AlignEq.ino

// -----------------------------------------------------------------------------------
// GEOMETRIC ALIGN FOR EQ MOUNTS
//
// by Howard Dutton
//
// Copyright (C) 2012 to 2018 Howard Dutton
//

// -----------------------------------------------------------------------------------
// ADVANCED GEOMETRIC ALIGN FOR EQUATORIAL MOUNTS (GOTO ASSIST)

#ifndef MOUNT_TYPE_ALTAZM
#define GOTO_ASSIST_DEBUG_OFF

// Initialize
void TGeoAlign::init() {
  avgDec=0.0;
  avgHA =0.0;
  
  ax1Cor=0;  // align internal index for Axis1
  ax2Cor=0;  // align internal index for Axis2
  altCor=0;  // for geometric coordinate correction/align, - is below the pole, + above
  azmCor=0;  // - is right of the pole, + is left
  doCor =0;  // declination/optics orthogonal correction
  pdCor =0;  // declination/polar orthogonal correction
  dfCor =0;  // fork or declination axis flex
  tfCor =0;  // tube flex

  geo_ready=false;
}

// remember the alignment between sessions
void TGeoAlign::readCoe() {
  ax1Cor=nv.readFloat(EE_ax1Cor);
  ax2Cor=nv.readFloat(EE_ax2Cor);
  dfCor=nv.readFloat(EE_dfCor);  // dfCor is ffCor for fork mounts
  tfCor=nv.readFloat(EE_tfCor);
  doCor=nv.readFloat(EE_doCor);
  pdCor=nv.readFloat(EE_pdCor);
  altCor=nv.readFloat(EE_altCor);
  azmCor=nv.readFloat(EE_azmCor);
}

void TGeoAlign::writeCoe() {
  nv.writeFloat(EE_ax1Cor,ax1Cor);
  nv.writeFloat(EE_ax2Cor,ax2Cor);
  nv.writeFloat(EE_dfCor,dfCor);  // dfCor is ffCor for fork mounts
  nv.writeFloat(EE_tfCor,tfCor);
  nv.writeFloat(EE_doCor,doCor);
  nv.writeFloat(EE_pdCor,pdCor);
  nv.writeFloat(EE_altCor,altCor);
  nv.writeFloat(EE_azmCor,azmCor);
}

// Status
bool TGeoAlign::isReady() {
  return geo_ready;
}

/*
Alignment Logic:
Near the celestial equator (Dec=0, HA=0)...
the azmCor term is 0% in Dec
the altCor term is 100% in Dec
the doCor  term is 100% in HA
the pdCor  term is 0% in HA

Near HA=6 and Dec=45...
the azmCor term is 100% in Dec
the altCor term is 0% in Dec
the doCor  term is 0% in HA
the pdCor  term is 100% in HA
*/

// I=1 for 1st star, I=2 for 2nd star, I=3 for 3rd star
// N=total number of stars for this align (1 to 9)
// RA, Dec (all in degrees)
bool TGeoAlign::addStar(int I, int N, double RA, double Dec) {

  // First star:
  // Near the celestial equator (Dec=0, HA=0), telescope West of the pier if multi-star align
  if (I==1) {
    // set the indexAxis1/2 offset
    if (syncEqu(RA,Dec)!=0) return true;
  }

  mount[I-1].ha=getInstrAxis1()/Rad;
  mount[I-1].dec=getInstrAxis2()/Rad;
  actual[I-1].ha=haRange(LST()*15.0-RA)/Rad;
  actual[I-1].dec=Dec/Rad;
  if (getInstrPierSide()==PierSideWest) { actual[I-1].side=-1; mount[I-1].side=-1; } else
  if (getInstrPierSide()==PierSideEast) { actual[I-1].side=1; mount[I-1].side=1; } else { actual[I-1].side=0; mount[I-1].side=0; }

  // two or more stars and finished
  if ((I>=2) && (I==N)) {
#ifdef GOTO_ASSIST_DEBUG_ON
    DL("");
#endif
    autoModel(N,true);
  }

  return true;
}

// returns the correction to be added to the requested RA,Dec to yield the actual RA,Dec that we will arrive at
void TGeoAlign::correct(double ha, double dec, double pierSide, double sf, double _deo, double _pd, double _pz, double _pe, double _da, double _ff, double _tf, double *h1, double *d1) {
  double DO1,DOh;
  double PD,PDh;
  double PZ,PA;
  double DF,DFd,TF,FF,FFd,TFh,TFd;
  double lat;

  lat=latitude/Rad;

// ------------------------------------------------------------
// A. Misalignment due to tube/optics not being perp. to Dec axis
// negative numbers are further (S) from the NCP, swing to the
// equator and the effect on declination is 0. At the SCP it
// becomes a (N) offset.  Unchanged with meridian flips.
  DO1 =((_deo*sf)/3600.0)/Rad;
// works on HA.  meridian flips effect this in HA
  DOh = DO1*(1.0/cos(dec))*pierSide;

// ------------------------------------------------------------
// B. Misalignment, Declination axis relative to Polar axis
// expressed as a correction to where the Polar axis is pointing
// negative numbers are further (S) from the NCP, swing to the
// equator and the effect on declination is 0.
// At the SCP it is, again, a (S) offset
  PD  =((_pd*sf)/3600.0)/Rad;
// works on HA.
  PDh = -PD*tan(dec)*pierSide;

// ------------------------------------------------------------
// Misalignment, relative to NCP
// negative numbers are east of the pole
// C. polar left-right misalignment
  PZ  =((_pz*sf)/3600.0)/Rad;
// D. negative numbers are below the pole
// polar below-above misalignment
  PA  =((_pe*sf)/3600.0)/Rad;

// ------------------------------------------------------------
// Axis flex
  DF  =((_da*sf)/3600.0)/Rad;
  DFd =-DF*(cos(lat)*cos(ha)+sin(lat)*tan(dec));

// ------------------------------------------------------------
// Fork flex
  FF  =((_ff*sf)/3600.0)/Rad;
  FFd =FF*cos(ha);

// ------------------------------------------------------------
// Optical axis sag
  TF  =((_tf*sf)/3600.0)/Rad;

  TFh =TF*(cos(lat)*sin(ha)*(1.0/cos(dec)));
  TFd =TF*(cos(lat)*cos(ha)-sin(lat)*cos(dec));

// ------------------------------------------------------------
  *h1  =(-PZ*cos(ha)*tan(dec) + PA*sin(ha)*tan(dec) + DOh +  PDh +       TFh);
  *d1  =(+PZ*sin(ha)          + PA*cos(ha)                +  DFd + FFd + TFd);
}

void TGeoAlign::do_search(double sf, int p1, int p2, int p3, int p4, int p5, int p6, int p7, int p8, int p9)
{
  long l,

  _deo_m,_deo_p,
  _pd_m,_pd_p,
  _pz_m,_pz_p,
  _pe_m,_pe_p,
  _df_m,_df_p,
  _tf_m,_tf_p,
  _ff_m,_ff_p,
  _oh_m,_oh_p,
  _od_m,_od_p,
  
  _deo,_pd,_pz,_pe, _df,_tf,_ff, _ode,_ohe;

  // search
  // set Parameter Space
  _deo_m=-p1+round(best_deo/sf); _deo_p=p1+round(best_deo/sf);
  _pd_m =-p2+round(best_pd/sf);  _pd_p=p2+round(best_pd/sf);
  _pz_m =-p3+round(best_pz/sf);  _pz_p=p3+round(best_pz/sf);
  _pe_m =-p4+round(best_pe/sf);  _pe_p=p4+round(best_pe/sf);
  _tf_m =-p5+round(best_tf/sf);  _tf_p=p5+round(best_tf/sf);
  _ff_m =-p6+round(best_ff/sf);  _ff_p=p6+round(best_ff/sf);
  _df_m =-p7+round(best_df/sf);  _df_p=p7+round(best_df/sf);
  _od_m =-p8+round(best_ode/sf); _od_p=p8+round(best_ode/sf);
  _oh_m =-p9+round(best_ohe/sf); _oh_p=p9+round(best_ohe/sf);

  double md,mh;
  for (_deo=_deo_m; _deo<=_deo_p; _deo++)
  for (_pd=_pd_m; _pd<=_pd_p; _pd++)
  for (_pz=_pz_m; _pz<=_pz_p; _pz++)
  for (_pe=_pe_m; _pe<=_pe_p; _pe++)
  for (_df=_df_m; _df<=_df_p; _df++)
  for (_ff=_ff_m; _ff<=_ff_p; _ff++)
  for (_tf=_tf_m; _tf<=_tf_p; _tf++)
  for (_ohe=_oh_m; _ohe<=_oh_p; _ohe++)
  for (_ode=_od_m; _ode<=_od_p; _ode++) {
    ode=((((double)_ode)*sf)/(3600.0*Rad));
    odw=-ode;
    ohe=((((double)_ohe)*sf)/(3600.0*Rad));
    ohw=ohe;
    
    // check the combinations for all samples
    for (l=0; l<num; l++) {
      mh=mount[l].ha;
      md=mount[l].dec;
      
      if (mount[l].side==-1) // west of the mount
      {
        mh=mh+ohw;
        md=md+odw;
      } else
      if (mount[l].side==1) // east of the mount, default (fork mounts)
      {
        mh=mh+ohe;
        md=md+ode;
      }
      correct(mh,md,mount[l].side,sf,_deo,_pd,_pz,_pe,_df,_ff,_tf,&h1,&d1);

      delta[l].ha=actual[l].ha-(mh-h1);
      if (delta[l].ha>PI) delta[l].ha=delta[l].ha-PI*2.0;
      if (delta[l].ha<-PI) delta[l].ha=delta[l].ha+PI*2.0;
      delta[l].dec=actual[l].dec-(md-d1);
      delta[l].side=mount[l].side;
    }

    // calculate the standard deviations
    sum1=0.0; for (l=0; l<num; l++) sum1=sum1+sq(delta[l].ha*cos(actual[l].dec)); sh=sqrt(sum1/(num-1));
    sum1=0.0; for (l=0; l<num; l++) sum1=sum1+sq(delta[l].dec); sd=sqrt(sum1/(num-1));
    max_dist=sqrt(sq(sh)+sq(sd));

    // remember the best fit
    if (max_dist<best_dist) {
      best_dist   =max_dist;
      best_deo    =((double)_deo)*sf;
      best_pd     =((double)_pd)*sf;
      best_pz     =((double)_pz)*sf;
      best_pe     =((double)_pe)*sf;

      best_tf     =((double)_tf)*sf;
      best_df     =((double)_df)*sf;
      best_ff     =((double)_ff)*sf;
      
      if (p8!=0) best_odw=odw*Rad*3600.0; else best_odw=best_pe/2.0;
      if (p8!=0) best_ode=ode*Rad*3600.0; else best_ode=-best_pe/2.0;
      if (p9!=0) best_ohw=ohw*Rad*3600.0;
      if (p9!=0) best_ohe=ohe*Rad*3600.0;
    }
  }
}

void TGeoAlign::autoModel(int n, bool start) {
  static int step=51;
  if (start) step=0;
  if (step>50) return;
  step++;

  if (step==1) {
    num=n; // how many stars?
  
    best_dist   =3600.0*180.0;
    best_deo    =0.0;
    best_pd     =0.0;
    best_pz     =0.0;
    best_pe     =0.0;
    best_tf     =0.0;
    best_ff     =0.0;
    best_df     =0.0;
    best_ode    =0.0;
    best_ohe    =0.0;
  
    // figure out the average HA offset as a starting point
    ohe=0;
    for (l=1; l<num; l++) {
      h1=actual[l].ha-mount[l].ha;
      if (h1>PI)  h1=h1-PI*2.0;
      if (h1<-PI) h1=h1+PI*2.0;
      ohe=ohe+h1;
    }
    ohe=ohe/num; best_ohe=round(ohe*Rad*3600.0); best_ohw=best_ohe;
  
#if defined(MOUNT_TYPE_FORK) || defined(MOUNT_TYPE_FORK_ALT) || defined(MOUNT_TYPE_ALTAZM)
    Ff=1; Df=0;
#else
    Ff=0; Df=1;
#endif
  }
  
#ifdef HAL_SLOW_PROCESSOR
  // search, this can handle about 4.5 degrees of polar misalignment, and 1 degree of cone error
  //                           DoPdPzPeTfFfDfOdOh
  if (step==2)  do_search( 8192,0,0,1,1,0,0,0,1,1);
  if (step==4)  do_search( 4096,0,0,1,1,0,0,0,1,1);
  if (step==6)  do_search( 2048,1,0,1,1,0,0,0,1,1);
  if (step==20) do_search( 1024,1,0,1,1,0,0,0,1,1);
  if (step==30) do_search(  512,1,0,1,1,0,0,0,1,1);
  if (step==40) do_search(  256,1,0,1,1,0,0,0,1,1);
#elif HAL_FAST_PROCESSOR
  // search, this can handle about 9 degrees of polar misalignment, and 2 degrees of cone error, 8' of FF/DF/PD
  //                           DoPdPzPeTfFf Df OdOh
  if (step==2)  do_search(16384,0,0,1,1,0, 0, 0,1,1);
  if (step==4)  do_search( 8192,0,0,1,1,0, 0, 0,1,1);
  if (step==6)  do_search( 4096,1,0,1,1,0, 0, 0,1,1);
  if (step==8)  do_search( 2048,1,0,1,1,0, 0, 0,1,1);
  if (step==10) do_search( 1024,1,0,1,1,0, 0, 0,1,1);
  if (step==15) do_search(  512,1,0,1,1,0, 0, 0,1,1);
  if (num>4) {
  if (step==20) do_search(  256,1,1,1,1,0,Ff,Df,1,1);
  if (step==30) do_search(  128,1,1,1,1,0,Ff,Df,1,1);
  if (step==40) do_search(   64,1,1,1,1,0,Ff,Df,1,1);
  } else {
  if (step==20) do_search(  256,1,0,1,1,0, 0, 0,1,1);
  if (step==30) do_search(  128,1,0,1,1,0, 0, 0,1,1);
  if (step==40) do_search(   64,1,0,1,1,0, 0, 0,1,1);
  }
#else
  // search, this can handle about 9 degrees of polar misalignment, and 2 degrees of cone error
  //                           DoPdPzPeTfFf Df OdOh
  if (step==2)  do_search(16384,0,0,1,1,0, 0, 0,1,1);
  if (step==4)  do_search( 8192,0,0,1,1,0, 0, 0,1,1);
  if (step==6)  do_search( 4096,1,0,1,1,0, 0, 0,1,1);
  if (step==8)  do_search( 2048,1,0,1,1,0, 0, 0,1,1);
  if (step==10) do_search( 1024,1,0,1,1,0, 0, 0,1,1);
  if (step==20) do_search(  512,1,0,1,1,0, 0, 0,1,1);
  if (step==30) do_search(  256,1,0,1,1,0, 0, 0,1,1);
  if (step==40) do_search(  128,1,0,1,1,0, 0, 0,1,1);
#endif

  if (step==50) {
    // geometric corrections
    doCor=best_deo/3600.0;
    pdCor=best_pd/3600.0;
    azmCor=best_pz/3600.0;
    altCor=best_pe/3600.0;

    tfCor=best_tf/3600.0;
#if defined(MOUNT_TYPE_FORK) || defined(MOUNT_TYPE_FORK_ALT) || defined(MOUNT_TYPE_ALTAZM)
    dfCor=best_df/3600.0;
#else
    dfCor=best_ff/3600.0;
#endif

    ax1Cor=best_ohw/3600.0;
    ax2Cor=best_odw/3600.0;

    geo_ready=true;
  }
}

// takes the topocentric refracted coordinates and applies corrections to arrive at instrument equatorial coordinates 
void TGeoAlign::EquToInstr(double Lat, double HA, double Dec, double *HA1, double *Dec1, int PierSide) {
  double p=1.0; if (PierSide==PierSideWest) p=-1.0;

  if (Dec>90.0) Dec=90.0;
  if (Dec<-90.0) Dec=-90.0;

  // breaks-down near the pole (limited to >1' from pole)
  if (abs(Dec)<89.9833) {

    // initial rough guess at instrument HA,Dec
    double h=HA/Rad;
    double d=Dec/Rad;
    
    for (int pass=0; pass<3; pass++) {
      double sinDec=sin(d);
      double cosDec=cos(d);
      double sinHA =sin(h);
      double cosHA =cos(h);
  
      // ------------------------------------------------------------
      // misalignment due to tube/optics not being perp. to Dec axis
      // negative numbers are further (S) from the NCP, swing to the
      // equator and the effect on declination is 0. At the SCP it
      // becomes a (N) offset.  Unchanged with meridian flips.
      // expressed as a correction to the Polar axis misalignment
      double DOh=doCor*(1.0/cosDec)*p;
  
      // ------------------------------------------------------------
      // misalignment due to Dec axis being perp. to RA axis
      double PDh=-pdCor*(sinDec/cosDec)*p;
  
  #if defined (MOUNT_TYPE_FORK) || defined(MOUNT_TYPE_FORK_ALT)
      // Fork flex
      double DFd=dfCor*cosHA;
  #else
      // Axis flex
      double DFd=-dfCor*(cosLat*cosHA+sinLat*(sinDec/cosDec));
  #endif
  
      // Tube flex
      double TFh=tfCor*(cosLat*sinHA*(1.0/cosDec));
      double TFd=tfCor*(cosLat*cosHA-sinLat*cosDec);
  
      // polar misalignment
      double h1=-azmCor*cosHA*(sinDec/cosDec) + altCor*sinHA*(sinDec/cosDec);
      double d1=+azmCor*sinHA                 + altCor*cosHA;
      *HA1 =HA +(h1+PDh+DOh+TFh);
      *Dec1=Dec+(d1+DFd+TFd);

      // improved guess at instrument HA,Dec
      h=*HA1/Rad;
      d=*Dec1/Rad;
    }
  } else {
    // just ignore the the correction if right on the pole
    *HA1 =HA;
    *Dec1=Dec;
  }

  // finally, apply the index offsets
  *HA1=*HA1-ax1Cor;
  *Dec1=*Dec1-ax2Cor*-p;
}

// takes the instrument equatorial coordinates and applies corrections to arrive at topocentric refracted coordinates
void TGeoAlign::InstrToEqu(double Lat, double HA, double Dec, double *HA1, double *Dec1, int PierSide) { 
  double p=1.0; if (PierSide==PierSideWest) p=-1.0;
  
  HA =HA +ax1Cor;
  Dec=Dec+ax2Cor*-p;
  if (Dec>90.0) Dec=90.0;
  if (Dec<-90.0) Dec=-90.0;

  // breaks-down near the pole (limited to >1' from pole)
  if (abs(Dec)<89.98333333) {
    double h=HA/Rad;
    double d=Dec/Rad;
    double sinDec=sin(d);
    double cosDec=cos(d);
    double sinHA =sin(h);
    double cosHA =cos(h);

    // ------------------------------------------------------------
    // misalignment due to tube/optics not being perp. to Dec axis
    // negative numbers are further (S) from the NCP, swing to the
    // equator and the effect on declination is 0. At the SCP it
    // becomes a (N) offset.  Unchanged with meridian flips.
    // expressed as a correction to the Polar axis misalignment
    double DOh=doCor*(1.0/cosDec)*p;

    // as the above offset becomes zero near the equator, the affect
    // works on HA instead.  meridian flips affect this in HA
    double PDh=-pdCor*(sinDec/cosDec)*p;

#if defined (MOUNT_TYPE_FORK) || defined(MOUNT_TYPE_FORK_ALT)
    // Fork flex
    double DFd=dfCor*cosHA;
#else
    // Axis flex
    double DFd=-dfCor*(cosLat*cosHA+sinLat*(sinDec/cosDec));
#endif

    // Tube flex
    double TFh=tfCor*(cosLat*sinHA*(1.0/cosDec));
    double TFd=tfCor*(cosLat*cosHA-sinLat*cosDec);
   
    // ------------------------------------------------------------
    // polar misalignment
    double h1=-azmCor*cosHA*(sinDec/cosDec) + altCor*sinHA*(sinDec/cosDec);
    double d1=+azmCor*sinHA                 + altCor*cosHA;

    *HA1 =HA -(h1+PDh+DOh+TFh);
    *Dec1=Dec-(d1+DFd+TFd);
  } else {
    // just ignore the the correction if right on the pole
    *HA1=HA;
    *Dec1=Dec;
  }

  while (*HA1>180.0) *HA1-=360.0;
  while (*HA1<-180.0) *HA1+=360.0;
  if (*Dec1>90.0) *Dec1=90.0;
  if (*Dec1<-90.0) *Dec1=-90.0;
}
#endif