def EulerAngles(equinox, targetEquinox, coord=None, rot=None):
#Return the Euler angles (passive Z(-Y)X) to go from equinox to targetEquinox in degrees
#Rot is an extra rotation, after precessing
#If coord is provided, the inverse coordinate transformation is applied first, then the precession, then the direct coordinate transformation, and then the rotation is calculated
deg=apUnits.degree;
#Unit vector in current epoch
x0=array([1,0,0])
y0=array([0,1,0])
z0=array([0,0,1])
#Go to original coordinates
rCoord=Rotator(coord=coord)
x=rCoord.I(x0)
y=rCoord.I(y0)
z=rCoord.I(z0)
#Change to longitude and latitude
xLonLat=vec2dir(x,lonlat=True)
yLonLat=vec2dir(y,lonlat=True)
zLonLat=vec2dir(z,lonlat=True)
#Put them in astropy
xAP=SkyCoord(ra=xLonLat[0]*deg,dec=xLonLat[1]*deg,frame=FK5(equinox=equinox))
yAP=SkyCoord(ra=yLonLat[0]*deg,dec=yLonLat[1]*deg,frame=FK5(equinox=equinox))
zAP=SkyCoord(ra=zLonLat[0]*deg,dec=zLonLat[1]*deg,frame=FK5(equinox=equinox))
#Precess
xpAP=xAP.transform_to(FK5(equinox=targetEquinox))
ypAP=yAP.transform_to(FK5(equinox=targetEquinox))
zpAP=zAP.transform_to(FK5(equinox=targetEquinox))
#Go back to vectors
xp=dir2vec(theta=xpAP.ra.degree, phi=xpAP.dec.degree, lonlat=True)
yp=dir2vec(theta=ypAP.ra.degree, phi=ypAP.dec.degree, lonlat=True)
zp=dir2vec(theta=zpAP.ra.degree, phi=zpAP.dec.degree, lonlat=True)
#Go back to target coordinates
xp=rCoord(xp)
yp=rCoord(yp)
zp=rCoord(zp)
#Perform final rotation from argument rot
rf = Rotator(rot=rot)
xp=array(rf(xp))
yp=array(rf(yp))
zp=array(rf(zp))
#Get Euler angles
if fabs(zp[0])==1:
alpha=0.0
beta=zp[0]*pi/2
gamma=arctan2(xp[1],xp[2])
else:
alpha=arctan2(yp[0],xp[0])
beta=arcsin(zp[0])
gamma=arctan2(zp[1],zp[2])
return (rad2deg(alpha),rad2deg(beta),rad2deg(gamma))
def vec2xy(self, vx, vy=None, vz=None, direct=False):
if not direct:
theta,phi=R.vec2dir(self.rotator(vx,vy,vz))
else:
theta,phi=R.vec2dir(vx,vy,vz)
flip = self._flip
# set phi in [-pi,pi]
x = flip*((phi+pi)%(2*pi)-pi)
x /= dtor # convert in degree
y = pi/2. - theta
y /= dtor # convert in degree
return x,y
def vec2xy(self, vx, vy=None, vz=None, direct=False):
if not direct:
theta, phi = R.vec2dir(self.rotator(vx, vy, vz))
else:
theta, phi = R.vec2dir(vx, vy, vz)
flip = self._flip
# set phi in [-pi,pi]
x = flip * ((phi + pi) % (2 * pi) - pi)
x /= dtor # convert in degree
y = pi / 2. - theta
y /= dtor # convert in degree
return x, y
def precess(ra,dec,equinox,targetEquinox):
#Function to check that the above one actually works
vec=dir2vec(ra,dec,lonlat=True)
R=Rotator(rot=EulerAngles(equinox,targetEquinox))
vec=R(vec)
[oRA,oDec]=vec2dir(vec,lonlat=True)
while oRA<0:
oRA = oRA+360
return (oRA,oDec)
def xy2ang(self, x, y=None, lonlat=False, direct=False):
vec = self.xy2vec(x,y,direct=direct)
return R.vec2dir(vec,lonlat=lonlat)
def xy2ang(self, x, y=None, lonlat=False, direct=False):
vec = self.xy2vec(x, y, direct=direct)
return R.vec2dir(vec, lonlat=lonlat)