def finiteTranslateOffset(fareyVector, N, P, Q):
'''
Translate offset required when mapping Farey vectors to finite angles
Returns translate offset and perp Boolean flag pair
Wraps function from Farey module
'''
return farey.finiteTranslateOffset(fareyVector, N, P, Q)
def finiteProjection(projection, angle, P, Q, N, center=False):
'''
Convert a Mojette projection taken at angle into a finite (FRT) projection.
'''
dyadic = True
if N % 2 == 1: # if odd, assume prime
dyadic = False
shiftQ = int(N / 2.0 + 0.5) - int(Q / 2.0 + 0.5)
shiftP = int(N / 2.0 + 0.5) - int(P / 2.0 + 0.5)
finiteProj = np.zeros(N)
p, q = farey.get_pq(angle)
m, inv = farey.toFinite(angle, N)
# print "p:", p, "q:", q, "m:", m, "inv:", inv
translateOffset, perp = farey.finiteTranslateOffset(angle, N, P, Q)
angleSign = p * q
if dyadic:
for translate, bin in enumerate(projection):
if angleSign >= 0 and perp: #Reverse for perp
translateMojette = translateOffset - translate
else:
translateMojette = translate - translateOffset
translateFinite = (inv * translateMojette) % N
if center:
translateFinite = (translateFinite + shiftQ + m *
(N - shiftP)) % N
finiteProj[translateFinite] += bin
else:
for translate, bin in enumerate(projection):
if angleSign >= 0 and perp: #Reverse for perp
translateMojette = int(translateOffset) - int(translate)
else:
translateMojette = int(translate) - int(translateOffset)
if translateMojette < 0:
translateFinite = (N - (inv * abs(translateMojette)) % N) % N
else:
translateFinite = (inv * translateMojette
) % N #has issues in C, may need checking
if center:
translateFinite = (translateFinite + shiftQ + m *
(N - shiftP)) % N
finiteProj[translateFinite] += bin
return finiteProj
def angleSetSliceCoordinates(angles, P, Q, N, center=False):
'''
Compute the 2D coordinates of each translate (in NxN DFT space) of every projection having angle in angles.
Returns a list of u, v coordinate arrays [[u_0[...],v_0[...]], [u_1[...],v_1[...]], ...] per angle
'''
coords = []
translateOffset = 0
translateMojette = 0
translateFinite = 0
m = 0
offset = 0.0
if center:
offset = N / 2.0
for index, angle in enumerate(angles):
u = []
v = []
coordinateList = []
p = int(angle.imag)
q = int(angle.real)
angleSign = p * q
m, inv = farey.toFinite(angle, N)
translateOffset, perp = farey.finiteTranslateOffset(angle, N)
B = projectionLength(angle, P, Q)
for translate in range(0, B):
if angleSign >= 0 and perp: #Reverse for perp
translateMojette = translateOffset - translate
else:
translateMojette = translate - translateOffset
translateFinite = (inv * translateMojette
) % N #has issues in C, may need checking
# frtSpace[m][translateFinite] += bin
u.append((translateFinite + offset) % N)
v.append((m * translateFinite + offset) % N)
coordinateList.append(u)
coordinateList.append(v)
coords.append(coordinateList)
return coords