/*
** The HAE to HEEQ transformation is given by the matrix
**
** S2 = <theta0,Z>*<i,X>*<Omega,Z>
**
** where the rotation angle theta0 is the the longitude of the Sun's
** central meridian, i is the the inclination of the Sun's equator and
** Omega is the the ecliptic longitude of the ascending node of the Sun's
** equator. This transformation comprises a rotation in the plane of the
** ecliptic from the First Point of Aries to the ascending node of the
** solar equator, then a rotation from the plane of the ecliptic to the
** plane of the equator and finally a rotation in the plane of the solar
** equator from the ascending node to the central meridian.
**
** Implemented by Kristi Keller on 2/2/2004
*/
void
mat_S2(const double et, Mat mat)
{
Mat mat_tmp;
double Omega = 73.6667+0.013958*(MJD(et)+3242)/365.25;
double theta0 = atand(cosd(7.25) * tand(lambda0(et)-Omega));
double angle_1 = lambda0(et)-Omega;
angle_1=fmod(angle_1,360.0);
if (angle_1 < 0.0) angle_1+=360.0;
theta0=fmod(theta0,360.0);
if (theta0 < 0.0) theta0+=360.0;
if (angle_1 < 180.0) {
if (theta0 < 180.0) theta0+=180.0;
}
if (angle_1 > 180.0) {
if (theta0 > 180.0) theta0-=180.0;
}
hapgood_matrix(theta0, Z, mat);
hapgood_matrix(7.25, X, mat_tmp);
mat_times_mat(mat, mat_tmp, mat);
hapgood_matrix(Omega, Z, mat_tmp);
mat_times_mat(mat, mat_tmp, mat);
}
/*
** The GEI2000 to GEI transformation is given by the matrix
**
** P = <-zA,Z>*<thetaA,Y>*<-zetaA,Z>
**
** where the rotation angles zA, thetaA and zetaA are the precession
** angles. This transformation is a precession correction as described
** by Hapgood (1995).
**
** zA = 0.64062 T0 + 0.00030 T0^2 degrees
** thetaA = 0.55675 T0 - 0.00012 T0^2 degrees
** zetaA = 0.64062 T0 + 0.00008 T0^2 degrees
*/
void
mat_P(const double et, Mat mat)
{
Mat mat_tmp;
double t0 = T0(et);
hapgood_matrix(-1.0*(0.64062 * t0 + 0.00030 * t0*t0), Z, mat);
hapgood_matrix(0.55675 * t0 - 0.00012 * t0*t0, Y, mat_tmp);
mat_times_mat(mat, mat_tmp, mat);
hapgood_matrix(-1.0*(0.64062 * t0 + 0.00008 * t0*t0), Z, mat_tmp);
mat_times_mat(mat, mat_tmp, mat);
}
/*
** vec_Qe
**
** don't ask.
*/
void
vec_Qe(double et, Vec Qe)
{
double lat = mag_lat(et);
double lon = mag_lon(et);
double cos_lat = cos(lat);
double sin_lat = sin(lat);
double cos_lon = cos(lon);
double sin_lon = sin(lon);
Mat mat_tmp, mat;
Vec Qg;
Qg[0] = cos_lat * cos_lon;
Qg[1] = cos_lat * sin_lon;
Qg[2] = sin_lat;
/* printf("lat=%lf lon=%lf\n", 90.0 - lat, lon);*/
mat_T2(et, mat);
mat_T1(et, mat_tmp);
mat_transpose(mat_tmp, mat_tmp);
mat_times_mat(mat, mat_tmp, mat);
mat_times_vec(mat, Qg, Qe);
}
Mat* create_look_at_mat(Vec* cam_pos, Vec* targ_pos, Vec* up) {
Mat* p = create_translation_mat(-cam_pos->x, -cam_pos->y, -cam_pos->z);
Vec* d = vec_minus_vec(targ_pos, cam_pos);
Vec* f = normalize_vec(d);
Vec* c1 = cross_vec(f, up);
Vec* r = normalize_vec(c1);
Vec* c2 = cross_vec(r, f);
Vec* u = normalize_vec(c2);
Mat* ori = identity_mat();
ori->m[0] = r->x;
ori->m[4] = r->y;
ori->m[8] = r->z;
ori->m[1] = u->x;
ori->m[5] = u->y;
ori->m[9] = u->z;
ori->m[2] = -f->x;
ori->m[6] = -f->y;
ori->m[10] = -f->z;
Mat* ret = mat_times_mat(ori, p);
delete_mat(p);
delete_mat(ori);
delete_vec(d);
delete_vec(f);
delete_vec(r);
delete_vec(u);
delete_vec(c1);
delete_vec(c2);
return ret;
}
/*
** The GEO to MAG transformation is given by the matrix
**
** T5 = <lat-90,Y>*<long,Z>
**
** where the rotation angle lat is the latitude and angle long is the
** longitude of the geomagnetic pole (as defined by the axis of the
** dipole component of the geomagnetic field). This transformation is
** a rotation in the plane of the Earth's equator from the Greenwich
** meridian to the meridian containing the dipole axis, followed by
** a rotation in that meridian from the rotation axis to the dipole axis.
*/
void
mat_T5(const double et, Mat mat)
{
Mat mat_tmp;
hapgood_matrix((mag_lat(et)*RADIANS_TO_DEGREES) - 90.0, Y, mat);
hapgood_matrix((mag_lon(et)*RADIANS_TO_DEGREES), Z, mat_tmp);
mat_times_mat(mat, mat_tmp, mat);
}
/*
** The GEI to GSE transformation is given by the matrix
**
** T2 = <lambdaO,Z>*<epsilon,X>
**
** where the rotation angle lambdaO is the Sun's ecliptic longitude and
** the angle epsilon is the obliquity of the ecliptic. This transformation
** is a rotation from the Earth's equator to the plane of the ecliptic
** followed by a rotation in the plane of the ecliptic from the First Point
** of Aries to the Earth-Sun direction.
*/
void
mat_T2(const double et, Mat mat)
{
Mat mat_tmp;
hapgood_matrix(lambda0(et), Z, mat);
hapgood_matrix(epsilon(et), X, mat_tmp);
mat_times_mat(mat, mat_tmp, mat);
}