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skypoint.cpp

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/***************************************************************************
                          skypoint.cpp  -  K Desktop Planetarium
                             -------------------
    begin                : Sun Feb 11 2001
    copyright            : (C) 2001-2005 by Jason Harris
    email                : jharris@30doradus.org
    copyright            : (C) 2004-2005 by Pablo de Vicente
    email                : p.devicente@wanadoo.es
 ***************************************************************************/

/***************************************************************************
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU General Public License as published by  *
 *   the Free Software Foundation; either version 2 of the License, or     *
 *   (at your option) any later version.                                   *
 *                                                                         *
 ***************************************************************************/

#include <kdebug.h>
#include <klocale.h>

#include "skypoint.h"
#include "skyobject.h"
#include "dms.h"
#include "ksnumbers.h"
#include "csegment.h"

void SkyPoint::set( const dms& r, const dms& d ) {
    RA0.set( r );
    Dec0.set( d );
    RA.set( r );
    Dec.set( d );
}

void SkyPoint::set( double r, double d ) {
    RA0.setH( r );
    Dec0.setD( d );
    RA.setH( r );
    Dec.setD( d );
}

SkyPoint::~SkyPoint(){
}

void SkyPoint::EquatorialToHorizontal( const dms *LST, const dms *lat ) {
    double AltRad, AzRad;
    double sindec, cosdec, sinlat, coslat, sinHA, cosHA;
  double sinAlt, cosAlt;

    dms HourAngle = LST->Degrees() - ra()->Degrees();

    lat->SinCos( sinlat, coslat );
    dec()->SinCos( sindec, cosdec );
    HourAngle.SinCos( sinHA, cosHA );

    sinAlt = sindec*sinlat + cosdec*coslat*cosHA;
    AltRad = asin( sinAlt );
    cosAlt = cos( AltRad );

    double arg = ( sindec - sinlat*sinAlt )/( coslat*cosAlt );
    if ( arg <= -1.0 ) AzRad = dms::PI;
    else if ( arg >= 1.0 ) AzRad = 0.0;
    else AzRad = acos( arg );
    
    if ( sinHA > 0.0 ) AzRad = 2.0*dms::PI - AzRad; // resolve acos() ambiguity

    Alt.setRadians( AltRad );
    Az.setRadians( AzRad );
}

void SkyPoint::HorizontalToEquatorial( const dms *LST, const dms *lat ) {
    double HARad, DecRad;
    double sinlat, coslat, sinAlt, cosAlt, sinAz, cosAz;
  double sinDec, cosDec;

    lat->SinCos( sinlat, coslat );
    alt()->SinCos( sinAlt, cosAlt );
    Az.SinCos( sinAz,  cosAz );

    sinDec = sinAlt*sinlat + cosAlt*coslat*cosAz;
    DecRad = asin( sinDec );
    cosDec = cos( DecRad );
    Dec.setRadians( DecRad );

    double x = ( sinAlt - sinlat*sinDec )/( coslat*cosDec );

//Under certain circumstances, x can be very slightly less than -1.0000, or slightly
//greater than 1.0000, leading to a crash on acos(x).  However, the value isn't
//*really* out of range; it's a kind of roundoff error.
    if ( x < -1.0 && x > -1.000001 ) HARad = dms::PI;
    else if ( x > 1.0 && x < 1.000001 ) HARad = 0.0;
    else if ( x < -1.0 ) {
        kdWarning() << i18n( "Coordinate out of range." );
        HARad = dms::PI;
    } else if ( x > 1.0 ) {
        kdWarning() << i18n( "Coordinate out of range." );
        HARad = 0.0;
    } else HARad = acos( x );

    if ( sinAz > 0.0 ) HARad = 2.0*dms::PI - HARad; // resolve acos() ambiguity

    RA.setRadians( LST->radians() - HARad );
    RA.setD( RA.reduce().Degrees() );  // 0 <= RA < 24
}

void SkyPoint::findEcliptic( const dms *Obliquity, dms &EcLong, dms &EcLat ) {
    double sinRA, cosRA, sinOb, cosOb, sinDec, cosDec, tanDec;
    ra()->SinCos( sinRA, cosRA );
    dec()->SinCos( sinDec, cosDec );
    Obliquity->SinCos( sinOb, cosOb );

    tanDec = sinDec/cosDec;
    double y = sinRA*cosOb + tanDec*sinOb;
    double ELongRad = atan( y/cosRA );
    //resolve atan ambiguity
    if ( cosRA < 0 ) ELongRad += dms::PI;
    if ( cosRA > 0 && y < 0 ) ELongRad += 2.0*dms::PI;

    EcLong.setRadians( ELongRad );
    EcLat.setRadians( asin( sinDec*cosOb - cosDec*sinOb*sinRA ) );
}

void SkyPoint::setFromEcliptic( const dms *Obliquity, const dms *EcLong, const dms *EcLat ) {
    double sinLong, cosLong, sinLat, cosLat, sinObliq, cosObliq;
    EcLong->SinCos( sinLong, cosLong );
    EcLat->SinCos( sinLat, cosLat );
    Obliquity->SinCos( sinObliq, cosObliq );

    double sinDec = sinLat*cosObliq + cosLat*sinObliq*sinLong;

    double y = sinLong*cosObliq - (sinLat/cosLat)*sinObliq;
    double RARad =  atan( y / cosLong );

    //resolve ambiguity of atan:
    if ( cosLong < 0 ) RARad += dms::PI;
    if ( cosLong > 0 && y < 0 ) RARad += 2.0*dms::PI;

    //DMS_SPEED
    //dms newRA, newDec;
    //newRA.setRadians( RARad );
    //newDec.setRadians( asin( sinDec ) );
    RA.setRadians( RARad );
    Dec.setRadians( asin(sinDec) );
}

void SkyPoint::precess( const KSNumbers *num) {
    double cosRA0, sinRA0, cosDec0, sinDec0;
    double v[3], s[3];

    RA0.SinCos( sinRA0, cosRA0 );
    Dec0.SinCos( sinDec0, cosDec0 );

    s[0] = cosRA0*cosDec0;
    s[1] = sinRA0*cosDec0;
    s[2] = sinDec0;
    //Multiply P2 and s to get v, the vector representing the new coords.
    for ( unsigned int i=0; i<3; ++i ) {
        v[i] = 0.0;
        for (uint j=0; j< 3; ++j) {
            v[i] += num->p2( j, i )*s[j];
        }
    }

    //Extract RA, Dec from the vector:
    RA.setRadians( atan( v[1]/v[0] ) );
    Dec.setRadians( asin( v[2] ) );

    //resolve ambiguity of atan()
    if ( v[0] < 0.0 ) {
        RA.setD( RA.Degrees() + 180.0 );
    } else if( v[1] < 0.0 ) {
        RA.setD( RA.Degrees() + 360.0 );
    }
}

void SkyPoint::nutate(const KSNumbers *num) {
    double cosRA, sinRA, cosDec, sinDec, tanDec;
    dms dRA1, dRA2, dDec1, dDec2;
    double cosOb, sinOb;

    RA.SinCos( sinRA, cosRA );
    Dec.SinCos( sinDec, cosDec );

    num->obliquity()->SinCos( sinOb, cosOb );

    //Step 2: Nutation
    if ( fabs( Dec.Degrees() ) < 80.0 ) { //approximate method
        tanDec = sinDec/cosDec;

        dRA1.setD( num->dEcLong()*( cosOb + sinOb*sinRA*tanDec ) - num->dObliq()*cosRA*tanDec );
        dDec1.setD( num->dEcLong()*( sinOb*cosRA ) + num->dObliq()*sinRA );

        RA.setD( RA.Degrees() + dRA1.Degrees() );
        Dec.setD( Dec.Degrees() + dDec1.Degrees() );
    } else { //exact method
        dms EcLong, EcLat;
        findEcliptic( num->obliquity(), EcLong, EcLat );

        //Add dEcLong to the Ecliptic Longitude
        dms newLong( EcLong.Degrees() + num->dEcLong() );
        setFromEcliptic( num->obliquity(), &newLong, &EcLat );
    }
}

void SkyPoint::aberrate(const KSNumbers *num) {
    double cosRA, sinRA, cosDec, sinDec;
    dms dRA2, dDec2;
    double cosOb, sinOb, cosL, sinL, cosP, sinP;

    double K = num->constAberr().Degrees();  //constant of aberration
    double e = num->earthEccentricity();

    RA.SinCos( sinRA, cosRA );
    Dec.SinCos( sinDec, cosDec );

    num->obliquity()->SinCos( sinOb, cosOb );
    double tanOb = sinOb/cosOb;

    num->sunTrueLongitude().SinCos( sinL, cosL );
    num->earthPerihelionLongitude().SinCos( sinP, cosP );


    //Step 3: Aberration
    dRA2.setD( -1.0 * K * ( cosRA * cosL * cosOb + sinRA * sinL )/cosDec
        + e * K * ( cosRA * cosP * cosOb + sinRA * sinP )/cosDec );

    dDec2.setD( -1.0 * K * ( cosL * cosOb * ( tanOb * cosDec - sinRA * sinDec ) + cosRA * sinDec * sinL )
        + e * K * ( cosP * cosOb * ( tanOb * cosDec - sinRA * sinDec ) + cosRA * sinDec * sinP ) );

    RA.setD( RA.Degrees() + dRA2.Degrees() );
    Dec.setD( Dec.Degrees() + dDec2.Degrees() );
}

void SkyPoint::updateCoords( KSNumbers *num, bool /*includePlanets*/, const dms *lat, const dms *LST ) {
    dms pRA, pDec;
    //Correct the catalog coordinates for the time-dependent effects
    //of precession, nutation and aberration

    precess(num);
    nutate(num);
    aberrate(num);

    if ( lat || LST )
        kdWarning() << i18n( "lat and LST parameters should only be used in KSPlanetBase objects." ) << endl;
}

void SkyPoint::precessFromAnyEpoch(long double jd0, long double jdf){

    double cosRA, sinRA, cosDec, sinDec;
        double v[3], s[3];

    RA.setD( RA0.Degrees() );
    Dec.setD( Dec0.Degrees() );

    RA.SinCos( sinRA, cosRA );
    Dec.SinCos( sinDec, cosDec );

    if (jd0 == jdf)
        return;

    if ( jd0 == B1950) {
        B1950ToJ2000();
        jd0 = J2000;
        RA.SinCos( sinRA, cosRA );
        Dec.SinCos( sinDec, cosDec );

    }

    if (jd0 !=jdf) {
        // The original coordinate is referred to the FK5 system and
        // is NOT J2000.
        if ( jd0 != J2000 ) {

        //v is a column vector representing input coordinates.

            KSNumbers *num = new KSNumbers (jd0);

            v[0] = cosRA*cosDec;
            v[1] = sinRA*cosDec;
            v[2] = sinDec;

            //Need to first precess to J2000.0 coords
            //s is the product of P1 and v; s represents the
            //coordinates precessed to J2000
            for ( unsigned int i=0; i<3; ++i ) {
                s[i] = num->p1( 0, i )*v[0] +
                    num->p1( 1, i )*v[1] +
                    num->p1( 2, i )*v[2];
            }
            delete num;

        //Input coords already in J2000, set s accordingly.
        } else {

            s[0] = cosRA*cosDec;
            s[1] = sinRA*cosDec;
            s[2] = sinDec;
        }

        if ( jdf == B1950) {

            RA.setRadians( atan2( s[1],s[0] ) );
            Dec.setRadians( asin( s[2] ) );
            J2000ToB1950();

            return;
        }

        KSNumbers *num = new KSNumbers (jdf);

        for ( unsigned int i=0; i<3; ++i ) {
            v[i] = num->p2( 0, i )*s[0] +
            num->p2( 1, i )*s[1] +
            num->p2( 2, i )*s[2];
        }

        delete num;

        RA.setRadians( atan2( v[1],v[0] ) );
        Dec.setRadians( asin( v[2] ) );

        if (RA.Degrees() < 0.0 )
            RA.setD( RA.Degrees() + 360.0 );

        return;
    } 

}

void SkyPoint::apparentCoord(long double jd0, long double jdf){

    precessFromAnyEpoch(jd0,jdf);

    KSNumbers *num = new KSNumbers (jdf);

    nutate(num);
    aberrate(num);

    delete num;
}

void SkyPoint::Equatorial1950ToGalactic(dms &galLong, dms &galLat) {
    
    double a = 192.25;
    dms b, c;
    double sinb, cosb, sina_RA, cosa_RA, sinDEC, cosDEC, tanDEC;

    c.setD(303);
    b.setD(27.4);
    tanDEC = tan( Dec.radians() );

    b.SinCos(sinb,cosb);
    dms( a - RA.Degrees() ).SinCos(sina_RA,cosa_RA);
    Dec.SinCos(sinDEC,cosDEC);

    galLong.setRadians( c.radians() - atan2( sina_RA, cosa_RA*sinb-tanDEC*cosb) );
    galLong = galLong.reduce();

    galLat.setRadians( asin(sinDEC*sinb+cosDEC*cosb*cosa_RA) );
}

void SkyPoint::GalacticToEquatorial1950(const dms* galLong, const dms* galLat) {

    double a = 123.0;
    dms b, c, galLong_a;
    double sinb, cosb, singLat, cosgLat, tangLat, singLong_a, cosgLong_a;

    c.setD(12.25);
    b.setD(27.4);
    tangLat = tan( galLat->radians() );


    galLat->SinCos(singLat,cosgLat);

    dms( galLong->Degrees()-a ).SinCos(singLong_a,cosgLong_a);
    b.SinCos(sinb,cosb);

    RA.setRadians(c.radians() + atan2(singLong_a,cosgLong_a*sinb-tangLat*cosb) );
    RA = RA.reduce();
//  raHourCoord = dms( raCoord.Hours() );

    Dec.setRadians( asin(singLat*sinb+cosgLat*cosb*cosgLong_a) );
}

void SkyPoint::B1950ToJ2000(void) {
    double cosRA, sinRA, cosDec, sinDec;
//  double cosRA0, sinRA0, cosDec0, sinDec0;
        double v[3], s[3];

    // 1984 January 1 0h
    KSNumbers *num = new KSNumbers (2445700.5);

    // Eterms due to aberration
    addEterms();
    RA.SinCos( sinRA, cosRA );
    Dec.SinCos( sinDec, cosDec );

    // Precession from B1950 to J1984
    s[0] = cosRA*cosDec;
    s[1] = sinRA*cosDec;
    s[2] = sinDec;
    for ( unsigned int i=0; i<3; ++i ) {
        v[i] = num->p2b( 0, i )*s[0] + num->p2b( 1, i )*s[1] +
        num->p2b( 2, i )*s[2];
    }

    // RA zero-point correction at 1984 day 1, 0h.
    RA.setRadians( atan2( v[1],v[0] ) );
    Dec.setRadians( asin( v[2] ) );

    RA.setH( RA.Hours() + 0.06390/3600. );
    RA.SinCos( sinRA, cosRA );
    Dec.SinCos( sinDec, cosDec );

    s[0] = cosRA*cosDec;
    s[1] = sinRA*cosDec;
    s[2] = sinDec;

    // Precession from 1984 to J2000.

    for ( unsigned int i=0; i<3; ++i ) {
        v[i] = num->p1( 0, i )*s[0] +
        num->p1( 1, i )*s[1] +
        num->p1( 2, i )*s[2];
    }

    RA.setRadians( atan2( v[1],v[0] ) );
    Dec.setRadians( asin( v[2] ) );

    delete num;
}

void SkyPoint::J2000ToB1950(void) {
    double cosRA, sinRA, cosDec, sinDec;
//  double cosRA0, sinRA0, cosDec0, sinDec0;
        double v[3], s[3];

    // 1984 January 1 0h
    KSNumbers *num = new KSNumbers (2445700.5);

    RA.SinCos( sinRA, cosRA );
    Dec.SinCos( sinDec, cosDec );

    s[0] = cosRA*cosDec;
    s[1] = sinRA*cosDec;
    s[2] = sinDec;

    // Precession from J2000 to 1984 day, 0h.

    for ( unsigned int i=0; i<3; ++i ) {
        v[i] = num->p2( 0, i )*s[0] +
        num->p2( 1, i )*s[1] +
        num->p2( 2, i )*s[2];
    }

    RA.setRadians( atan2( v[1],v[0] ) );
    Dec.setRadians( asin( v[2] ) );

    // RA zero-point correction at 1984 day 1, 0h.

    RA.setH( RA.Hours() - 0.06390/3600. );
    RA.SinCos( sinRA, cosRA );
    Dec.SinCos( sinDec, cosDec );

    // Precession from B1950 to J1984

    s[0] = cosRA*cosDec;
    s[1] = sinRA*cosDec;
    s[2] = sinDec;
    for ( unsigned int i=0; i<3; ++i ) {
        v[i] = num->p1b( 0, i )*s[0] + num->p1b( 1, i )*s[1] +
        num->p1b( 2, i )*s[2];
    }

    RA.setRadians( atan2( v[1],v[0] ) );
    Dec.setRadians( asin( v[2] ) );

    // Eterms due to aberration
    subtractEterms();

    delete num;
}

SkyPoint SkyPoint::Eterms(void) {

    double sd, cd, sinEterm, cosEterm;
    dms raTemp, raDelta, decDelta;

    Dec.SinCos(sd,cd);
    raTemp.setH( RA.Hours() + 11.25);
    raTemp.SinCos(sinEterm,cosEterm);

    raDelta.setH( 0.0227*sinEterm/(3600.*cd) );
    decDelta.setD( 0.341*cosEterm*sd/3600. + 0.029*cd/3600. );

    SkyPoint spDelta = SkyPoint (raDelta, decDelta);

    return spDelta;
}

void SkyPoint::addEterms(void) {

    SkyPoint spd = Eterms();

    RA.setD( RA.Degrees() + spd.ra()->Degrees() );
    Dec.setD( Dec.Degrees() + spd.dec()->Degrees() );

}

void SkyPoint::subtractEterms(void) {

    SkyPoint spd = Eterms();

    RA.setD( RA.Degrees() - spd.ra()->Degrees() );
    Dec.setD( Dec.Degrees() - spd.dec()->Degrees() );
}

dms SkyPoint::angularDistanceTo(SkyPoint *sp) {

    double dalpha = ra()->radians() - sp->ra()->radians() ;
    double ddelta = dec()->radians() - sp->dec()->radians() ;

    double sa = sin(dalpha/2.);
    double sd = sin(ddelta/2.);
    
    double hava = sa*sa;
    double havd = sd*sd;

    double aux = havd + cos (dec()->radians()) * cos(sp->dec()->radians()) 
        * hava;
    
    dms angDist;
    angDist.setRadians( 2 * fabs(asin( sqrt(aux) )) );
    
    return angDist;
}

QString SkyPoint::constellation( QPtrList<CSegment> &csegmentList, QPtrList<SkyObject> &cnameList ) const {
    //Identify the constellation that contains point p.
    //First, find all CSegments that bracket the RA of p.
    //Then, identify the pair of these bracketing segments which bracket p in the Dec direction.
    //Each segment has two cnames, identifying the 2 constellations which the segment delineates.
    //There will be a name in common between the pair, this is the constellation that p is in.
    //
    //Corner case 1: points near the celestial poles are not bracketed by csegments.
    //Corner case 2: it is possible that *both* cnames are shared between the two segments.
    //In this case, we have to do more work to decide which is truly correct.
    
    QPtrList<SkyPoint> p1List, p2List;
    QStringList name1List, name2List;
    QString abbrev("");

    double pdc = dec()->Degrees();
    double pra(0.0); //defined in the loop, because we may modify it there

    for ( CSegment *seg = csegmentList.first(); seg; seg = csegmentList.next() ) {
        SkyPoint *p1 = seg->firstNode();
        for ( SkyPoint *p2 = seg->nextNode(); p2; p2 = seg->nextNode() ) {
            pra = ra()->Degrees(); 
            double p1ra = p1->ra()->Degrees();
            double p2ra = p2->ra()->Degrees();
            if ( p1ra > 330. && p2ra < 30. ) { //wrap RA coordinate, if necessary
                p1ra -= 360.0; 
                if ( pra > 330. ) pra -= 360.;
            }
            if ( p2ra > 330. && p1ra < 30. ) { //wrap RA coordinate, if necessary
                p2ra -= 360.0; 
                if ( pra > 330. ) pra -= 360.;
            }
            
            if ( p1ra <= pra && p2ra >= pra ) { //bracketing segment?
                p1List.append( p1 );
                p2List.append( p2 );
                name1List.append( seg->name1() );
                name2List.append( seg->name2() );
                break;
            } else if ( p2ra <= pra && p1ra >= pra ) { //bracketing segment? (RA order reversed)
                p1List.append( p2 ); //make sure p1List gets the smaller bracketing RA
                p2List.append( p1 );
                name1List.append( seg->name1() );
                name2List.append( seg->name2() );
                break;
            }
            p1 = p2;
        }
    }

    //Should not happen:
    if ( p1List.count() == 0 ) {
        kdWarning() << "A: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
        return i18n("Unknown");
    }

    //Normal case: more than one segment brackets in RA.  Find segments which also bracket in Dec.
    double dupper(90.), dlower(-90.);
    int iupper(-1), ilower(-1);
    for ( uint i=0; i < p1List.count(); ++i ) {
        SkyPoint *p1 = p1List.at(i);
        SkyPoint *p2 = p2List.at(i);
        
        //Find Dec value along segment at RA of p:
        double f = ( pra - p1->ra()->Degrees() ) / ( p2->ra()->Degrees() - p1->ra()->Degrees()); //fractional distance along segment
        double segDec = f*p2->dec()->Degrees() + (1.0-f)*p1->dec()->Degrees();
        if ( segDec >= pdc && segDec < dupper ) { dupper = segDec; iupper = i; }
        if ( segDec <= pdc && segDec > dlower ) { dlower = segDec; ilower = i; }
    }

    //Corner case 1: Points near one of the poles are not bracketed by segments in the Dec direction.
    //In this case, either iupper or ilower will remain at its preassigned invalid value (-1)
    //Identify the constellation by extrapolating away from the pole to the next segment.
    //This will identify which of the two names is the neighboring constellation
    //so our target constell. is the other one.
    //(note that we can't just assume Ursa Minor or Octans, because of precession: these constellations 
    //are not near the pole at all epochs
    if ( iupper == -1 ) { //point near north pole
        int ilow2(-1);
        double dlow2(-90.);
        for ( uint i=0; i < p1List.count(); ++i ) {
            if ( i != ilower ) {
                SkyPoint *p1 = p1List.at(i);
                SkyPoint *p2 = p2List.at(i);
                
                //Find Dec value along segment at RA of p:
                double f = ( pra - p1->ra()->Degrees() ) / ( p2->ra()->Degrees() - p1->ra()->Degrees()); //fractional distance along segment
                double segDec = f*p2->dec()->Degrees() + (1.0-f)*p1->dec()->Degrees();
                if ( segDec > dlow2 && segDec < dlower ) { dlow2 = segDec; ilow2 = i; }
            }
        }

        if ( ilow2 == -1 ) { //whoops, what happened?
            kdWarning() << "B: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
            return i18n("Unknown");
        }

        //If name1(ilower) is the adjacent constellation, then name2(ilower) must be the answer
        if ( name1List[ ilower ] == name1List[ ilow2 ] || name1List[ ilower ] == name2List[ ilow2 ] )
            abbrev = name2List[ ilower ];

        //If name2(ilower) is the adjacent constellation, then name1(ilower) must be the answer
        else if ( name2List[ ilower ] == name1List[ ilow2 ] || name2List[ ilower ] == name2List[ ilow2 ] )
            abbrev = name1List[ ilower ];

        else { //doh!
            kdWarning() << "C: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
            return i18n("Unknown");
        }

    } else if ( ilower == -1 ) { //point near south pole
        int iup2(-1);
        double dup2(90.);
        for ( uint i=0; i < p1List.count(); ++i ) {
            if ( i != iupper ) {
                SkyPoint *p1 = p1List.at(i);
                SkyPoint *p2 = p2List.at(i);
                
                //Find Dec value along segment at RA of p:
                double f = ( pra - p1->ra()->Degrees() ) / ( p2->ra()->Degrees() - p1->ra()->Degrees()); //fractional distance along segment
                double segDec = f*p2->dec()->Degrees() + (1.0-f)*p1->dec()->Degrees();
                if ( segDec < dup2 && segDec > dupper ) { dup2 = segDec; iup2 = i; }
            }
        }

        if ( iup2 == -1 ) { //whoops, what happened?
            kdWarning() << "D: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
            return i18n("Unknown");
        }

        //If name1(iupper) is the adjacent constellation, then name2(iupper) must be the answer
        if ( name1List[ iupper ] == name1List[ iup2 ] || name1List[ iupper ] == name2List[ iup2 ] )
            abbrev = name2List[ iupper ] ;

        //If name2(iupper) is the adjacent constellation, then name1(iupper) must be the answer
        else if ( name2List[ iupper ] == name1List[ iup2 ] || name2List[ iupper ] == name2List[ iup2 ] )
            abbrev = name1List[ iupper ];

        else { //doh!
            kdWarning() << "E: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
            return i18n("Unknown");
        }
    }

    //Corner case 2: Both name1 and name2 are in common in the bracketing segments
    //This can happen if a constellation is both above and below the true bracketing constellation
    //Resolve it by again extending up or down to the next segment, which will share one of the ambiguous 
    //names.  The answer is the one not shared in this next segment.
    //To ensure that there will be a next segment, go up if dec is negative, otherwise go down.
    else if ( (name1List[ iupper ] == name1List[ ilower ] || name1List[ iupper ] == name2List[ ilower ]) 
        && (name2List[ iupper ] == name1List[ ilower ] || name2List[ iupper ] == name2List[ ilower ]) ) {
        if ( pdc < 0.0 ) { //find next segment up
            int iup2(0);
            double dup2(90.0);

            for ( uint i=0; i < p1List.count(); ++i ) {
                if ( i != iupper ) {
                    SkyPoint *p1 = p1List.at(i);
                    SkyPoint *p2 = p2List.at(i);
                    
                    //Find Dec value along segment at RA of p:
                    double f = ( pra - p1->ra()->Degrees() ) / ( p2->ra()->Degrees() - p1->ra()->Degrees()); //fractional distance along segment
                    double segDec = f*p2->dec()->Degrees() + (1.0-f)*p1->dec()->Degrees();
                    if ( segDec < dup2 && segDec > dupper ) { dup2 = segDec; iup2 = i; }
                }
            }

            //If name1(iupper) is the adjacent constellation, then name2(iupper) must be the answer
            if ( name1List[ iupper ] == name1List[ iup2 ] || name1List[ iupper ] == name2List[ iup2 ] )
                abbrev = name2List[ iupper ];
    
            //If name2(iupper) is the adjacent constellation, then name1(iupper) must be the answer
            else if ( name2List[ iupper ] == name1List[ iup2 ] || name2List[ iupper ] == name2List[ iup2 ] )
                abbrev = name1List[ iupper ];
    
            else { //doh!
                kdWarning() << "F: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
                return i18n("Unknown");
            }
        } else { //pdc > 0.0, so search down
            int ilow2(-1);
            double dlow2(-90.);
            for ( uint i=0; i < p1List.count(); ++i ) {
                if ( i != ilower ) {
                    SkyPoint *p1 = p1List.at(i);
                    SkyPoint *p2 = p2List.at(i);
                    
                    //Find Dec value along segment at RA of p:
                    double f = ( pra - p1->ra()->Degrees() ) / ( p2->ra()->Degrees() - p1->ra()->Degrees()); //fractional distance along segment
                    double segDec = f*p2->dec()->Degrees() + (1.0-f)*p1->dec()->Degrees();
                    if ( segDec > dlow2 && segDec < dlower ) { dlow2 = segDec; ilow2 = i; }
                }
            }
    
            if ( ilow2 == -1 ) { //whoops, what happened?
                kdWarning() << "G: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
                return i18n("Unknown");
            }
    
            //If name1(ilower) is the adjacent constellation, then name2(ilower) must be the answer
            if ( name1List[ ilower ] == name1List[ ilow2 ] || name1List[ ilower ] == name2List[ ilow2 ] )
                abbrev = name2List[ ilower ];
    
            //If name2(ilower) is the adjacent constellation, then name1(ilower) must be the answer
            else if ( name2List[ ilower ] == name1List[ ilow2 ] || name2List[ ilower ] == name2List[ ilow2 ] )
                abbrev = name1List[ ilower ];
    
            else { //doh!
                kdWarning() << "H: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
                return i18n("Unknown");
            }
        }
    }

    //Normal case: one of the pair of names (name1/name2) should be shared between 
    //the two bracketing segments
    else if ( name1List[ iupper ] == name1List[ ilower ] || name1List[ iupper ] == name2List[ ilower ] ) 
        abbrev = name1List[ iupper ];

    else if ( name2List[ iupper ] == name1List[ ilower ] || name2List[ iupper ] == name2List[ ilower ] ) 
        abbrev = name2List[ iupper ];

    //If we reach here, then neither name1 nor name2 were shared between the bracketing segments!
    else {
        kdWarning() << "I: " << i18n("No constellation found for point: (%1, %2)").arg(ra()->toHMSString()).arg(dec()->toDMSString()) << endl;
        return i18n("Unknown");
    }

    //Finally, match the abbreviated name to the full constellation name, and return that name
    for ( SkyObject *o = cnameList.first(); o; o = cnameList.next() ) {
        if ( abbrev.lower() == o->name2().lower() ) {
            QString r = i18n( "Constellation name (optional)", o->name().local8Bit().data() );
            r = r.left(1) + r.mid(1).lower(); //lowercase letters (except first letter)
            int i = r.find(" ");
            i++;
            if ( i>0 ) r = r.left(i) + r.mid(i,1).upper() + r.mid(i+1); //capitalize 2nd word
            return r;
        }
    }

    return i18n("Unknown");
}

double SkyPoint::vRSun(long double jd0) {

    dms asun,dsun;
    double ca, sa, cd, sd, vsun;
    double cosRA, sinRA, cosDec, sinDec;
    
    /* Sun apex (where the sun goes) coordinates */
    
    asun.setD(270.9592);    // Right ascention: 18h 3m 50.2s [J2000]
    dsun.setD(30.00467);    // Declination: 30^o 0' 16.8'' [J2000]
    vsun=20.;       // [km/s]
    
    asun.SinCos(sa,ca);
    dsun.SinCos(sd,cd);
    
    /* We need an auxiliary SkyPoint since we need the 
    * source referred to the J2000 equinox and we do not want to ovewrite
    * the current values
    */
    
    SkyPoint aux;
    aux.set(RA0,Dec0);
    
    aux.precessFromAnyEpoch(jd0, J2000);
            
    aux.ra()->SinCos( sinRA, cosRA );
    aux.dec()->SinCos( sinDec, cosDec );
        
    /* Computation is done performing the scalar product of a unitary vector 
    in the direction of the source with the vector velocity of Sun, both being in the
    LSR reference system:
    Vlsr    = Vhel + Vsun.u_radial => 
    Vlsr    = Vhel + vsun(cos D cos A,cos D sen A,sen D).(cos d cos a,cos d sen a,sen d)
    Vhel    = Vlsr - Vsun.u_radial
    */

    return vsun *(cd*cosDec*(cosRA*ca + sa*sinRA) + sd*sinDec);

}

double SkyPoint::vHeliocentric(double vlsr, long double jd0) {

    return vlsr - vRSun(jd0);
}

double SkyPoint::vHelioToVlsr(double vhelio, long double jd0) {

    return vhelio + vRSun(jd0);
}

double SkyPoint::vREarth(long double jd0)
{
  
    double sinRA, sinDec, cosRA, cosDec, vREarth;

    /* u_radial = unitary vector in the direction of the source
        Vlsr    = Vhel + Vsun.u_radial
            = Vgeo + VEarth.u_radial + Vsun.u_radial  => 
            
        Vgeo    = (Vlsr -Vsun.u_radial) - VEarth.u_radial
            =  Vhel - VEarth.u_radial
            =  Vhel - (vx, vy, vz).(cos d cos a,cos d sen a,sen d)
    */
    
    /* We need an auxiliary SkyPoint since we need the 
    * source referred to the J2000 equinox and we do not want to ovewrite
    * the current values
    */
    
    SkyPoint aux;
    aux.set(RA0,Dec0);
    
    aux.precessFromAnyEpoch(jd0, J2000);
            
    aux.ra()->SinCos( sinRA, cosRA );
    aux.dec()->SinCos( sinDec, cosDec );

    /* vEarth is referred to the J2000 equinox, hence we need that
    the source coordinates are also in the same reference system.
    */
    
    KSNumbers *num = new KSNumbers(jd0);
    
    vREarth = num->vEarth(0) * cosDec * cosRA + 
        num->vEarth(1) * cosDec * sinRA +
        num->vEarth(2) * sinDec;
        
    return vREarth;
}


double SkyPoint::vGeocentric(double vhelio, long double jd0)
{
    return vhelio - vREarth(jd0);
}

double SkyPoint::vGeoToVHelio(double vgeo, long double jd0)
{
    return vgeo + vREarth(jd0);
}

double SkyPoint::vRSite(double vsite[3])
{
  
    double sinRA, sinDec, cosRA, cosDec, vREarth;

    RA.SinCos( sinRA, cosRA );
    Dec.SinCos( sinDec, cosDec );

    return vsite[0]*cosDec*cosRA + vsite[1]*cosDec*sinRA + vsite[2]*sinDec;
}

double SkyPoint::vTopoToVGeo(double vtopo, double vsite[3])
{
    return vtopo + vRSite(vsite); 
}

double SkyPoint::vTopocentric(double vgeo, double vsite[3])
{
    return vgeo - vRSite(vsite); 
}

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