//gamma is useless but I keep it for simmetry
//with Euler_direction
void Euler_direction2angles(Matrix1D<DOUBLE> &v0,
DOUBLE &alpha, DOUBLE &beta)
{
DOUBLE abs_ca, sb, cb;
DOUBLE aux_alpha;
DOUBLE aux_beta;
DOUBLE error, newerror;
Matrix1D<DOUBLE> v_aux;
Matrix1D<DOUBLE> v;
//if not normalized do it so
v.resize(3);
v = v0;
v.selfNormalize();
v_aux.resize(3);
cb = v(2);
if (fabs((cb)) > 0.999847695)/*one degree */
{
std::cerr << "\nWARNING: Routine Euler_direction2angles is not reliable\n"
"for small tilt angles. Up to 0.001 deg it should be OK\n"
"for most applications but you never know";
}
if (fabs((cb - 1.)) < FLT_EPSILON)
{
alpha = 0.;
beta = 0.;
}
else
{/*1*/
aux_beta = acos(cb); /* beta between 0 and PI */
sb = sin(aux_beta);
abs_ca = fabs(v(0)) / sb;
if (fabs((abs_ca - 1.)) < FLT_EPSILON)
aux_alpha = 0.;
else
aux_alpha = acos(abs_ca);
v_aux(0) = sin(aux_beta) * cos(aux_alpha);
v_aux(1) = sin(aux_beta) * sin(aux_alpha);
v_aux(2) = cos(aux_beta);
error = fabs(dotProduct(v, v_aux) - 1.);
alpha = aux_alpha;
beta = aux_beta;
v_aux(0) = sin(aux_beta) * cos(-1. * aux_alpha);
v_aux(1) = sin(aux_beta) * sin(-1. * aux_alpha);
v_aux(2) = cos(aux_beta);
newerror = fabs(dotProduct(v, v_aux) - 1.);
if (error > newerror)
{
alpha = -1. * aux_alpha;
beta = aux_beta;
error = newerror;
}
v_aux(0) = sin(-aux_beta) * cos(-1. * aux_alpha);
v_aux(1) = sin(-aux_beta) * sin(-1. * aux_alpha);
v_aux(2) = cos(-aux_beta);
newerror = fabs(dotProduct(v, v_aux) - 1.);
if (error > newerror)
{
alpha = -1. * aux_alpha;
beta = -1. * aux_beta;
error = newerror;
}
v_aux(0) = sin(-aux_beta) * cos(aux_alpha);
v_aux(1) = sin(-aux_beta) * sin(aux_alpha);
v_aux(2) = cos(-aux_beta);
newerror = fabs(dotProduct(v, v_aux) - 1.);
if (error > newerror)
{
alpha = aux_alpha;
beta = -1. * aux_beta;
error = newerror;
}
}/*else 1 end*/
beta = RAD2DEG(beta);
alpha = RAD2DEG(alpha);
}/*Eulerdirection2angles end*/
