/**
   * Converts grid-relative winds to true (or absolute) winds. The U and V components of true wind
   * are {@link WesterlyWind} and {@link SoutherlyWind}, respectively. If the input {@link
   * visad.Field} is not a time-series, then it must be a {@link visad.FlatField} and it must be
   * compatible with the argument of {@link #cartesianHorizontalWind(FlatField)}. If, however, the
   * the input {@link visad.Field} is a time-series, then its domain must be a temporal {@link
   * visad.Gridded1DSet} or a {@link visad.SingletonSet} and its range values must be compatible
   * with the argument of {@link #cartesianHorizontalWind(FlatField)}.
   *
   * @param rel The grid-relative winds.
   * @return The time-series of true wind corresponding to the input.
   * @throws NullPointerException if <code>rel</code> is <code>null</code>.
   * @throws IllegalArgumentException if the input field is not a time-series and is incompatible
   *     with {@link #cartesianHorizontalWind(FlatField)}, or if the input field is a time-series
   *     but its range values are incompatible with {@link #cartesianHorizontalWind(FlatField)}.
   * @throws VisADException if a VisAD failure occurs.
   * @throws RemoteException if a Java RMI failure occurs.
   */
  public static Field cartesianHorizontalWind(Field rel) throws VisADException, RemoteException {

    RealTupleType domType = ((FunctionType) rel.getType()).getDomain();
    Field result = null;
    if (RealType.Time.equalsExceptNameButUnits(domType)
        || RealType.TimeInterval.equalsExceptNameButUnits(domType)) {
      result = timeSeriesCartesianHorizontalWind(rel);
    } else {
      result = cartesianHorizontalWind((FlatField) rel);
    }
    return result;
  }
  /**
   * Converts a time-series of grid-relative winds to a time-series of true (or absolute) winds. The
   * U and V components of true wind are {@link WesterlyWind} and {@link SoutherlyWind},
   * respectively. The domain of the input {@link visad.Field} must be a temporal {@link
   * visad.Gridded1DSet} or a {@link visad.SingletonSet}. The range values of the input {@link
   * visad.Field} must be {@link visad.FlatField}s. The domains of the range {@link
   * visad.FlatField}s must have a manifold dimension of two or greater and they must have a
   * reference system which contains {@link visad.RealType#Latitude} and {@link
   * visad.RealType#Longitude}. The number of components in the range of the {@link
   * visad.FlatField}s must be two. Both components must have units convertible with {@link
   * #DEFAULT_SPEED_UNIT}. The first and second components are assumed to be the wind components in
   * the direction of increasing first and second manifold dimension indexes, respectively. The
   * domains of the {@link visad.FlatField}s must be equal. The {@link visad.Field} returned by this
   * method has the same domain as the input {@link visad.Field}. The range values of the returned
   * {@link visad.Field} are {@link visad.FlatField}s that have the same domain as the input {@link
   * visad.FlatField}s. The {@link visad.MathType} of the range of the returned {@link
   * visad.FlatField}s will be <code>CartesianHorizontalWind.getEarthVectorType()</code>.
   *
   * @param rel The time-series of grid-relative wind.
   * @return The time-series of true wind corresponding to the input.
   * @throws NullPointerException if <code>rel</code> is <code>null</code>.
   * @throws IllegalArgumentException if the input field doesn't have a time-series domain, or if
   *     the range values aren't {@link visad.FlatField} with the same domain, or if the domain of
   *     the {@link visad.FlatField}s doesn't have a transformation to latitude and longitude, or if
   *     the domain is irregular or has too few points, or if the {@link visad.FlatField}s don't
   *     have two and only two components in their range, or if the default units of the {@link
   *     visad.FlatField}s range aren't equal.
   * @throws VisADException if a VisAD failure occurs.
   * @throws RemoteException if a Java RMI failure occurs.
   * @see CartesianHorizontalWind
   */
  public static Field timeSeriesCartesianHorizontalWind(Field rel)
      throws VisADException, RemoteException {

    FunctionType outerFuncType = (FunctionType) rel.getType();
    RealTupleType outerDomType = outerFuncType.getDomain();

    if (!(RealType.Time.equalsExceptNameButUnits(outerDomType)
        || !RealType.TimeInterval.equalsExceptNameButUnits(outerDomType))) {
      throw new IllegalArgumentException(outerDomType.toString());
    }

    MathType innerFuncType = outerFuncType.getRange();

    if (!(innerFuncType instanceof FunctionType)) {
      throw new IllegalArgumentException(innerFuncType.toString());
    }

    Field innerField = (Field) rel.getSample(0);
    Set innerDom = innerField.getDomainSet();
    if (innerDom instanceof SingletonSet) {
      return rel;
    } else if (innerDom instanceof GriddedSet) {
      int[] lengths = ((GriddedSet) innerDom).getLengths();
      if ((lengths[0] == 1) && (lengths[1] == 1)) {
        return rel;
      }
    }

    // account for null units, assume m/sec
    Unit[] rangeUnits = innerField.getDefaultRangeUnits();
    if ((rangeUnits == null) || (rangeUnits[0] == null) || rangeUnits[0].isDimensionless()) {
      rangeUnits = CartesianHorizontalWind.getEarthVectorType().getDefaultUnits();
    }
    FunctionType innerType =
        new FunctionType(
            ((SetType) innerDom.getType()).getDomain(),
            CartesianHorizontalWind.getEarthVectorType());

    FlatField uvField =
        new FlatField(innerType, innerDom, (CoordinateSystem) null, (Set[]) null, rangeUnits);

    Field result =
        new FieldImpl(new FunctionType(outerDomType, uvField.getType()), rel.getDomainSet());

    // System.out.println("making rHatField");
    Field rHatField = (doNewCode ? hatFieldNew(innerDom, 0) : hatFieldOld(innerDom, 0));
    // System.out.println("making sHatField");
    Field sHatField = (doNewCode ? hatFieldNew(innerDom, 1) : hatFieldOld(innerDom, 1));

    float[][] rHats = rHatField.getFloats(false);
    // ucar.unidata.util.Misc.printArray("rHats[0]", rHats[0]);
    // ucar.unidata.util.Misc.printArray("rHats[1]", rHats[1]);
    // System.out.println("\n");
    float[][] sHats = sHatField.getFloats(false);
    // ucar.unidata.util.Misc.printArray("sHats[0]", sHats[0]);
    // ucar.unidata.util.Misc.printArray("sHats[1]", sHats[1]);
    // System.out.println("\n");
    float[] us = new float[innerDom.getLength()];
    float[] vs = new float[us.length];

    for (int i = 0, n = rel.getLength(); i < n; i++) {
      if (i > 0) {
        innerField = (Field) rel.getSample(i);
        Set dom = innerField.getDomainSet();
        if (!innerDom.equals(dom)) {
          // System.out.println("new domain");
          innerDom = dom;
          rHatField = (doNewCode ? hatFieldNew(innerDom, 0) : hatFieldOld(innerDom, 0));
          sHatField = (doNewCode ? hatFieldNew(innerDom, 1) : hatFieldOld(innerDom, 1));

          rHats = rHatField.getFloats(false);
          sHats = sHatField.getFloats(false);
          /*
          throw new IllegalArgumentException("template="
                  + innerDom.toString() + "; domain="
                  + dom.toString());
          */
        }
        uvField =
            new FlatField(innerType, innerDom, (CoordinateSystem) null, (Set[]) null, rangeUnits);
        us = new float[innerDom.getLength()];
        vs = new float[us.length];
      }

      float[][] rsWinds = innerField.getFloats(false);
      float[] rWinds = rsWinds[0];
      float[] sWinds = rsWinds[1];
      // ucar.unidata.util.Misc.printArray("rWinds", rWinds);
      // System.out.println("\n");
      // ucar.unidata.util.Misc.printArray("sWinds", sWinds);
      // System.out.println("\n");

      for (int j = 0; j < us.length; j++) {
        us[j] = rWinds[j] * rHats[0][j] + sWinds[j] * sHats[0][j];
        vs[j] = rWinds[j] * rHats[1][j] + sWinds[j] * sHats[1][j];
      }
      // ucar.unidata.util.Misc.printArray("us", us);
      // System.out.println("\n");
      // ucar.unidata.util.Misc.printArray("vs", vs);
      // System.out.println("\n");

      uvField.setSamples(new float[][] {us, vs}, false);
      result.setSample(i, uvField, false);
    }

    return result;
  }
  public synchronized void drag_direct(VisADRay ray, boolean first, int mouseModifiers) {
    if (barbValues == null || ref == null || shadow == null) return;

    if (first) {
      stop = false;
    } else {
      if (stop) return;
    }

    // modify direction if mshift != 0
    // modify speed if mctrl != 0
    // modify speed and direction if neither
    int mshift = mouseModifiers & InputEvent.SHIFT_MASK;
    int mctrl = mouseModifiers & InputEvent.CTRL_MASK;

    float o_x = (float) ray.position[0];
    float o_y = (float) ray.position[1];
    float o_z = (float) ray.position[2];
    float d_x = (float) ray.vector[0];
    float d_y = (float) ray.vector[1];
    float d_z = (float) ray.vector[2];

    if (pickCrawlToCursor) {
      if (first) {
        offset_count = OFFSET_COUNT_INIT;
      } else {
        if (offset_count > 0) offset_count--;
      }
      if (offset_count > 0) {
        float mult = ((float) offset_count) / ((float) OFFSET_COUNT_INIT);
        o_x += mult * offsetx;
        o_y += mult * offsety;
        o_z += mult * offsetz;
      }
    }

    if (first || refirst) {
      point_x = barbValues[2];
      point_y = barbValues[3];
      point_z = 0.0f;
      line_x = 0.0f;
      line_y = 0.0f;
      line_z = 1.0f; // lineAxis == 2 in DataRenderer.drag_direct
    } // end if (first || refirst)

    float[] x = new float[3]; // x marks the spot
    // DirectManifoldDimension = 2
    // intersect ray with plane
    float dot = (point_x - o_x) * line_x + (point_y - o_y) * line_y + (point_z - o_z) * line_z;
    float dot2 = d_x * line_x + d_y * line_y + d_z * line_z;
    if (dot2 == 0.0) return;
    dot = dot / dot2;
    // x is intersection
    x[0] = o_x + dot * d_x;
    x[1] = o_y + dot * d_y;
    x[2] = o_z + dot * d_z;
    /*
    System.out.println("x = " + x[0] + " " + x[1] + " " + x[2]);
    */
    try {

      Tuple data = (Tuple) link.getData();
      int n = ((TupleType) data.getType()).getNumberOfRealComponents();
      Real[] reals = new Real[n];

      int k = 0;
      int m = data.getDimension();
      for (int i = 0; i < m; i++) {
        Data component = data.getComponent(i);
        if (component instanceof Real) {
          reals[k++] = (Real) component;
        } else if (component instanceof RealTuple) {
          for (int j = 0; j < ((RealTuple) component).getDimension(); j++) {
            reals[k++] = (Real) ((RealTuple) component).getComponent(j);
          }
        }
      }

      if (first || refirst) {
        // get first Data flow vector
        for (int i = 0; i < 3; i++) {
          int j = flowToComponent[i];
          data_flow[i] = (j >= 0) ? (float) reals[j].getValue() : 0.0f;
        }

        if (coord != null) {
          float[][] ds = {{data_flow[0]}, {data_flow[1]}, {data_flow[2]}};
          ds = coord.toReference(ds);
          data_flow[0] = ds[0][0];
          data_flow[1] = ds[1][0];
          data_flow[2] = ds[2][0];
        }

        data_speed =
            (float)
                Math.sqrt(
                    data_flow[0] * data_flow[0]
                        + data_flow[1] * data_flow[1]
                        + data_flow[2] * data_flow[2]);
        float barb0 = barbValues[2] - barbValues[0];
        float barb1 = barbValues[3] - barbValues[1];
        /*
        System.out.println("data_flow = " + data_flow[0] + " " + data_flow[1] +
                           " " + data_flow[2]);
        System.out.println("barbValues = " + barbValues[0] + " " + barbValues[1] +
                           "   " + barbValues[2] + " " + barbValues[3]);
        System.out.println("data_speed = " + data_speed);
        */
      } // end if (first || refirst)

      // convert x to a flow vector, and from spatial to earth
      if (getRealVectorTypes(which_barb) instanceof EarthVectorType) {
        // don't worry about vector magnitude -
        // data_speed & display_speed take care of that
        float eps = 0.0001f; // estimate derivative with a little vector
        float[][] spatial_locs = {
          {barbValues[0], barbValues[0] + eps * (x[0] - barbValues[0])},
          {barbValues[1], barbValues[1] + eps * (x[1] - barbValues[1])},
          {0.0f, 0.0f}
        };
        /*
        System.out.println("spatial_locs = " + spatial_locs[0][0] + " " +
                           spatial_locs[0][1] + " " + spatial_locs[1][0] + " " +
                           spatial_locs[1][1]);
        */
        float[][] earth_locs = spatialToEarth(spatial_locs);
        // WLH - 18 Aug 99
        if (earth_locs == null) return;
        /*
        System.out.println("earth_locs = " + earth_locs[0][0] + " " +
                           earth_locs[0][1] + " " + earth_locs[1][0] + " " +
                           earth_locs[1][1]);
        */
        x[2] = 0.0f;
        x[0] =
            (earth_locs[1][1] - earth_locs[1][0])
                * ((float) Math.cos(Data.DEGREES_TO_RADIANS * earth_locs[0][0]));
        x[1] = earth_locs[0][1] - earth_locs[0][0];
        /*
        System.out.println("x = " + x[0] + " " + x[1] + " " + x[2]);
        */
      } else { // if (!(getRealVectorTypes(which_barb) instanceof EarthVectorType))
        // convert x to vector
        x[0] -= barbValues[0];
        x[1] -= barbValues[1];

        // adjust for spatial map scalings but don't worry about vector
        // magnitude - data_speed & display_speed take care of that
        // also, spatial is Cartesian
        double[] ranges = getRanges();
        for (int i = 0; i < 3; i++) {
          x[i] /= ranges[i];
        }
        /*
        System.out.println("ranges = " + ranges[0] + " " + ranges[1] +
                           " " + ranges[2]);
        System.out.println("x = " + x[0] + " " + x[1] + " " + x[2]);
        */
      }

      // WLH 6 August 99
      x[0] = -x[0];
      x[1] = -x[1];
      x[2] = -x[2];

      /* may need to do this for performance
            float[] xx = {x[0], x[1], x[2]};
            addPoint(xx);
      */

      float x_speed = (float) Math.sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
      /* WLH 16 April 2002 - from Ken
            if (x_speed < 0.000001f) x_speed = 0.000001f;
      */
      if (x_speed < 0.01f) x_speed = 0.01f;
      if (first || refirst) {
        display_speed = x_speed;
      }
      refirst = false;

      if (mshift != 0) {
        // only modify data_flow direction
        float ratio = data_speed / x_speed;
        x[0] *= ratio;
        x[1] *= ratio;
        x[2] *= ratio;
        /*
        System.out.println("direction, ratio = " + ratio + " " +
                           data_speed + " " + x_speed);
        System.out.println("x = " + x[0] + " " + x[1] + " " + x[2]);
        */
      } else if (mctrl != 0) {
        // only modify data_flow speed
        float ratio = x_speed / display_speed;
        if (data_speed < EPS) {
          data_flow[0] = 2.0f * EPS;
          refirst = true;
        }
        x[0] = ratio * data_flow[0];
        x[1] = ratio * data_flow[1];
        x[2] = ratio * data_flow[2];
        /*
        System.out.println("speed, ratio = " + ratio + " " +
                           x_speed + " " + display_speed);
        System.out.println("x = " + x[0] + " " + x[1] + " " + x[2]);
        */
      } else {
        // modify data_flow speed and direction
        float ratio = data_speed / display_speed;
        /*
        System.out.println("data_speed = " + data_speed +
                           " display_speed = " + display_speed +
                           " ratio = " + ratio + " EPS = " + EPS);
        System.out.println("x = " + x[0] + " " + x[1] +" " + x[2] +
                           " x_speed = " + x_speed);
          data_speed = 21.213203 display_speed = 0.01 ratio = 2121.3203 EPS = 0.2
          x = 1.6170928E-4 1.6021729E-4 -0.0 x_speed = 0.01
          wind = (0.3430372, 0.33987218) at (-35.0, 5.0)
        */
        if (data_speed < EPS) {
          data_flow[0] = 2.0f * EPS;
          x[0] = data_flow[0];
          x[1] = data_flow[1];
          x[2] = data_flow[2];
          refirst = true;
        } else {
          x[0] *= ratio;
          x[1] *= ratio;
          x[2] *= ratio;
        }
      }

      if (coord != null) {
        float[][] xs = {{x[0]}, {x[1]}, {x[2]}};
        xs = coord.fromReference(xs);
        x[0] = xs[0][0];
        x[1] = xs[1][0];
        x[2] = xs[2][0];
      }

      // now replace flow values
      Vector vect = new Vector();
      for (int i = 0; i < 3; i++) {
        int j = flowToComponent[i];
        if (j >= 0) {
          RealType rtype = (RealType) reals[j].getType();
          reals[j] = new Real(rtype, (double) x[i], rtype.getDefaultUnit(), null);

          // WLH 31 Aug 2000
          Real r = reals[j];
          Unit overrideUnit = null;
          if (directMap[i] != null) {
            overrideUnit = directMap[i].getOverrideUnit();
          }
          Unit rtunit = rtype.getDefaultUnit();
          // units not part of Time string
          if (overrideUnit != null
              && !overrideUnit.equals(rtunit)
              && !RealType.Time.equals(rtype)) {
            double d = (float) overrideUnit.toThis((double) x[0], rtunit);
            r = new Real(rtype, d, overrideUnit);
            String valueString = r.toValueString();
            vect.addElement(rtype.getName() + " = " + valueString);
          } else {
            // create location string
            vect.addElement(rtype.getName() + " = " + x[i]);
          }
        }
      }
      getDisplayRenderer().setCursorStringVector(vect);

      Data newData = null;
      // now build new RealTuple or Flat Tuple
      if (data instanceof RealTuple) {
        newData =
            new RealTuple(
                ((RealTupleType) data.getType()), reals, ((RealTuple) data).getCoordinateSystem());
      } else {
        Data[] new_components = new Data[m];
        k = 0;
        for (int i = 0; i < m; i++) {
          Data component = data.getComponent(i);
          if (component instanceof Real) {
            new_components[i] = reals[k++];
          } else if (component instanceof RealTuple) {
            Real[] sub_reals = new Real[((RealTuple) component).getDimension()];
            for (int j = 0; j < ((RealTuple) component).getDimension(); j++) {
              sub_reals[j] = reals[k++];
            }
            new_components[i] =
                new RealTuple(
                    ((RealTupleType) component.getType()),
                    sub_reals,
                    ((RealTuple) component).getCoordinateSystem());
          }
        }
        newData = new Tuple(new_components, false);
      }
      ref.setData(newData);
    } catch (VisADException e) {
      // do nothing
      System.out.println("drag_direct " + e);
      e.printStackTrace();
    } catch (RemoteException e) {
      // do nothing
      System.out.println("drag_direct " + e);
      e.printStackTrace();
    }
  }