void iauC2txy(double tta, double ttb, double uta, double utb, double x, double y, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - ** i a u C 2 t x y ** - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1, ** the CIP coordinates and the polar motion. IAU 2000. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** x,y double Celestial Intermediate Pole (Note 2) ** xp,yp double coordinates of the pole (radians, Note 3) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any o ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 3) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 4) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 5) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauC2ixy celestial-to-intermediate matrix, given X,Y ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2009 April 1 ** ** Original version 2012-03-01 ** ** Copyright (C) 2013 Naoki Arita. See notes at end. */ { double rc2i[3][3], era, sp, rpom[3][3]; /* Form the celestial-to-intermediate matrix for this TT. */ iauC2ixy(tta, ttb, x, y, rc2i); /* Predict the Earth rotation angle for this UT1. */ era = iauEra00(uta, utb); /* Estimate s'. */ sp = iauSp00(tta, ttb); /* Form the polar motion matrix. */ iauPom00(xp, yp, sp, rpom); /* Combine to form the celestial-to-terrestrial matrix. */ iauC2tcio(rc2i, era, rpom, rc2t); return; /*---------------------------------------------------------------------- ** ** Celes is a wrapper of the SOFA Library for Ruby. ** ** This file is redistributed and relicensed in accordance with ** the SOFA Software License (http://www.iausofa.org/tandc.html). ** ** The original library is available from IAU Standards of ** Fundamental Astronomy (http://www.iausofa.org/). ** ** ** ** ** ** Copyright (C) 2013, Naoki Arita ** All rights reserved. ** ** Redistribution and use in source and binary forms, with or without ** modification, are permitted provided that the following conditions ** are met: ** ** 1 Redistributions of source code must retain the above copyright ** notice, this list of conditions and the following disclaimer. ** ** 2 Redistributions in binary form must reproduce the above copyright ** notice, this list of conditions and the following disclaimer in ** the documentation and/or other materials provided with the ** distribution. ** ** 3 Neither the name of the Standards Of Fundamental Astronomy Board, ** the International Astronomical Union nor the names of its ** contributors may be used to endorse or promote products derived ** from this software without specific prior written permission. ** ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ** POSSIBILITY OF SUCH DAMAGE. ** **--------------------------------------------------------------------*/ }
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { size_t numRow,numVec; mxArray *retMat; double *xVec, *retData; double TT1, TT2, UT11, UT12; //The if-statements below should properly initialize all of the EOP. //The following initializations to zero are to suppress warnings when //compiling with -Wconditional-uninitialized. double dX=0; double dY=0; double xp=0; double yp=0; double deltaT=0; double LOD=0; double ITRS2GCRS[3][3]; double TIRS2GCRS[3][3]; double invrPom[3][3];//Inverse polar motion matrix. TIRS=IPOM*ITRS. double Omega[3]; if(nrhs<3||nrhs>7){ mexErrMsgTxt("Wrong number of inputs"); } if(nlhs>2) { mexErrMsgTxt("Wrong number of outputs."); return; } checkRealDoubleArray(prhs[0]); numRow = mxGetM(prhs[0]); numVec = mxGetN(prhs[0]); if(!(numRow==3||numRow==6)) { mexErrMsgTxt("The input vector has a bad dimensionality."); } xVec=(double*)mxGetData(prhs[0]); TT1=getDoubleFromMatlab(prhs[1]); TT2=getDoubleFromMatlab(prhs[2]); //If some values from the function getEOP will be needed. if(nrhs<=6||mxIsEmpty(prhs[3])||mxIsEmpty(prhs[4])||mxIsEmpty(prhs[5])||mxIsEmpty(prhs[6])) { mxArray *retVals[5]; double *xpyp, *dXdY; mxArray *JulUTCMATLAB[2]; double JulUTC[2]; int retVal; //Get the time in UTC to look up the parameters by going to TAI and //then UTC. retVal=iauTttai(TT1, TT2, &JulUTC[0], &JulUTC[1]); if(retVal!=0) { mexErrMsgTxt("An error occurred computing TAI."); } retVal=iauTaiutc(JulUTC[0], JulUTC[1], &JulUTC[0], &JulUTC[1]); switch(retVal){ case 1: mexWarnMsgTxt("Dubious Date entered."); break; case -1: mexErrMsgTxt("Unacceptable date entered"); break; default: break; } JulUTCMATLAB[0]=doubleMat2Matlab(&JulUTC[0],1,1); JulUTCMATLAB[1]=doubleMat2Matlab(&JulUTC[1],1,1); //Get the Earth orientation parameters for the given date. mexCallMATLAB(5,retVals,2,JulUTCMATLAB,"getEOP"); mxDestroyArray(JulUTCMATLAB[0]); mxDestroyArray(JulUTCMATLAB[1]); checkRealDoubleArray(retVals[0]); checkRealDoubleArray(retVals[1]); if(mxGetM(retVals[0])!=2||mxGetN(retVals[0])!=1||mxGetM(retVals[1])!=2||mxGetN(retVals[1])!=1) { mxDestroyArray(retVals[0]); mxDestroyArray(retVals[1]); mxDestroyArray(retVals[2]); mxDestroyArray(retVals[3]); mxDestroyArray(retVals[4]); mexErrMsgTxt("Error using the getEOP function."); return; } xpyp=(double*)mxGetData(retVals[0]); dXdY=(double*)mxGetData(retVals[1]); xp=xpyp[0]; yp=xpyp[1]; dX=dXdY[0]; dY=dXdY[1]; //This is TT-UT1 deltaT=getDoubleFromMatlab(retVals[3]); LOD=getDoubleFromMatlab(retVals[4]); //Free the returned arrays. mxDestroyArray(retVals[0]); mxDestroyArray(retVals[1]); mxDestroyArray(retVals[2]); mxDestroyArray(retVals[3]); mxDestroyArray(retVals[4]); } //If deltaT=TT-UT1 is given if(nrhs>3&&!mxIsEmpty(prhs[3])) { deltaT=getDoubleFromMatlab(prhs[3]); } //Obtain UT1 from terestrial time and deltaT. iauTtut1(TT1, TT2, deltaT, &UT11, &UT12); //If no values for the polar motion coordinates are given, then use //zeros. if(nrhs>4&&!mxIsEmpty(prhs[4])) { size_t dim1, dim2; checkRealDoubleArray(prhs[4]); dim1 = mxGetM(prhs[4]); dim2 = mxGetN(prhs[4]); if((dim1==2&&dim2==1)||(dim1==1&&dim2==2)) { double *xpyp=(double*)mxGetData(prhs[4]); xp=xpyp[0]; yp=xpyp[1]; } else { mexErrMsgTxt("The celestial pole offsets have the wrong dimensionality."); return; } } if(nrhs>5&&!mxIsEmpty(prhs[5])) { size_t dim1, dim2; checkRealDoubleArray(prhs[5]); dim1 = mxGetM(prhs[5]); dim2 = mxGetN(prhs[5]); if((dim1==2&&dim2==1)||(dim1==1&&dim2==2)) { double *dXdY=(double*)mxGetData(prhs[5]); dX=dXdY[0]; dY=dXdY[1]; } else { mexErrMsgTxt("The polar motion coordinates have the wrong dimensionality."); return; } } //If LOD is given if(nrhs>6&&!mxIsEmpty(prhs[6])) { LOD=getDoubleFromMatlab(prhs[6]); } //Compute the rotation matrix for going from ITRS to GCRS as well as //the instantaneous vector angular momentum due to the Earth's rotation //in TIRS coordinates. { double x, y, s, era, sp; double rpom[3][3], rc2i[3][3]; double GCRS2ITRS[3][3]; double omega; //Get the X,Y coordinates of the Celestial Intermediate Pole (CIP) and //the Celestial Intermediate Origin (CIO) locator s, using the IAU 2006 //precession and IAU 2000A nutation models. iauXys06a(TT1, TT2, &x, &y, &s); //Add the CIP offsets. x += dX; y += dY; //Get the GCRS-to-CIRS matrix iauC2ixys(x, y, s, rc2i); //Find the Earth rotation angle for the given UT1 time. era = iauEra00(UT11, UT12); //Get the Terrestrial Intermediate Origin (TIO) locator s' in radians sp=iauSp00(TT1,TT2); //Get the polar motion matrix iauPom00(xp,yp,sp,rpom); //Combine the GCRS-to-CIRS matrix, the Earth rotation angle, and the //polar motion matrix to get a transformation matrix to get the //rotation matrix to go from GCRS to ITRS. iauC2tcio(rc2i, era, rpom,GCRS2ITRS); //To go from the ITRS to the GCRS, we need to use the inverse rotation //matrix, which is just the transpose of the rotation matrix. iauTr(GCRS2ITRS, ITRS2GCRS); //Next, to be able to transform the velocity, the rotation of the Earth //has to be taken into account. This requires first transforming from //ITRS to TIRS coordinates, where the rotational axis is the z-axis. //That transformation requires the inverse polar motion matrix, which, //being a rotation matrix, is given by its transpose. iauTr(rpom, invrPom); //Then, one must transform from TIRS to GCRS, which can be done by //taking the inverse of the rotation matrix from GCRS to ITRS computed //using the identity matrix for polar motion (i.e. no polar motion //means leaving it in the TIRS. { double rident[3][3]={{1,0,0},{0,1,0},{0,0,1}}; double GCRS2TIRS[3][3]; iauC2tcio(rc2i, era, rident,GCRS2TIRS); iauTr(GCRS2TIRS, TIRS2GCRS); } //The angular velocity vector of the Earth in the TIRS in radians. omega=getScalarMatlabClassConst("Constants","IERSMeanEarthRotationRate"); //Adjust for LOD omega=omega*(1-LOD/86400.0);//86400.0 is the number of seconds in a TT day. Omega[0]=0; Omega[1]=0; Omega[2]=omega; } //Allocate space for the return vectors. retMat=mxCreateDoubleMatrix(numRow,numVec,mxREAL); retData=(double*)mxGetData(retMat); { size_t curVec; for(curVec=0;curVec<numVec;curVec++) { //Multiply the position vector with the rotation matrix. iauRxp(ITRS2GCRS, xVec+numRow*curVec, retData+numRow*curVec); //If a velocity vector was given. if(numRow>3) { double posTIRS[3]; double velTIRS[3]; double *posITRS=xVec+numRow*curVec; double *velITRS=xVec+numRow*curVec+3;//Velocity in GCRS double *retDataVel=retData+numRow*curVec+3; double rotVel[3]; //If a velocity was provided with the position, then first //convert into the TIRS, then account for the rotation of //the Earth, then rotate into the GCRS. //Convert velocity from ITRS to TIRS. iauRxp(invrPom, velITRS, velTIRS); //Convert position from ITRS to TIRS iauRxp(invrPom, posITRS, posTIRS); //Evaluate the cross product for the angular velocity due //to the Earth's rotation. iauPxp(Omega, posTIRS, rotVel); //Add the instantaneous velocity due to rotation. iauPpp(velTIRS, rotVel, retDataVel); //Rotate from TIRS to GCRS iauRxp(TIRS2GCRS, retDataVel, retDataVel); } } } plhs[0]=retMat; if(nlhs>1) { double *elPtr; size_t i,j; plhs[1]=mxCreateDoubleMatrix(3,3,mxREAL); elPtr=(double*)mxGetData(plhs[1]); for (i=0;i<3;i++) { for(j=0;j<3;j++) { elPtr[i+3*j]=ITRS2GCRS[i][j]; } } } }
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { size_t numRow,numVec; mxArray *retMat; double *retData; double ITRS2TIRS[3][3];//Inverse polar motion matrix double *xVec, TT1, TT2; double xp=0; double yp=0;//The polar motion coordinates if(nrhs<3||nrhs>4){ mexErrMsgTxt("Wrong number of inputs"); } if(nlhs>2) { mexErrMsgTxt("Wrong number of outputs."); } numRow = mxGetM(prhs[0]); numVec = mxGetN(prhs[0]); if(!(numRow==3||numRow==6)) { mexErrMsgTxt("The input vector has a bad dimensionality."); } checkRealDoubleArray(prhs[0]); xVec=(double*)mxGetData(prhs[0]); TT1=getDoubleFromMatlab(prhs[1]); TT2=getDoubleFromMatlab(prhs[2]); //If xpyp should be found using the function getEOP. if(nrhs<4||mxIsEmpty(prhs[3])) { mxArray *retVals[1]; double *xpyp; mxArray *JulUTCMATLAB[2]; double JulUTC[2]; int retVal; //Get the time in UTC to look up the parameters by going to TAI and //then UTC. retVal=iauTttai(TT1, TT2, &JulUTC[0], &JulUTC[1]); if(retVal!=0) { mexErrMsgTxt("An error occurred computing TAI."); } retVal=iauTaiutc(JulUTC[0], JulUTC[1], &JulUTC[0], &JulUTC[1]); switch(retVal){ case 1: mexWarnMsgTxt("Dubious Date entered."); break; case -1: mexErrMsgTxt("Unacceptable date entered"); break; default: break; } JulUTCMATLAB[0]=doubleMat2Matlab(&JulUTC[0],1,1); JulUTCMATLAB[1]=doubleMat2Matlab(&JulUTC[1],1,1); //Get the Earth orientation parameters for the given date. mexCallMATLAB(1,retVals,2,JulUTCMATLAB,"getEOP"); mxDestroyArray(JulUTCMATLAB[0]); mxDestroyArray(JulUTCMATLAB[1]); checkRealDoubleArray(retVals[0]); if(mxGetM(retVals[0])!=2||mxGetN(retVals[0])!=1) { mxDestroyArray(retVals[0]); mexErrMsgTxt("Error using the getEOP function."); return; } xpyp=(double*)mxGetData(retVals[0]); xp=xpyp[0]; yp=xpyp[1]; //Free the returned array. mxDestroyArray(retVals[0]); } //Get polar motion coordinates, if given. if(nrhs>3&&!mxIsEmpty(prhs[3])) { size_t dim1, dim2; checkRealDoubleArray(prhs[3]); dim1 = mxGetM(prhs[3]); dim2 = mxGetN(prhs[3]); if((dim1==2&&dim2==1)||(dim1==1&&dim2==2)) { double *xpyp=(double*)mxGetData(prhs[3]); xp=xpyp[0]; yp=xpyp[1]; } else { mexErrMsgTxt("The polar motion coordinates have the wrong dimensionality."); return; } } //Get the rotation matrix from TIRS to ITRS. { double sp; double TIRS2ITRS[3][3];//Polar motion matrix //Get the Terrestrial Intermediate Origin (TIO) locator s' in //radians sp=iauSp00(TT1,TT2); //Get the polar motion matrix iauPom00(xp,yp,sp,TIRS2ITRS); //The inverse polar motion matrix is given by the transpose of the //polar motion matrix. iauTr(TIRS2ITRS, ITRS2TIRS); } //Allocate space for the return vectors. retMat=mxCreateDoubleMatrix(numRow,numVec,mxREAL); retData=(double*)mxGetData(retMat); { size_t curVec; for(curVec=0;curVec<numVec;curVec++) { //Multiply the position vector with the rotation matrix. iauRxp(ITRS2TIRS, xVec+numRow*curVec, retData+numRow*curVec); //Multiply the velocity vector with the rotation matrix. if(numRow>3) { double *velITRS=xVec+numRow*curVec+3;//Velocity in ITRS double *retDataVel=retData+numRow*curVec+3;//Velocity in ITRS //Convert velocity from ITRS to TIRS. iauRxp(ITRS2TIRS, velITRS, retDataVel); } } } plhs[0]=retMat; if(nlhs>1) { double *elPtr; size_t i,j; plhs[1]=mxCreateDoubleMatrix(3,3,mxREAL); elPtr=(double*)mxGetData(plhs[1]); for (i=0;i<3;i++) { for(j=0;j<3;j++) { elPtr[i+3*j]=ITRS2TIRS[i][j]; } } } }
int iauApio13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p i o 1 3 ** - - - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between CIRS and observed ** coordinates. The caller supplies UTC, site coordinates, ambient air ** conditions and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 1,2) ** dut1 double UT1-UTC (seconds) ** elong double longitude (radians, east +ve, Note 3) ** phi double geodetic latitude (radians, Note 3) ** hm double height above ellipsoid (m, geodetic Notes 4,6) ** xp,yp double polar motion coordinates (radians, Note 5) ** phpa double pressure at the observer (hPa = mB, Note 6) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 7) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 2) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 4) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 5) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many applications, ** xp and yp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto ** the local meridian. ** ** 6) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to the ** pressure and that an accurate phpa value is important for ** precise work. ** ** 7) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 8) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 9) In cases where the caller wishes to supply his own Earth ** rotation information and refraction constants, the function ** iauApc can be used instead of the present function. ** ** 10) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 11) The context structure astrom produced by this function is used ** by iauAtioq and iauAtoiq. ** ** Called: ** iauUtctai UTC to TAI ** iauTaitt TAI to TT ** iauUtcut1 UTC to UT1 ** iauSp00 the TIO locator s', IERS 2000 ** iauEra00 Earth rotation angle, IAU 2000 ** iauRefco refraction constants for given ambient conditions ** iauApio astrometry parameters, CIRS-observed ** ** This revision: 2013 October 9 ** ** SOFA release 2013-12-02 ** ** Copyright (C) 2013 IAU SOFA Board. See notes at end. */ { int j; double tai1, tai2, tt1, tt2, ut11, ut12, sp, theta, refa, refb; /* UTC to other time scales. */ j = iauUtctai(utc1, utc2, &tai1, &tai2); if ( j < 0 ) return -1; j = iauTaitt(tai1, tai2, &tt1, &tt2); j = iauUtcut1(utc1, utc2, dut1, &ut11, &ut12); if ( j < 0 ) return -1; /* TIO locator s'. */ sp = iauSp00(tt1, tt2); /* Earth rotation angle. */ theta = iauEra00(ut11, ut12); /* Refraction constants A and B. */ iauRefco(phpa, tc, rh, wl, &refa, &refb); /* CIRS <-> observed astrometry parameters. */ iauApio(sp, theta, elong, phi, hm, xp, yp, refa, refb, astrom); /* Return any warning status. */ return j; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2013 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
void iauC2t06a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t 0 6 a ** - - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1 and ** the polar motion, using the IAU 2006 precession and IAU 2000A ** nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** xp,yp double coordinates of the pole (radians, Note 2) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 3) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RC2I is the ** celestial-to-intermediate matrix, ERA is the Earth rotation ** angle and RPOM is the polar motion matrix. ** ** Called: ** iauC2i06a celestial-to-intermediate matrix, IAU 2006/2000A ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** This revision: 2009 April 1 ** ** SOFA release 2012-03-01 ** ** Copyright (C) 2012 IAU SOFA Board. See notes at end. */ { double rc2i[3][3], era, sp, rpom[3][3]; /* Form the celestial-to-intermediate matrix for this TT. */ iauC2i06a(tta, ttb, rc2i); /* Predict the Earth rotation angle for this UT1. */ era = iauEra00(uta, utb); /* Estimate s'. */ sp = iauSp00(tta, ttb); /* Form the polar motion matrix. */ iauPom00(xp, yp, sp, rpom); /* Combine to form the celestial-to-terrestrial matrix. */ iauC2tcio(rc2i, era, rpom, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2012 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }