/* Copyright 2002-2021 CS GROUP
    * Licensed to CS GROUP (CS) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *   http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.orekit.models.earth.ionosphere;
  
  import java.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.InputStreamReader;
  import java.nio.charset.StandardCharsets;
  import java.util.Collections;
  import java.util.List;
  import java.util.regex.Pattern;
  
  import org.hipparchus.Field;
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.FieldSinCos;
  import org.hipparchus.util.MathArrays;
  import org.hipparchus.util.SinCos;
  import org.orekit.annotation.DefaultDataContext;
  import org.orekit.bodies.BodyShape;
  import org.orekit.bodies.FieldGeodeticPoint;
  import org.orekit.bodies.GeodeticPoint;
  import org.orekit.data.DataContext;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.frames.TopocentricFrame;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.DateComponents;
  import org.orekit.time.DateTimeComponents;
  import org.orekit.time.FieldAbsoluteDate;
  import org.orekit.time.TimeScale;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.TimeStampedFieldPVCoordinates;
  import org.orekit.utils.TimeStampedPVCoordinates;
  
  /**
   * NeQuick ionospheric delay model.
   *
   * @author Bryan Cazabonne
   *
   * @see "European Union (2016). European GNSS (Galileo) Open Service-Ionospheric Correction
   *       Algorithm for Galileo Single Frequency Users. 1.2."
   *
   * @since 10.1
   */
  public class NeQuickModel implements IonosphericModel {
  
      /** NeQuick resources base directory. */
      private static final String NEQUICK_BASE = "/assets/org/orekit/nequick/";
  
      /** Serializable UID. */
      private static final long serialVersionUID = 201928051L;
  
      /** Pattern for delimiting regular expressions. */
      private static final Pattern SEPARATOR = Pattern.compile("\\s+");
  
      /** Mean Earth radius in m (Ref Table 2.5.2). */
      private static final double RE = 6371200.0;
  
      /** Meters to kilometers converter. */
      private static final double M_TO_KM = 0.001;
  
      /** Factor for the electron density computation. */
      private static final double DENSITY_FACTOR = 1.0e11;
  
      /** Factor for the path delay computation. */
      private static final double DELAY_FACTOR = 40.3e16;
  
      /** The three ionospheric coefficients broadcast in the Galileo navigation message. */
      private final double[] alpha;
  
      /** MODIP grid. */
      private final double[][] stModip;
  
      /** Month used for loading CCIR coefficients. */
      private int month;
  
      /** F2 coefficients used by the F2 layer. */
      private double[][][] f2;
  
      /** Fm3 coefficients used by the F2 layer. */
      private double[][][] fm3;
 
     /** UTC time scale. */
     private final TimeScale utc;
 
     /**
      * Build a new instance.
      *
      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
      *
      * @param alpha effective ionisation level coefficients
      * @see #NeQuickModel(double[], TimeScale)
      */
     @DefaultDataContext
     public NeQuickModel(final double[] alpha) {
         this(alpha, DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /**
      * Build a new instance.
      * @param alpha effective ionisation level coefficients
      * @param utc UTC time scale.
      * @since 10.1
      */
     public NeQuickModel(final double[] alpha,
                         final TimeScale utc) {
         // F2 layer values
         this.month = 0;
         this.f2    = null;
         this.fm3   = null;
         // Read modip grid
         final MODIPLoader parser = new MODIPLoader();
         parser.loadMODIPGrid();
         this.stModip = parser.getMODIPGrid();
         // Ionisation level coefficients
         this.alpha = alpha.clone();
         this.utc = utc;
     }
 
     @Override
     public double pathDelay(final SpacecraftState state, final TopocentricFrame baseFrame,
                             final double frequency, final double[] parameters) {
         // Point
         final GeodeticPoint recPoint = baseFrame.getPoint();
         // Date
         final AbsoluteDate date = state.getDate();
 
         // Reference body shape
         final BodyShape ellipsoid = baseFrame.getParentShape();
         // Satellite geodetic coordinates
         final TimeStampedPVCoordinates pv = state.getPVCoordinates(ellipsoid.getBodyFrame());
         final GeodeticPoint satPoint = ellipsoid.transform(pv.getPosition(), ellipsoid.getBodyFrame(), state.getDate());
 
         // Total Electron Content
         final double tec = stec(date, recPoint, satPoint);
 
         // Ionospheric delay
         final double factor = DELAY_FACTOR / (frequency * frequency);
         return factor * tec;
     }
 
     @Override
     public <T extends CalculusFieldElement<T>> T pathDelay(final FieldSpacecraftState<T> state, final TopocentricFrame baseFrame,
                                                        final double frequency, final T[] parameters) {
         // Date
         final FieldAbsoluteDate<T> date = state.getDate();
         // Point
         final FieldGeodeticPoint<T> recPoint = baseFrame.getPoint(date.getField());
 
 
         // Reference body shape
         final BodyShape ellipsoid = baseFrame.getParentShape();
         // Satellite geodetic coordinates
         final TimeStampedFieldPVCoordinates<T> pv = state.getPVCoordinates(ellipsoid.getBodyFrame());
         final FieldGeodeticPoint<T> satPoint = ellipsoid.transform(pv.getPosition(), ellipsoid.getBodyFrame(), state.getDate());
 
         // Total Electron Content
         final T tec = stec(date, recPoint, satPoint);
 
         // Ionospheric delay
         final double factor = DELAY_FACTOR / (frequency * frequency);
         return tec.multiply(factor);
     }
 
     @Override
     public List<ParameterDriver> getParametersDrivers() {
         return Collections.emptyList();
     }
 
     /**
      * This method allows the computation of the Stant Total Electron Content (STEC).
      * <p>
      * This method follows the Gauss algorithm exposed in section 2.5.8.2.8 of
      * the reference document.
      * </p>
      * @param date current date
      * @param recP receiver position
      * @param satP satellite position
      * @return the STEC in TECUnits
      */
     public double stec(final AbsoluteDate date, final GeodeticPoint recP, final GeodeticPoint satP) {
 
         // Ray-perigee parameters
         final Ray ray = new Ray(recP, satP);
 
         // Load the correct CCIR file
         final DateTimeComponents dateTime = date.getComponents(utc);
         loadsIfNeeded(dateTime.getDate());
 
         // Tolerance for the integration accuracy. Defined inside the reference document, section 2.5.8.1.
         final double h1 = recP.getAltitude();
         final double tolerance;
         if (h1 < 1000000.0) {
             tolerance = 0.001;
         } else {
             tolerance = 0.01;
         }
 
         // Integration
         int n = 8;
         final Segment seg1 = new Segment(n, ray);
         double gn1 = stecIntegration(seg1, dateTime);
         n *= 2;
         final Segment seg2 = new Segment(n, ray);
         double gn2 = stecIntegration(seg2, dateTime);
 
         int count = 1;
         while (FastMath.abs(gn2 - gn1) > tolerance * FastMath.abs(gn1) && count < 20) {
             gn1 = gn2;
             n *= 2;
             final Segment seg = new Segment(n, ray);
             gn2 = stecIntegration(seg, dateTime);
             count += 1;
         }
 
         // If count > 20 the integration did not converge
         if (count == 20) {
             throw new OrekitException(OrekitMessages.STEC_INTEGRATION_DID_NOT_CONVERGE);
         }
 
         // Eq. 202
         return (gn2 + ((gn2 - gn1) / 15.0)) * 1.0e-16;
     }
 
     /**
      * This method allows the computation of the Stant Total Electron Content (STEC).
      * <p>
      * This method follows the Gauss algorithm exposed in section 2.5.8.2.8 of
      * the reference document.
      * </p>
      * @param <T> type of the elements
      * @param date current date
      * @param recP receiver position
      * @param satP satellite position
      * @return the STEC in TECUnits
      */
     public <T extends CalculusFieldElement<T>> T stec(final FieldAbsoluteDate<T> date,
                                                   final FieldGeodeticPoint<T> recP,
                                                   final FieldGeodeticPoint<T> satP) {
 
         // Field
         final Field<T> field = date.getField();
 
         // Ray-perigee parameters
         final FieldRay<T> ray = new FieldRay<>(field, recP, satP);
 
         // Load the correct CCIR file
         final DateTimeComponents dateTime = date.getComponents(utc);
         loadsIfNeeded(dateTime.getDate());
 
         // Tolerance for the integration accuracy. Defined inside the reference document, section 2.5.8.1.
         final T h1 = recP.getAltitude();
         final double tolerance;
         if (h1.getReal() < 1000000.0) {
             tolerance = 0.001;
         } else {
             tolerance = 0.01;
         }
 
         // Integration
         int n = 8;
         final FieldSegment<T> seg1 = new FieldSegment<>(field, n, ray);
         T gn1 = stecIntegration(field, seg1, dateTime);
         n *= 2;
         final FieldSegment<T> seg2 = new FieldSegment<>(field, n, ray);
         T gn2 = stecIntegration(field, seg2, dateTime);
 
         int count = 1;
         while (FastMath.abs(gn2.subtract(gn1)).getReal() > FastMath.abs(gn1).multiply(tolerance).getReal() && count < 20) {
             gn1 = gn2;
             n *= 2;
             final FieldSegment<T> seg = new FieldSegment<>(field, n, ray);
             gn2 = stecIntegration(field, seg, dateTime);
             count += 1;
         }
 
         // If count > 20 the integration did not converge
         if (count == 20) {
             throw new OrekitException(OrekitMessages.STEC_INTEGRATION_DID_NOT_CONVERGE);
         }
 
         // Eq. 202
         return gn2.add(gn2.subtract(gn1).divide(15.0)).multiply(1.0e-16);
     }
 
     /**
      * This method perfoms the STEC integration.
      * @param seg coordinates along the integration path
      * @param dateTime current date and time componentns
      * @return result of the integration
      */
     private double stecIntegration(final Segment seg, final DateTimeComponents dateTime) {
         // Integration points
         final double[] heightS    = seg.getHeights();
         final double[] latitudeS  = seg.getLatitudes();
         final double[] longitudeS = seg.getLongitudes();
 
         // Compute electron density
         double density = 0.0;
         for (int i = 0; i < heightS.length; i++) {
             final NeQuickParameters parameters = new NeQuickParameters(dateTime, f2, fm3,
                                                                        latitudeS[i], longitudeS[i],
                                                                        alpha, stModip);
             density += electronDensity(heightS[i], parameters);
         }
 
         return 0.5 * seg.getInterval() * density;
     }
 
     /**
      * This method perfoms the STEC integration.
      * @param <T> type of the elements
      * @param field field of the elements
      * @param seg coordinates along the integration path
      * @param dateTime current date and time componentns
      * @return result of the integration
      */
     private <T extends CalculusFieldElement<T>> T stecIntegration(final Field<T> field,
                                                               final FieldSegment<T> seg,
                                                               final DateTimeComponents dateTime) {
         // Integration points
         final T[] heightS    = seg.getHeights();
         final T[] latitudeS  = seg.getLatitudes();
         final T[] longitudeS = seg.getLongitudes();
 
         // Compute electron density
         T density = field.getZero();
         for (int i = 0; i < heightS.length; i++) {
             final FieldNeQuickParameters<T> parameters = new FieldNeQuickParameters<>(field, dateTime, f2, fm3,
                                                                                       latitudeS[i], longitudeS[i],
                                                                                       alpha, stModip);
             density = density.add(electronDensity(field, heightS[i], parameters));
         }
 
         return seg.getInterval().multiply(density).multiply(0.5);
     }
 
     /**
      * Computes the electron density at a given height.
      * @param h height in m
      * @param parameters NeQuick model parameters
      * @return electron density [m^-3]
      */
     private double electronDensity(final double h, final NeQuickParameters parameters) {
         // Convert height in kilometers
         final double hInKm = h * M_TO_KM;
         // Electron density
         final double n;
         if (hInKm <= parameters.getHmF2()) {
             n = bottomElectronDensity(hInKm, parameters);
         } else {
             n = topElectronDensity(hInKm, parameters);
         }
         return n;
     }
 
     /**
      * Computes the electron density at a given height.
      * @param <T> type of the elements
      * @param field field of the elements
      * @param h height in m
      * @param parameters NeQuick model parameters
      * @return electron density [m^-3]
      */
     private <T extends CalculusFieldElement<T>> T electronDensity(final Field<T> field,
                                                               final T h,
                                                               final FieldNeQuickParameters<T> parameters) {
         // Convert height in kilometers
         final T hInKm = h.multiply(M_TO_KM);
         // Electron density
         final T n;
         if (hInKm.getReal() <= parameters.getHmF2().getReal()) {
             n = bottomElectronDensity(field, hInKm, parameters);
         } else {
             n = topElectronDensity(field, hInKm, parameters);
         }
         return n;
     }
 
     /**
      * Computes the electron density of the bottomside.
      * @param h height in km
      * @param parameters NeQuick model parameters
      * @return the electron density N in m-3
      */
     private double bottomElectronDensity(final double h, final NeQuickParameters parameters) {
 
         // Select the relevant B parameter for the current height (Eq. 109 and 110)
         final double be;
         if (h > parameters.getHmE()) {
             be = parameters.getBETop();
         } else {
             be = parameters.getBEBot();
         }
         final double bf1;
         if (h > parameters.getHmF1()) {
             bf1 = parameters.getB1Top();
         } else {
             bf1 = parameters.getB1Bot();
         }
         final double bf2 = parameters.getB2Bot();
 
         // Useful array of constants
         final double[] ct = new double[] {
             1.0 / bf2, 1.0 / bf1, 1.0 / be
         };
 
         // Compute the exponential argument for each layer (Eq. 111 to 113)
         // If h < 100km we use h = 100km as recommended in the reference document
         final double   hTemp = FastMath.max(100.0, h);
         final double   exp   = clipExp(10.0 / (1.0 + FastMath.abs(hTemp - parameters.getHmF2())));
         final double[] arguments = new double[3];
         arguments[0] = (hTemp - parameters.getHmF2()) / bf2;
         arguments[1] = ((hTemp - parameters.getHmF1()) / bf1) * exp;
         arguments[2] = ((hTemp - parameters.getHmE()) / be) * exp;
 
         // S coefficients
         final double[] s = new double[3];
         // Array of corrective terms
         final double[] ds = new double[3];
 
         // Layer amplitudes
         final double[] amplitudes = parameters.getLayerAmplitudes();
 
         // Fill arrays (Eq. 114 to 118)
         for (int i = 0; i < 3; i++) {
             if (FastMath.abs(arguments[i]) > 25.0) {
                 s[i]  = 0.0;
                 ds[i] = 0.0;
             } else {
                 final double expA   = clipExp(arguments[i]);
                 final double opExpA = 1.0 + expA;
                 s[i]  = amplitudes[i] * (expA / (opExpA * opExpA));
                 ds[i] = ct[i] * ((1.0 - expA) / (1.0 + expA));
             }
         }
 
         // Electron density
         final double aNo = MathArrays.linearCombination(s[0], 1.0, s[1], 1.0, s[2], 1.0);
         if (h >= 100) {
             return aNo * DENSITY_FACTOR;
         } else {
             // Chapman parameters (Eq. 119 and 120)
             final double bc = 1.0 - 10.0 * (MathArrays.linearCombination(s[0], ds[0], s[1], ds[1], s[2], ds[2]) / aNo);
             final double z  = 0.1 * (h - 100.0);
             // Electron density (Eq. 121)
             return aNo * clipExp(1.0 - bc * z - clipExp(-z)) * DENSITY_FACTOR;
         }
     }
 
     /**
      * Computes the electron density of the bottomside.
      * @param <T> type of the elements
      * @param field field of the elements
      * @param h height in km
      * @param parameters NeQuick model parameters
      * @return the electron density N in m-3
      */
     private <T extends CalculusFieldElement<T>> T bottomElectronDensity(final Field<T> field,
                                                                     final T h,
                                                                     final FieldNeQuickParameters<T> parameters) {
 
         // Zero and One
         final T zero = field.getZero();
         final T one  = field.getOne();
 
         // Select the relevant B parameter for the current height (Eq. 109 and 110)
         final T be;
         if (h.getReal() > parameters.getHmE().getReal()) {
             be = parameters.getBETop();
         } else {
             be = parameters.getBEBot();
         }
         final T bf1;
         if (h.getReal() > parameters.getHmF1().getReal()) {
             bf1 = parameters.getB1Top();
         } else {
             bf1 = parameters.getB1Bot();
         }
         final T bf2 = parameters.getB2Bot();
 
         // Useful array of constants
         final T[] ct = MathArrays.buildArray(field, 3);
         ct[0] = bf2.reciprocal();
         ct[1] = bf1.reciprocal();
         ct[2] = be.reciprocal();
 
         // Compute the exponential argument for each layer (Eq. 111 to 113)
         // If h < 100km we use h = 100km as recommended in the reference document
         final T   hTemp = FastMath.max(zero.add(100.0), h);
         final T   exp   = clipExp(field, FastMath.abs(hTemp.subtract(parameters.getHmF2())).add(1.0).divide(10.0).reciprocal());
         final T[] arguments = MathArrays.buildArray(field, 3);
         arguments[0] = hTemp.subtract(parameters.getHmF2()).divide(bf2);
         arguments[1] = hTemp.subtract(parameters.getHmF1()).divide(bf1).multiply(exp);
         arguments[2] = hTemp.subtract(parameters.getHmE()).divide(be).multiply(exp);
 
         // S coefficients
         final T[] s = MathArrays.buildArray(field, 3);
         // Array of corrective terms
         final T[] ds = MathArrays.buildArray(field, 3);
 
         // Layer amplitudes
         final T[] amplitudes = parameters.getLayerAmplitudes();
 
         // Fill arrays (Eq. 114 to 118)
         for (int i = 0; i < 3; i++) {
             if (FastMath.abs(arguments[i]).getReal() > 25.0) {
                 s[i]  = zero;
                 ds[i] = zero;
             } else {
                 final T expA   = clipExp(field, arguments[i]);
                 final T opExpA = expA.add(1.0);
                 s[i]  = amplitudes[i].multiply(expA.divide(opExpA.multiply(opExpA)));
                 ds[i] = ct[i].multiply(expA.negate().add(1.0).divide(expA.add(1.0)));
             }
         }
 
         // Electron density
         final T aNo = one.linearCombination(s[0], one, s[1], one, s[2], one);
         if (h.getReal() >= 100) {
             return aNo.multiply(DENSITY_FACTOR);
         } else {
             // Chapman parameters (Eq. 119 and 120)
             final T bc = s[0].multiply(ds[0]).add(one.linearCombination(s[0], ds[0], s[1], ds[1], s[2], ds[2])).divide(aNo).multiply(10.0).negate().add(1.0);
             final T z  = h.subtract(100.0).multiply(0.1);
             // Electron density (Eq. 121)
             return aNo.multiply(clipExp(field, bc.multiply(z).add(clipExp(field, z.negate())).negate().add(1.0))).multiply(DENSITY_FACTOR);
         }
     }
 
     /**
      * Computes the electron density of the topside.
      * @param h height in km
      * @param parameters NeQuick model parameters
      * @return the electron density N in m-3
      */
     private double topElectronDensity(final double h, final NeQuickParameters parameters) {
 
         // Constant parameters (Eq. 122 and 123)
         final double g = 0.125;
         final double r = 100.0;
 
         // Arguments deltaH and z (Eq. 124 and 125)
         final double deltaH = h - parameters.getHmF2();
         final double z      = deltaH / (parameters.getH0() * (1.0 + (r * g * deltaH) / (r * parameters.getH0() + g * deltaH)));
 
         // Exponential (Eq. 126)
         final double ee = clipExp(z);
 
         // Electron density (Eq. 127)
         if (ee > 1.0e11) {
             return (4.0 * parameters.getNmF2() / ee) * DENSITY_FACTOR;
         } else {
             final double opExpZ = 1.0 + ee;
             return ((4.0 * parameters.getNmF2() * ee) / (opExpZ * opExpZ)) * DENSITY_FACTOR;
         }
     }
 
     /**
      * Computes the electron density of the topside.
      * @param <T> type of the elements
      * @param field field of the elements
      * @param h height in km
      * @param parameters NeQuick model parameters
      * @return the electron density N in m-3
      */
     private <T extends CalculusFieldElement<T>> T topElectronDensity(final Field<T> field,
                                                                  final T h,
                                                                  final FieldNeQuickParameters<T> parameters) {
 
         // Constant parameters (Eq. 122 and 123)
         final double g = 0.125;
         final double r = 100.0;
 
         // Arguments deltaH and z (Eq. 124 and 125)
         final T deltaH = h.subtract(parameters.getHmF2());
         final T z      = deltaH.divide(parameters.getH0().multiply(deltaH.multiply(r).multiply(g).divide(parameters.getH0().multiply(r).add(deltaH.multiply(g))).add(1.0)));
 
         // Exponential (Eq. 126)
         final T ee = clipExp(field, z);
 
         // Electron density (Eq. 127)
         if (ee.getReal() > 1.0e11) {
             return parameters.getNmF2().multiply(4.0).divide(ee).multiply(DENSITY_FACTOR);
         } else {
             final T opExpZ = ee.add(field.getOne());
             return parameters.getNmF2().multiply(4.0).multiply(ee).divide(opExpZ.multiply(opExpZ)).multiply(DENSITY_FACTOR);
         }
     }
 
     /**
      * Lazy loading of CCIR data.
      * @param date current date components
      */
     private void loadsIfNeeded(final DateComponents date) {
 
         // Current month
         final int currentMonth = date.getMonth();
 
         // Check if date have changed or if f2 and fm3 arrays are null
         if (currentMonth != month || f2 == null || fm3 == null) {
             this.month = currentMonth;
 
             // Read file
             final CCIRLoader loader = new CCIRLoader();
             loader.loadCCIRCoefficients(date);
 
             // Update arrays
             this.f2 = loader.getF2();
             this.fm3 = loader.getFm3();
         }
     }
 
     /**
      * A clipped exponential function.
      * <p>
      * This function, describe in section F.2.12.2 of the reference document, is
      * recommanded for the computation of exponential values.
      * </p>
      * @param power power for exponential function
      * @return clipped exponential value
      */
     private double clipExp(final double power) {
         if (power > 80.0) {
             return 5.5406E34;
         } else if (power < -80) {
             return 1.8049E-35;
         } else {
             return FastMath.exp(power);
         }
     }
 
     /**
      * A clipped exponential function.
      * <p>
      * This function, describe in section F.2.12.2 of the reference document, is
      * recommanded for the computation of exponential values.
      * </p>
      * @param <T> type of the elements
      * @param field field of the elements
      * @param power power for exponential function
      * @return clipped exponential value
      */
     private <T extends CalculusFieldElement<T>> T clipExp(final Field<T> field, final T power) {
         final T zero = field.getZero();
         if (power.getReal() > 80.0) {
             return zero.add(5.5406E34);
         } else if (power.getReal() < -80) {
             return zero.add(1.8049E-35);
         } else {
             return FastMath.exp(power);
         }
     }
 
     /** Get a data stream.
      * @param name file name of the resource stream
      * @return stream
      */
     private static InputStream getStream(final String name) {
         return NeQuickModel.class.getResourceAsStream(name);
     }
 
     /**
      * Parser for Modified Dip Latitude (MODIP) grid file.
      * <p>
      * The MODIP grid allows to estimate MODIP μ [deg] at a given point (φ,λ)
      * by interpolation of the relevant values contained in the support file.
      * </p> <p>
      * The file contains the values of MODIP (expressed in degrees) on a geocentric grid
      * from 90°S to 90°N with a 5-degree step in latitude and from 180°W to 180°E with a
      * 10-degree in longitude.
      * </p>
      */
     private static class MODIPLoader {
 
         /** Supported name for MODIP grid. */
         private static final String SUPPORTED_NAME = NEQUICK_BASE + "modip.txt";
 
         /** MODIP grid. */
         private double[][] grid;
 
         /**
          * Build a new instance.
          */
         MODIPLoader() {
             this.grid = null;
         }
 
         /** Returns the MODIP grid array.
          * @return the MODIP grid array
          */
         public double[][] getMODIPGrid() {
             return grid.clone();
         }
 
         /**
          * Load the data using supported names.
          */
         public void loadMODIPGrid() {
             try (InputStream in = getStream(SUPPORTED_NAME)) {
                 loadData(in, SUPPORTED_NAME);
             } catch (IOException e) {
                 throw new OrekitException(OrekitMessages.INTERNAL_ERROR, e);
             }
 
             // Throw an exception if MODIP grid was not loaded properly
             if (grid == null) {
                 throw new OrekitException(OrekitMessages.MODIP_GRID_NOT_LOADED, SUPPORTED_NAME);
             }
         }
 
         /**
          * Load data from a stream.
          * @param input input stream
          * @param name name of the file
          * @throws IOException if data can't be read
          */
         public void loadData(final InputStream input, final String name)
             throws IOException {
 
             // Grid size
             final int size = 39;
 
             // Initialize array
             final double[][] array = new double[size][size];
 
             // Open stream and parse data
             int   lineNumber = 0;
             String line      = null;
             try (InputStreamReader isr = new InputStreamReader(input, StandardCharsets.UTF_8);
                  BufferedReader    br = new BufferedReader(isr)) {
 
                 for (line = br.readLine(); line != null; line = br.readLine()) {
                     ++lineNumber;
                     line = line.trim();
 
                     // Read grid data
                     if (line.length() > 0) {
                         final String[] modip_line = SEPARATOR.split(line);
                         for (int column = 0; column < modip_line.length; column++) {
                             array[lineNumber - 1][column] = Double.valueOf(modip_line[column]);
                         }
                     }
 
                 }
 
             } catch (NumberFormatException nfe) {
                 throw new OrekitException(OrekitMessages.UNABLE_TO_PARSE_LINE_IN_FILE,
                                           lineNumber, name, line);
             }
 
             // Clone parsed grid
             grid = array.clone();
 
         }
     }
 
     /**
      * Parser for CCIR files.
      * <p>
      * Numerical grid maps which describe the regular variation of the ionosphere.
      * They are used to derive other variables such as critical frequencies and transmission factors.
      * </p> <p>
      * The coefficients correspond to low and high solar activity conditions.
      * </p> <p>
      * The CCIR file naming convention is ccirXX.asc where each XX means month + 10.
      * </p> <p>
      * Coefficients are store into tow arrays, F2 and Fm3. F2 coefficients are used for the computation
      * of the F2 layer critical frequency. Fm3 for the computation of the F2 layer maximum usable frequency factor.
      * The size of these two arrays is fixed and discussed into the section 2.5.3.2
      * of the reference document.
      * </p>
      */
     private static class CCIRLoader {
 
         /** Default supported files name pattern. */
         public static final String DEFAULT_SUPPORTED_NAME = "ccir**.asc";
 
         /** Total number of F2 coefficients contained in the file. */
         private static final int NUMBER_F2_COEFFICIENTS = 1976;
 
         /** Rows number for F2 and Fm3 arrays. */
         private static final int ROWS = 2;
 
         /** Columns number for F2 array. */
         private static final int TOTAL_COLUMNS_F2 = 76;
 
         /** Columns number for Fm3 array. */
         private static final int TOTAL_COLUMNS_FM3 = 49;
 
         /** Depth of F2 array. */
         private static final int DEPTH_F2 = 13;
 
         /** Depth of Fm3 array. */
         private static final int DEPTH_FM3 = 9;
 
         /** Regular expression for supported file name. */
         private String supportedName;
 
         /** F2 coefficients used for the computation of the F2 layer critical frequency. */
         private double[][][] f2Loader;
 
         /** Fm3 coefficients used for the computation of the F2 layer maximum usable frequency factor. */
         private double[][][] fm3Loader;
 
         /**
          * Build a new instance.
          */
         CCIRLoader() {
             this.supportedName = DEFAULT_SUPPORTED_NAME;
             this.f2Loader  = null;
             this.fm3Loader = null;
         }
 
         /**
          * Get the F2 coefficients used for the computation of the F2 layer critical frequency.
          * @return the F2 coefficients
          */
         public double[][][] getF2() {
             return f2Loader.clone();
         }
 
         /**
          * Get the Fm3 coefficients used for the computation of the F2 layer maximum usable frequency factor.
          * @return the F2 coefficients
          */
         public double[][][] getFm3() {
             return fm3Loader.clone();
         }
 
         /** Load the data for a given month.
          * @param dateComponents month given but its DateComponents
          */
         public void loadCCIRCoefficients(final DateComponents dateComponents) {
 
             // The files are named ccirXX.asc where XX substitute the month of the year + 10
             final int currentMonth = dateComponents.getMonth();
             this.supportedName = NEQUICK_BASE + String.format("ccir%02d.asc", currentMonth + 10);
             try (InputStream in = getStream(supportedName)) {
                 loadData(in, supportedName);
             } catch (IOException e) {
                 throw new OrekitException(OrekitMessages.INTERNAL_ERROR, e);
             }
             // Throw an exception if F2 or Fm3 were not loaded properly
             if (f2Loader == null || fm3Loader == null) {
                 throw new OrekitException(OrekitMessages.NEQUICK_F2_FM3_NOT_LOADED, supportedName);
             }
 
         }
 
         /**
          * Load data from a stream.
          * @param input input stream
          * @param name name of the file
          * @throws IOException if data can't be read
          */
         public void loadData(final InputStream input, final String name)
             throws IOException {
 
             // Initialize arrays
             final double[][][] f2Temp  = new double[ROWS][TOTAL_COLUMNS_F2][DEPTH_F2];
             final double[][][] fm3Temp = new double[ROWS][TOTAL_COLUMNS_FM3][DEPTH_FM3];
 
             // Placeholders for parsed data
             int    lineNumber       = 0;
             int    index            = 0;
             int    currentRowF2     = 0;
             int    currentColumnF2  = 0;
             int    currentDepthF2   = 0;
             int    currentRowFm3    = 0;
             int    currentColumnFm3 = 0;
             int    currentDepthFm3  = 0;
             String line             = null;
 
             try (InputStreamReader isr = new InputStreamReader(input, StandardCharsets.UTF_8);
                  BufferedReader    br = new BufferedReader(isr)) {
 
                 for (line = br.readLine(); line != null; line = br.readLine()) {
                     ++lineNumber;
                     line = line.trim();
 
                     // Read grid data
                     if (line.length() > 0) {
                         final String[] ccir_line = SEPARATOR.split(line);
                         for (int i = 0; i < ccir_line.length; i++) {
 
                             if (index < NUMBER_F2_COEFFICIENTS) {
                                 // Parse F2 coefficients
                                 if (currentDepthF2 >= DEPTH_F2 && currentColumnF2 < (TOTAL_COLUMNS_F2 - 1)) {
                                     currentDepthF2 = 0;
                                     currentColumnF2++;
                                 } else if (currentDepthF2 >= DEPTH_F2 && currentColumnF2 >= (TOTAL_COLUMNS_F2 - 1)) {
                                     currentDepthF2 = 0;
                                     currentColumnF2 = 0;
                                     currentRowF2++;
                                 }
                                 f2Temp[currentRowF2][currentColumnF2][currentDepthF2++] = Double.valueOf(ccir_line[i]);
                                 index++;
                             } else {
                                 // Parse Fm3 coefficients
                                 if (currentDepthFm3 >= DEPTH_FM3 && currentColumnFm3 < (TOTAL_COLUMNS_FM3 - 1)) {
                                     currentDepthFm3 = 0;
                                     currentColumnFm3++;
                                 } else if (currentDepthFm3 >= DEPTH_FM3 && currentColumnFm3 >= (TOTAL_COLUMNS_FM3 - 1)) {
                                     currentDepthFm3 = 0;
                                     currentColumnFm3 = 0;
                                     currentRowFm3++;
                                 }
                                 fm3Temp[currentRowFm3][currentColumnFm3][currentDepthFm3++] = Double.valueOf(ccir_line[i]);
                                 index++;
                             }
 
                         }
                     }
 
                 }
 
             } catch (NumberFormatException nfe) {
                 throw new OrekitException(OrekitMessages.UNABLE_TO_PARSE_LINE_IN_FILE,
                                           lineNumber, name, line);
             }
 
             f2Loader  = f2Temp.clone();
             fm3Loader = fm3Temp.clone();
 
         }
 
     }
 
     /**
      * Container for ray-perigee parameters.
      * By convention, point 1 is at lower height.
      */
     private static class Ray {
 
         /** Threshold for ray-perigee parameters computation. */
         private static final double THRESHOLD = 1.0e-10;
 
         /** Distance of the first point from the ray perigee [m]. */
         private final double s1;
 
         /** Distance of the second point from the ray perigee [m]. */
         private final double s2;
 
         /** Ray-perigee radius [m]. */
         private final double rp;
 
         /** Ray-perigee latitude [rad]. */
         private final double latP;
 
         /** Ray-perigee longitude [rad]. */
         private final double lonP;
 
         /** Sine and cosine of ray-perigee latitude. */
         private final SinCos scLatP;
 
         /** Sine of azimuth of satellite as seen from ray-perigee. */
         private final double sinAzP;
 
         /** Cosine of azimuth of satellite as seen from ray-perigee. */
         private final double cosAzP;
 
         /**
          * Constructor.
          * @param recP receiver position
          * @param satP satellite position
          */
         Ray(final GeodeticPoint recP, final GeodeticPoint satP) {
 
             // Integration limits in meters (Eq. 140 and 141)
             final double r1 = RE + recP.getAltitude();
             final double r2 = RE + satP.getAltitude();
 
             // Useful parameters
             final double lat1     = recP.getLatitude();
             final double lat2     = satP.getLatitude();
             final double lon1     = recP.getLongitude();
             final double lon2     = satP.getLongitude();
             final SinCos scLatSat = FastMath.sinCos(lat2);
             final SinCos scLatRec = FastMath.sinCos(lat1);
             final SinCos scLon21  = FastMath.sinCos(lon2 - lon1);
 
             // Zenith angle computation (Eq. 153 to 155)
             final double cosD = scLatRec.sin() * scLatSat.sin() +
                                 scLatRec.cos() * scLatSat.cos() * scLon21.cos();
             final double sinD = FastMath.sqrt(1.0 - cosD * cosD);
             final double z = FastMath.atan2(sinD, cosD - (r1 / r2));
 
             // Ray-perigee computation in meters (Eq. 156)
             this.rp = r1 * FastMath.sin(z);
 
             // Ray-perigee latitude and longitude
             if (FastMath.abs(FastMath.abs(lat1) - 0.5 * FastMath.PI) < THRESHOLD) {
 
                 // Ray-perigee latitude (Eq. 157)
                 if (lat1 < 0) {
                     this.latP = -z;
                 } else {
                     this.latP = z;
                 }
 
                 // Ray-perigee longitude (Eq. 164)
                 if (z < 0) {
                     this.lonP = lon2;
                 } else {
                     this.lonP = lon2 + FastMath.PI;
                 }
 
             } else {
 
                 // Ray-perigee latitude (Eq. 158 to 163)
                 final double deltaP   = 0.5 * FastMath.PI - z;
                 final SinCos scDeltaP = FastMath.sinCos(deltaP);
                 final double sinAz    = scLon21.sin() * scLatSat.cos() / sinD;
                 final double cosAz    = (scLatSat.sin() - cosD * scLatRec.sin()) / (sinD * scLatRec.cos());
                 final double sinLatP  = scLatRec.sin() * scDeltaP.cos() - scLatRec.cos() * scDeltaP.sin() * cosAz;
                 final double cosLatP  = FastMath.sqrt(1.0 - sinLatP * sinLatP);
                 this.latP = FastMath.atan2(sinLatP, cosLatP);
 
                 // Ray-perigee longitude (Eq. 165 to 167)
                 final double sinLonP = -sinAz * scDeltaP.sin() / cosLatP;
                 final double cosLonP = (scDeltaP.cos() - scLatRec.sin() * sinLatP) / (scLatRec.cos() * cosLatP);
                 this.lonP = FastMath.atan2(sinLonP, cosLonP) + lon1;
 
             }
 
             // Sine and cosine of ray-perigee latitude
             this.scLatP = FastMath.sinCos(latP);
 
             final SinCos scLon = FastMath.sinCos(lon2 - lonP);
             // Sine and cosine of azimuth of satellite as seen from ray-perigee
             final double psi   = greatCircleAngle(scLatSat, scLon);
             final SinCos scPsi = FastMath.sinCos(psi);
             if (FastMath.abs(FastMath.abs(latP) - 0.5 * FastMath.PI) < THRESHOLD) {
                 // Eq. 172 and 173
                 this.sinAzP = 0.0;
                 if (latP < 0.0) {
                     this.cosAzP = 1;
                 } else {
                     this.cosAzP = -1;
                 }
             } else {
                 // Eq. 174 and 175
                 this.sinAzP =  scLatSat.cos() * scLon.sin()                 /  scPsi.sin();
                 this.cosAzP = (scLatSat.sin() - scLatP.sin() * scPsi.cos()) / (scLatP.cos() * scPsi.sin());
             }
 
             // Integration en points s1 and s2 in meters (Eq. 176 and 177)
             this.s1 = FastMath.sqrt(r1 * r1 - rp * rp);
             this.s2 = FastMath.sqrt(r2 * r2 - rp * rp);
         }
 
         /**
          * Get the distance of the first point from the ray perigee.
          * @return s1 in meters
          */
         public double getS1() {
             return s1;
         }
 
         /**
          * Get the distance of the second point from the ray perigee.
          * @return s2 in meters
          */
         public double getS2() {
             return s2;
         }
 
         /**
          * Get the ray-perigee radius.
          * @return the ray-perigee radius in meters
          */
         public double getRadius() {
             return rp;
         }
 
         /**
          * Get the ray-perigee latitude.
          * @return the ray-perigee latitude in radians
          */
         public double getLatitude() {
             return latP;
         }
 
         /**
          * Get the ray-perigee longitude.
          * @return the ray-perigee longitude in radians
          */
         public double getLongitude() {
             return lonP;
         }
 
         /**
          * Get the sine of azimuth of satellite as seen from ray-perigee.
          * @return the sine of azimuth
          */
         public double getSineAz() {
             return sinAzP;
         }
 
         /**
          * Get the cosine of azimuth of satellite as seen from ray-perigee.
          * @return the cosine of azimuth
          */
         public double getCosineAz() {
             return cosAzP;
         }
 
         /**
          * Compute the great circle angle from ray-perigee to satellite.
          * <p>
          * This method used the equations 168 to 171 pf the reference document.
          * </p>
          * @param scLat sine and cosine of satellite latitude
          * @param scLon sine and cosine of satellite longitude minus receiver longitude
          * @return the great circle angle in radians
          */
         private double greatCircleAngle(final SinCos scLat, final SinCos scLon) {
             if (FastMath.abs(FastMath.abs(latP) - 0.5 * FastMath.PI) < THRESHOLD) {
                 return FastMath.abs(FastMath.asin(scLat.sin()) - latP);
             } else {
                 final double cosPhi = scLatP.sin() * scLat.sin() +
                                       scLatP.cos() * scLat.cos() * scLon.cos();
                 final double sinPhi = FastMath.sqrt(1.0 - cosPhi * cosPhi);
                 return FastMath.atan2(sinPhi, cosPhi);
             }
         }
     }
 
     /**
      * Container for ray-perigee parameters.
      * By convention, point 1 is at lower height.
      */
     private static class FieldRay <T extends CalculusFieldElement<T>> {
 
         /** Threshold for ray-perigee parameters computation. */
         private static final double THRESHOLD = 1.0e-10;
 
         /** Distance of the first point from the ray perigee [m]. */
         private final T s1;
 
         /** Distance of the second point from the ray perigee [m]. */
         private final T s2;
 
         /** Ray-perigee radius [m]. */
         private final T rp;
 
         /** Ray-perigee latitude [rad]. */
         private final T latP;
 
         /** Ray-perigee longitude [rad]. */
         private final T lonP;
 
         /** Sine and cosine of ray-perigee latitude. */
         private final FieldSinCos<T> scLatP;
 
         /** Sine of azimuth of satellite as seen from ray-perigee. */
         private final T sinAzP;
 
         /** Cosine of azimuth of satellite as seen from ray-perigee. */
         private final T cosAzP;
 
         /**
          * Constructor.
          * @param field field of the elements
          * @param recP receiver position
          * @param satP satellite position
          */
         FieldRay(final Field<T> field, final FieldGeodeticPoint<T> recP, final FieldGeodeticPoint<T> satP) {
 
             // Integration limits in meters (Eq. 140 and 141)
             final T r1 = recP.getAltitude().add(RE);
             final T r2 = satP.getAltitude().add(RE);
 
             // Useful parameters
             final T pi   = r1.getPi();
             final T lat1 = recP.getLatitude();
             final T lat2 = satP.getLatitude();
             final T lon1 = recP.getLongitude();
             final T lon2 = satP.getLongitude();
             final FieldSinCos<T> scLatSat = FastMath.sinCos(lat2);
             final FieldSinCos<T> scLatRec = FastMath.sinCos(lat1);
 
             // Zenith angle computation (Eq. 153 to 155)
             final T cosD = scLatRec.sin().multiply(scLatSat.sin()).
                             add(scLatRec.cos().multiply(scLatSat.cos()).multiply(FastMath.cos(lon2.subtract(lon1))));
             final T sinD = FastMath.sqrt(cosD.multiply(cosD).negate().add(1.0));
             final T z = FastMath.atan2(sinD, cosD.subtract(r1.divide(r2)));
 
             // Ray-perigee computation in meters (Eq. 156)
             this.rp = r1.multiply(FastMath.sin(z));
 
             // Ray-perigee latitude and longitude
             if (FastMath.abs(FastMath.abs(lat1).subtract(pi.multiply(0.5)).getReal()) < THRESHOLD) {
 
                 // Ray-perigee latitude (Eq. 157)
                 if (lat1.getReal() < 0) {
                     this.latP = z.negate();
                 } else {
                     this.latP = z;
                 }
 
                 // Ray-perigee longitude (Eq. 164)
                 if (z.getReal() < 0) {
                     this.lonP = lon2;
                 } else {
                     this.lonP = lon2.add(pi);
                 }
 
             } else {
 
                 // Ray-perigee latitude (Eq. 158 to 163)
                 final T deltaP = z.negate().add(pi.multiply(0.5));
                 final FieldSinCos<T> scDeltaP = FastMath.sinCos(deltaP);
                 final T sinAz    = FastMath.sin(lon2.subtract(lon1)).multiply(scLatSat.cos()).divide(sinD);
                 final T cosAz    = scLatSat.sin().subtract(cosD.multiply(scLatRec.sin())).divide(sinD.multiply(scLatRec.cos()));
                 final T sinLatP  = scLatRec.sin().multiply(scDeltaP.cos()).subtract(scLatRec.cos().multiply(scDeltaP.sin()).multiply(cosAz));
                 final T cosLatP  = FastMath.sqrt(sinLatP.multiply(sinLatP).negate().add(1.0));
                 this.latP = FastMath.atan2(sinLatP, cosLatP);
 
                 // Ray-perigee longitude (Eq. 165 to 167)
                 final T sinLonP = sinAz.negate().multiply(scDeltaP.sin()).divide(cosLatP);
                 final T cosLonP = scDeltaP.cos().subtract(scLatRec.sin().multiply(sinLatP)).divide(scLatRec.cos().multiply(cosLatP));
                 this.lonP = FastMath.atan2(sinLonP, cosLonP).add(lon1);
 
             }
 
             // Sine and cosine of ray-perigee latitude
             this.scLatP = FastMath.sinCos(latP);
 
             final FieldSinCos<T> scLon = FastMath.sinCos(lon2.subtract(lonP));
             // Sine and cosie of azimuth of satellite as seen from ray-perigee
             final T psi = greatCircleAngle(scLatSat, scLon);
             final FieldSinCos<T> scPsi = FastMath.sinCos(psi);
             if (FastMath.abs(FastMath.abs(latP).subtract(pi.multiply(0.5)).getReal()) < THRESHOLD) {
                 // Eq. 172 and 173
                 this.sinAzP = field.getZero();
                 if (latP.getReal() < 0.0) {
                     this.cosAzP = field.getOne();
                 } else {
                     this.cosAzP = field.getOne().negate();
                 }
             } else {
                 // Eq. 174 and 175
                 this.sinAzP = scLatSat.cos().multiply(scLon.sin()).divide(scPsi.sin());
                 this.cosAzP = scLatSat.sin().subtract(scLatP.sin().multiply(scPsi.cos())).divide(scLatP.cos().multiply(scPsi.sin()));
             }
 
             // Integration en points s1 and s2 in meters (Eq. 176 and 177)
             this.s1 = FastMath.sqrt(r1.multiply(r1).subtract(rp.multiply(rp)));
             this.s2 = FastMath.sqrt(r2.multiply(r2).subtract(rp.multiply(rp)));
         }
 
         /**
          * Get the distance of the first point from the ray perigee.
          * @return s1 in meters
          */
         public T getS1() {
             return s1;
         }
 
         /**
          * Get the distance of the second point from the ray perigee.
          * @return s2 in meters
          */
         public T getS2() {
             return s2;
         }
 
         /**
          * Get the ray-perigee radius.
          * @return the ray-perigee radius in meters
          */
         public T getRadius() {
             return rp;
         }
 
         /**
          * Get the ray-perigee latitude.
          * @return the ray-perigee latitude in radians
          */
         public T getLatitude() {
             return latP;
         }
 
         /**
          * Get the ray-perigee longitude.
          * @return the ray-perigee longitude in radians
          */
         public T getLongitude() {
             return lonP;
         }
 
         /**
          * Get the sine of azimuth of satellite as seen from ray-perigee.
          * @return the sine of azimuth
          */
         public T getSineAz() {
             return sinAzP;
         }
 
         /**
          * Get the cosine of azimuth of satellite as seen from ray-perigee.
          * @return the cosine of azimuth
          */
         public T getCosineAz() {
             return cosAzP;
         }
 
         /**
          * Compute the great circle angle from ray-perigee to satellite.
          * <p>
          * This method used the equations 168 to 171 pf the reference document.
          * </p>
          * @param scLat sine and cosine of satellite latitude
          * @param scLon sine and cosine of satellite longitude minus receiver longitude
          * @return the great circle angle in radians
          */
         private T greatCircleAngle(final FieldSinCos<T> scLat, final FieldSinCos<T> scLon) {
             if (FastMath.abs(FastMath.abs(latP).getReal() - 0.5 * FastMath.PI) < THRESHOLD) {
                 return FastMath.abs(FastMath.asin(scLat.sin()).subtract(latP));
             } else {
                 final T cosPhi = scLatP.sin().multiply(scLat.sin()).add(
                                  scLatP.cos().multiply(scLat.cos()).multiply(scLon.cos()));
                 final T sinPhi = FastMath.sqrt(cosPhi.multiply(cosPhi).negate().add(1.0));
                 return FastMath.atan2(sinPhi, cosPhi);
             }
         }
     }
 
     /** Performs the computation of the coordinates along the integration path. */
     private static class Segment {
 
         /** Latitudes [rad]. */
         private final double[] latitudes;
 
         /** Longitudes [rad]. */
         private final double[] longitudes;
 
         /** Heights [m]. */
         private final double[] heights;
 
         /** Integration step [m]. */
         private final double deltaN;
 
         /**
          * Constructor.
          * @param n number of points used for the integration
          * @param ray ray-perigee parameters
          */
         Segment(final int n, final Ray ray) {
             // Integration en points
             final double s1 = ray.getS1();
             final double s2 = ray.getS2();
 
             // Integration step (Eq. 195)
             this.deltaN = (s2 - s1) / n;
 
             // Segments
             final double[] s = getSegments(n, s1, s2);
 
             // Useful parameters
             final double rp = ray.getRadius();
             final SinCos scLatP = FastMath.sinCos(ray.getLatitude());
 
             // Geodetic coordinates
             final int size = s.length;
             heights    = new double[size];
             latitudes  = new double[size];
             longitudes = new double[size];
             for (int i = 0; i < size; i++) {
                 // Heights (Eq. 178)
                 heights[i] = FastMath.sqrt(s[i] * s[i] + rp * rp) - RE;
 
                 // Great circle parameters (Eq. 179 to 181)
                 final double tanDs = s[i] / rp;
                 final double cosDs = 1.0 / FastMath.sqrt(1.0 + tanDs * tanDs);
                 final double sinDs = tanDs * cosDs;
 
                 // Latitude (Eq. 182 to 183)
                 final double sinLatS = scLatP.sin() * cosDs + scLatP.cos() * sinDs * ray.getCosineAz();
                 final double cosLatS = FastMath.sqrt(1.0 - sinLatS * sinLatS);
                 latitudes[i] = FastMath.atan2(sinLatS, cosLatS);
 
                 // Longitude (Eq. 184 to 187)
                 final double sinLonS = sinDs * ray.getSineAz() * scLatP.cos();
                 final double cosLonS = cosDs - scLatP.sin() * sinLatS;
                 longitudes[i] = FastMath.atan2(sinLonS, cosLonS) + ray.getLongitude();
             }
         }
 
         /**
          * Computes the distance of a point from the ray-perigee.
          * @param n number of points used for the integration
          * @param s1 lower boundary
          * @param s2 upper boundary
          * @return the distance of a point from the ray-perigee in km
          */
         private double[] getSegments(final int n, final double s1, final double s2) {
             // Eq. 196
             final double g = 0.5773502691896 * deltaN;
             // Eq. 197
             final double y = s1 + (deltaN - g) * 0.5;
             final double[] segments = new double[2 * n];
             int index = 0;
             for (int i = 0; i < n; i++) {
                 // Eq. 198
                 segments[index] = y + i * deltaN;
                 index++;
                 segments[index] = y + i * deltaN + g;
                 index++;
             }
             return segments;
         }
 
         /**
          * Get the latitudes of the coordinates along the integration path.
          * @return the latitudes in radians
          */
         public double[] getLatitudes() {
             return latitudes;
         }
 
         /**
          * Get the longitudes of the coordinates along the integration path.
          * @return the longitudes in radians
          */
         public double[] getLongitudes() {
             return longitudes;
         }
 
         /**
          * Get the heights of the coordinates along the integration path.
          * @return the heights in m
          */
         public double[] getHeights() {
             return heights;
         }
 
         /**
          * Get the integration step.
          * @return the integration step in meters
          */
         public double getInterval() {
             return deltaN;
         }
     }
 
     /** Performs the computation of the coordinates along the integration path. */
     private static class FieldSegment <T extends CalculusFieldElement<T>> {
 
         /** Latitudes [rad]. */
         private final T[] latitudes;
 
         /** Longitudes [rad]. */
         private final T[] longitudes;
 
         /** Heights [m]. */
         private final T[] heights;
 
         /** Integration step [m]. */
         private final T deltaN;
 
         /**
          * Constructor.
          * @param field field of the elements
          * @param n number of points used for the integration
          * @param ray ray-perigee parameters
          */
         FieldSegment(final Field<T> field, final int n, final FieldRay<T> ray) {
             // Integration en points
             final T s1 = ray.getS1();
             final T s2 = ray.getS2();
 
             // Integration step (Eq. 195)
             this.deltaN = s2.subtract(s1).divide(n);
 
             // Segments
             final T[] s = getSegments(field, n, s1, s2);
 
             // Useful parameters
             final T rp = ray.getRadius();
             final FieldSinCos<T> scLatP = FastMath.sinCos(ray.getLatitude());
 
             // Geodetic coordinates
             final int size = s.length;
             heights    = MathArrays.buildArray(field, size);
             latitudes  = MathArrays.buildArray(field, size);
             longitudes = MathArrays.buildArray(field, size);
             for (int i = 0; i < size; i++) {
                 // Heights (Eq. 178)
                 heights[i] = FastMath.sqrt(s[i].multiply(s[i]).add(rp.multiply(rp))).subtract(RE);
 
                 // Great circle parameters (Eq. 179 to 181)
                 final T tanDs = s[i].divide(rp);
                 final T cosDs = FastMath.sqrt(tanDs.multiply(tanDs).add(1.0)).reciprocal();
                 final T sinDs = tanDs.multiply(cosDs);
 
                 // Latitude (Eq. 182 to 183)
                 final T sinLatS = scLatP.sin().multiply(cosDs).add(scLatP.cos().multiply(sinDs).multiply(ray.getCosineAz()));
                 final T cosLatS = FastMath.sqrt(sinLatS.multiply(sinLatS).negate().add(1.0));
                 latitudes[i] = FastMath.atan2(sinLatS, cosLatS);
 
                 // Longitude (Eq. 184 to 187)
                 final T sinLonS = sinDs.multiply(ray.getSineAz()).multiply(scLatP.cos());
                 final T cosLonS = cosDs.subtract(scLatP.sin().multiply(sinLatS));
                 longitudes[i] = FastMath.atan2(sinLonS, cosLonS).add(ray.getLongitude());
             }
         }
 
         /**
          * Computes the distance of a point from the ray-perigee.
          * @param field field of the elements
          * @param n number of points used for the integration
          * @param s1 lower boundary
          * @param s2 upper boundary
          * @return the distance of a point from the ray-perigee in km
          */
         private T[] getSegments(final Field<T> field, final int n, final T s1, final T s2) {
             // Eq. 196
             final T g = deltaN.multiply(0.5773502691896);
             // Eq. 197
             final T y = s1.add(deltaN.subtract(g).multiply(0.5));
             final T[] segments = MathArrays.buildArray(field, 2 * n);
             int index = 0;
             for (int i = 0; i < n; i++) {
                 // Eq. 198
                 segments[index] = y.add(deltaN.multiply(i));
                 index++;
                 segments[index] = y.add(deltaN.multiply(i)).add(g);
                 index++;
             }
             return segments;
         }
 
         /**
          * Get the latitudes of the coordinates along the integration path.
          * @return the latitudes in radians
          */
         public T[] getLatitudes() {
             return latitudes;
         }
 
         /**
          * Get the longitudes of the coordinates along the integration path.
          * @return the longitudes in radians
          */
         public T[] getLongitudes() {
             return longitudes;
         }
 
         /**
          * Get the heights of the coordinates along the integration path.
          * @return the heights in m
          */
         public T[] getHeights() {
             return heights;
         }
 
         /**
          * Get the integration step.
          * @return the integration step in meters
          */
         public T getInterval() {
             return deltaN;
         }
     }
 
 }