(final int series)
         {
             return this.periodNumber + 1;
         }
 
         /** {@inheritDoc} */
         @Override
         public final double getFlow(final int series, final int item)
         {
             if (this.invalid)
             {
                 return Double.NaN;
             }
             return getVehicleCount(this.firstMeasurement[series][item], this.secondMeasurement[series][item])
                 / this.aggregationPeriod.si;
         }
 
         /** {@inheritDoc} */
         @Override
         public final double getDensity(final int series, final int item)
         {
             return getFlow(series, item) / getSpeed(series, item);
         }
 
         /** {@inheritDoc} */
         @Override
         public final double getSpeed(final int series, final int item)
         {
             if (this.invalid)
             {
                 return Double.NaN;
             }
             return getSpeed(this.firstMeasurement[series][item], this.secondMeasurement[series][item]);
         }
 
         /** {@inheritDoc} */
         @Override
         public final boolean isAggregate()
         {
             return this.aggregateLanes;
         }
 
         /**
          * Returns the first and the second measurement of a trajectory. For a cross-section this is 1 and the vehicle speed if
          * the trajectory crosses the location, and for a path it is the traveled distance and the traveled time. If the
          * trajectory didn't cross the cross section or space-time range, both should be 0.
          * @param trajectory Trajectory&lt;?&gt;; trajectory
          * @param startTime Time; start time of aggregation period
          * @param endTime Time; end time of aggregation period
          * @param length Length; length of the section (to cut off possible lane overshoot of trajectories)
          * @param series int; series number in the section
          * @param measurements double[]; array with length 2 to place the first and second measurement in
          */
         protected abstract void getMeasurements(Trajectory<?> trajectory, Time startTime, Time endTime, Length length,
                 int series, double[] measurements);
 
         /**
          * Returns the vehicle count of two related measurement values. For a cross section: vehicle count & sum of speeds (or
          * sum of inverted speeds for the harmonic mean). For a path: total traveled distance & total traveled time.
          * <p>
          * The value will be divided by the aggregation time to calculate flow. Hence, for a cross section the first measurement
          * should be returned, while for a path the first measurement divided by the section length should be returned. That
          * will end up to equate to {@code q = sum(x)/XT}.
          * @param first double; first measurement value
          * @param second double; second measurement value
          * @return double; flow
          */
         protected abstract double getVehicleCount(double first, double second);
 
         /**
          * Returns the speed of two related measurement values. For a cross section: vehicle count & sum of speeds (or sum of
          * inverted speeds for the harmonic mean). For a path: total traveled distance & total traveled time.
          * @param first double; first measurement value
          * @param second double; second measurement value
          * @return double; speed
          */
         protected abstract double getSpeed(double first, double second);
 
     }
 
     /**
      * Class to group multiple sources in plot.
      */
     // TODO: when sub-sources recalculate responding to a click in the graph, they notify only their coupled plots, which are
     // none
     private static class MultiFdSource extends AbstractFdSource
     {
 
         /** Sources. */
         private FdSource[] sources;
 
         /** Source names. */
         private String[] sourceNames;
 
         /**
          * Constructor.
          * @param sources Map&lt;String, FdSource&gt;; sources
          */
         MultiFdSource(final Map<String, FdSource> sources)
         {
             Throw.when(sources == null || sources.size() == 0, IllegalArgumentException.class,
                 "At least 1 source is required.");
             this.sources = new FdSource[sources.size()];
             this.sourceNames = new String[sources.size()];
             int index = 0;
             for (Entry<String, FdSource> entry : sources.entrySet())
             {
                 this.sources[index] = entry.getValue();
                 this.sourceNames[index] = entry.getKey();
                 index++;
             }
         }
 
         /**
          * Returns from a series number overall, the index of the sub-source and the series index in that source.
          * @param series int; overall series number
          * @return index of the sub-source and the series index in that source
          */
         private int[] getSourceAndSeries(final int series)
         {
             int source = 0;
             int sourceSeries = series;
             while (sourceSeries >= this.sources[source].getNumberOfSeries())
             {
                 sourceSeries -= this.sources[source].getNumberOfSeries();
                 source++;
             }
             return new int[] {source, sourceSeries};
         }
 
         /** {@inheritDoc} */
         @Override
         public Duration getUpdateInterval()
         {
             return this.sources[0].getUpdateInterval();
         }
 
         /** {@inheritDoc} */
         @Override
         public void setUpdateInterval(final Duration interval, final Time time)
         {
             for (FdSource source : this.sources)
             {
                 source.setUpdateInterval(interval, time);
             }
         }
 
         /** {@inheritDoc} */
         @Override
         public Duration getAggregationPeriod()
         {
             return this.sources[0].getAggregationPeriod();
         }
 
         /** {@inheritDoc} */
         @Override
         public void setAggregationPeriod(final Duration period)
         {
             for (FdSource source : this.sources)
             {
                 source.setAggregationPeriod(period);
             }
         }
 
         /** {@inheritDoc} */
         @Override
         public void recalculate(final Time time)
         {
             for (FdSource source : this.sources)
             {
                 source.recalculate(time);
             }
         }
 
         /** {@inheritDoc} */
         @Override
         public Duration getDelay()
         {
             return this.sources[0].getDelay();
         }
 
         /** {@inheritDoc} */
         @Override
         public void increaseTime(final Time time)
         {
             for (FdSource source : this.sources)
             {
                 source.increaseTime(time);
             }
         }
 
         /** {@inheritDoc} */
         @Override
         public int getNumberOfSeries()
         {
             int numberOfSeries = 0;
             for (FdSource source : this.sources)
             {
                 numberOfSeries += source.getNumberOfSeries();
             }
             return numberOfSeries;
         }
 
         /** {@inheritDoc} */
         @Override
         public String getName(final int series)
         {
             int[] ss = getSourceAndSeries(series);
             return this.sourceNames[ss[0]] + (this.sources[ss[0]].isAggregate() ? "" : ": " + this.sources[ss[0]].getName(
                 ss[1]));
         }
 
         /** {@inheritDoc} */
         @Override
         public int getItemCount(final int series)
         {
             int[] ss = getSourceAndSeries(series);
             return this.sources[ss[0]].getItemCount(ss[1]);
         }
 
         /** {@inheritDoc} */
         @Override
         public double getFlow(final int series, final int item)
         {
             int[] ss = getSourceAndSeries(series);
             return this.sources[ss[0]].getFlow(ss[1], item);
         }
 
         /** {@inheritDoc} */
         @Override
         public double getDensity(final int series, final int item)
         {
             int[] ss = getSourceAndSeries(series);
             return this.sources[ss[0]].getDensity(ss[1], item);
         }
 
         /** {@inheritDoc} */
         @Override
         public double getSpeed(final int series, final int item)
         {
             int[] ss = getSourceAndSeries(series);
             return this.sources[ss[0]].getSpeed(ss[1], item);
         }
 
         /** {@inheritDoc} */
         @Override
         public boolean isAggregate()
         {
             return false;
         }
 
         /** {@inheritDoc} */
         @Override
         public void setAggregateName(final String aggregateName)
         {
             // invalid for this source type
         }
 
     }
 
     /**
      * Defines a line plot for a fundamental diagram.
      */
     public interface FdLine
     {
         /**
          * Return the values for the given quantity. For two quantities, this should result in a 2D fundamental diagram line.
          * @param quantity Quantity; quantity to return value for.
          * @return double[]; values for quantity
          */
         double[] getValues(Quantity quantity);
 
         /**
          * Returns the name of the line, as shown in the legend.
          * @return String; name of the line, as shown in the legend
          */
         String getName();
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString()
     {
         return "FundamentalDiagram [source=" + this.getSource() + ", domainQuantity=" + this.getDomainQuantity()
             + ", rangeQuantity=" + this.getRangeQuantity() + ", otherQuantity=" + this.getOtherQuantity() + ", seriesLabels="
             + this.seriesLabels + ", graphUpdater=" + this.graphUpdater + ", timeInfo=" + this.getTimeInfo() + ", legend="
             + this.legend + ", laneVisible=" + this.laneVisible + "]";
     }
 
     /**
      * Get the data source.
      * @return FdSource; the data source
      */
     public FdSource getSource()
     {
         return this.source;
     }
 
     /**
      * Retrievee the legend of this FundamentalDiagram.
      * @return LegendItemCollection; the legend
      */
     public LegendItemCollection getLegend()
     {
         return this.legend;
     }
 
     /**
      * Return the list of lane visibility flags.
      * @return List&lt;Boolean&gt;; the list of lane visibility flags
      */
     public List<Boolean> getLaneVisible()
     {
         return this.laneVisible;
     }
 
     /**
      * Return the domain quantity.
      * @return Quantity; the domain quantity
      */
     public Quantity getDomainQuantity()
     {
         return this.domainQuantity;
     }
 
     /**
      * Set the domain quantity.
      * @param domainQuantity Quantity; the new domain quantity
      */
     public void setDomainQuantity(final Quantity domainQuantity)
     {
         this.domainQuantity = domainQuantity;
     }
 
     /**
      * Get the other (non domain; vertical axis) quantity.
      * @return Quantity; the quantity for the vertical axis
      */
     public Quantity getOtherQuantity()
     {
         return this.otherQuantity;
     }
 
     /**
      * Set the other (non domain; vertical axis) quantity.
      * @param otherQuantity Quantity; the quantity for the vertical axis
      */
     public void setOtherQuantity(final Quantity otherQuantity)
     {
         this.otherQuantity = otherQuantity;
     }
 
     /**
      * Get the range quantity.
      * @return Quantity; the range quantity
      */
     public Quantity getRangeQuantity()
     {
         return this.rangeQuantity;
     }
 
     /**
      * Set the range quantity.
      * @param rangeQuantity Quantity; the new range quantity
      */
     public void setRangeQuantity(final Quantity rangeQuantity)
     {
         this.rangeQuantity = rangeQuantity;
     }
 
     /**
      * Retrieve the time info.
      * @return String; the time info
      */
     public String getTimeInfo()
     {
         return this.timeInfo;
     }
 
     /**
      * Set the time info.
      * @param timeInfo String; the new time info
      */
     public void setTimeInfo(final String timeInfo)
     {
         this.timeInfo = timeInfo;
     }
 
     /**
      * Return whether the plot has a fundamental diagram line.
      * @return boolean; whether the plot has a fundamental diagram line
      */
     public boolean hasLineFD()
     {
         return this.fdLine != null;
     }
 
 }