def matchArc(arc):
"""Take the raytraced arc, negate the dispersion direction, and
compute the translation and rotation transformations to
match the two spectra
"""
#Create the second arc by negating the dispersion direction
sh = np.shape(arc)
arc = [arc[0], arc[1], np.zeros(sh[1]), np.ones(sh[1])]
arc2 = np.copy(arc)
arc2[1] = -arc2[1]
#Transform second arc by pi/2
r = tr.rotation_matrix(pi / 2, [0, 0, 1])
arc2 = np.dot(r, arc2)
#Get gradients
dx = np.diff(arc2[0])[0]
gr = np.gradient(arc2[1], dx)
pdb.set_trace()
#Apply rotation to match slopes
angle = pi / 2 + np.arctan(gr[-1]) + np.arctan(gr[0])
print angle
r2 = tr.rotation_matrix(-angle, [0, 0, 1])
arc3 = np.dot(r2, arc2)
#Apply translation to match
pdb.set_trace()
## arc3[0] = arc3[0] + (arc[0][-1]-arc3[0][0])
## arc3[1] = arc3[1] + (arc[1][-1]-arc3[1][0])
t = tr.translation_matrix([(arc[0][-1]-arc3[0][0]),\
(arc[1][-1]-arc3[1][0]),\
0.])
arc3 = np.dot(t, arc3)
tra = np.dot(t, (np.dot(r2, r)))
#Get even closer
dist = np.sqrt((arc[0][0] - arc3[0][-1])**2 + (arc[1][0] - arc3[1][-1])**2)
lever = np.sqrt((arc[0][0] - arc[0][-1])**2 + (arc[1][0] - arc[1][-1])**2)
angle2 = dist / lever
new = tr.rotation_matrix(angle2, [0, 0, 1],
point=[arc3[0][0], arc3[1][0], 0])
tra2 = np.dot(new, tra)
#Return transformation
return tra2, angle, angle2, new, tra
def transformCoords_wMag(x,y,tx,ty,theta,mag):
"""Transforms coordinates x,y by magnifying x,y by a constant factor,
then translating tx,ty and rotating theta about x
Returns: x,y of new coords
"""
mag_x,mag_y = x*mag,y*mag
trans = tr.translation_matrix([tx,ty,0])
rot = tr.rotation_matrix(theta,[0,0,1],point=[np.mean(x),np.mean(y),0])
pos0 = np.array((mag_x,mag_y,np.repeat(0.,np.size(x)),np.repeat(1.,np.size(x))))
pos1 = np.dot(trans,np.dot(rot,pos0))
return pos1[0],pos1[1]
def transformCoords(x,y,tx,ty,theta):
"""Transforms coordinates x,y by translating tx,ty
and rotation theta about x
Returns: x,y of new coords
"""
trans = tr.translation_matrix([tx,ty,0])
rot = tr.rotation_matrix(theta,[0,0,1],point=[np.mean(x),np.mean(y),0])
pos0 = np.array((x,y,np.repeat(0.,np.size(x)),np.repeat(1.,np.size(x))))
pos1 = np.dot(trans,np.dot(rot,pos0))
return pos1[0],pos1[1]
def makeLayout(arc, sepAngle):
tra, angle = matchArc(arc) #Get nominal transformation for paired petal
tra2 = np.dot(tr.rotation_matrix(angle / 2, [0, 0, 1]), tra)
tra1 = tr.rotation_matrix(angle / 2, [0, 0, 1])
#Create the second arc by negating the dispersion direction
sh = np.shape(arc)
arc = [arc[0], arc[1], np.zeros(sh[1]), np.ones(sh[1])]
arc2 = np.copy(arc)
arc2[1] = -arc2[1]
#Apply transformations
arc2 = np.dot(tra2, arc2)
arc1 = np.dot(tra1, arc)
#Find center of second arc
xc, yc = fit.circle(arc2[0], arc2[1], 0, 0)[0]
#Rotate each petal about this point
tra1 = np.dot(tr.rotation_matrix(sepAngle, [0, 0, 1], point=[xc, yc, 0]),
tra1)
tra2 = np.dot(tr.rotation_matrix(-sepAngle, [0, 0, 1], point=[xc, yc, 0]),
tra2)
#Add translation to second petal
tra2 = np.dot(tr.translation_matrix([10 / np.sqrt(2), 10 / np.sqrt(2), 0]),
tra2)
#Now plot the petals with the correct translations
pet1 = plotPetal(arc[0], arc[1], tra=tra1, color='blue')
pet2 = plotPetal(arc[0], -arc[1], tra=tra2, color='red')
#Plot dashed line between corners closest to arcs
x1, x2, y1, y2 = pet1[1][0][3], pet2[1][0][2], pet1[1][1][3], pet2[1][1][2]
plt.plot([pet1[1][0][3], pet2[1][0][2]], [pet1[1][1][3], pet2[1][1][2]],
'k--')
def collectFocalPlaneRays(z):
tra2 = np.dot(tr.translation_matrix([40,-100,0]),\
tr.rotation_matrix(pi/2,[0,0,1,0]))
rot2 = tr.rotation_matrix(pi / 2, [0, 0, 1, 0])
tra3 = np.dot(tr.translation_matrix([1000,-1000,0]),\
tr.rotation_matrix(-pi/2,[0,0,1,0]))
rot3 = tr.rotation_matrix(-pi / 2, [0, 0, 1, 0])
tra4 = np.dot(tr.translation_matrix([1020,920,0]),\
tr.rotation_matrix(pi,[0,0,1,0]))
rot4 = tr.rotation_matrix(pi, [0, 0, 1, 0])
f = open(
'/home/rallured/Dropbox/Arcus/Raytrace/FocalPlaneLayout/160412_Rays.pkl',
'r')
rays = pickle.load(f)
f.close()
rays2 = np.copy(rays)
rays2 = [rays2[0],rays2[1],-rays2[2],rays2[3],\
rays2[4],-rays2[5],rays2[6],\
rays2[7],rays2[8],rays2[9]]
rays3 = np.copy(rays)
rays3 = [rays3[0],rays3[1],-rays3[2],rays3[3],\
rays3[4],-rays3[5],rays3[6],\
rays3[7],rays3[8],rays3[9]]
rays4 = np.copy(rays)
tran.itransform(rays2, 40, -100, 0, 0, 0, pi / 2)
tran.itransform(rays3, 1000, 1000, 0, 0, 0, -pi / 2)
tran.itransform(rays4, 1020, 920, 0, 0, 0, pi)
#Plot to make sure
plt.plot(rays[1], rays[2], '.')
plt.plot(rays2[1], rays2[2], '.')
plt.plot(rays3[1], rays3[2], '.')
plt.plot(rays4[1], rays4[2], '.')
#Transform everything up
r = [rays, rays2, rays3, rays4]
[tran.transform(ri, 0, 0, z, 0, 0, 0) for ri in r]
[surf.flat(ri) for ri in r]
plt.figure()
[plt.plot(ri[1], ri[2], '.') for ri in r]