def n2eap(nVectors, flip=True):
"""
unit vectors to equal-area projection
"""
nVecs = copy.deepcopy(nVectors)
nPnts = nVectors.shape[1]
retval = getMem((2, nPnts))
belowEquator, = num.where(nVecs[2, :] < -1e-4)
if len(belowEquator) > 0:
if flip:
nVecs[:, belowEquator] = -nVecs[:, belowEquator]
else:
'put on the equator'
nVecs[2, belowEquator] = 0.
# num.apply_along_axis(num.linalg.norm, 0, nVecs[0:2,belowEquator])
norms = num.sqrt(nVecs[0, belowEquator] * nVecs[0, belowEquator] +
nVecs[1, belowEquator] * nVecs[1, belowEquator])
nVecs[0:2, belowEquator] = nVecs[0:2, belowEquator] / norms
r2 = nVecs[0, :] * nVecs[0, :] + nVecs[1, :] * nVecs[1, :]
r2pos = num.where(r2 > 0.)
n31 = 1.0 - num.abs(nVecs[2, :])
den = num.ones(nPnts)
den[r2pos] = num.sqrt(2.0 * r2[r2pos])
dist_np = num.zeros(nPnts)
dist_np = num.sqrt(r2 + n31 * n31) / den
retval = num.vstack((nVecs[0, :] * dist_np, nVecs[1, :] * dist_np)) # .T
return retval
def n2eap(nVectors, flip=True):
"""
unit vectors to equal-area projection
"""
nVecs = copy.deepcopy(nVectors)
nPnts = nVectors.shape[1]
retval = getMem((2,nPnts))
belowEquator, = num.where(nVecs[2,:] < -1e-4)
if len(belowEquator) > 0:
if flip:
nVecs[:,belowEquator] = -nVecs[:,belowEquator]
else:
'put on the equator'
nVecs[2,belowEquator] = 0.
# num.apply_along_axis(num.linalg.norm, 0, nVecs[0:2,belowEquator])
norms = num.sqrt( nVecs[0,belowEquator]*nVecs[0,belowEquator] + nVecs[1,belowEquator]*nVecs[1,belowEquator] )
nVecs[0:2,belowEquator] = nVecs[0:2,belowEquator] / norms
r2 = nVecs[0,:]*nVecs[0,:] + nVecs[1,:]*nVecs[1,:]
r2pos = num.where(r2 > 0.)
n31 = 1.0 - num.abs(nVecs[2,:])
den = num.ones(nPnts)
den[r2pos] = num.sqrt(2.0*r2[r2pos])
dist_np = num.zeros(nPnts)
dist_np = num.sqrt(r2 + n31*n31) / den
retval = num.vstack((nVecs[0,:] * dist_np, nVecs[1,:] * dist_np)) # .T
return retval
def n2sph(nVectors):
assert nVectors.shape[0] == 3, 'shape[0] not 3'
sph = arrayutil.getMem((2, nVectors.shape[1]))
for iVector in range(nVectors.shape[1]):
x = nVectors[0, iVector]
y = nVectors[1, iVector]
z = nVectors[2, iVector]
r = sqrt(x * x + y * y)
sph[0, iVector] = atan2(r, z)
sph[1, iVector] = atan2(y, x)
return sph
def n2sph(nVectors):
assert nVectors.shape[0] == 3, 'shape[0] not 3'
sph = arrayutil.getMem((2,nVectors.shape[1]))
for iVector in range(nVectors.shape[1]):
x = nVectors[0,iVector]
y = nVectors[1,iVector]
z = nVectors[2,iVector]
r = sqrt(x*x+y*y)
sph[0,iVector] = atan2(r,z)
sph[1,iVector] = atan2(y,x)
return sph
def sph2n(coords_sph):
'''convert from chi/eta spherical coordinates to normal vectors;
can use with coords from femODF.FemHemisphere
'''
assert coords_sph.shape[0] == 2, 'shape[0] not 2'
z = num.cos(coords_sph[0, :])
rho = num.sin(coords_sph[0, :])
x = rho * num.cos(coords_sph[1, :])
y = rho * num.sin(coords_sph[1, :])
# nVectors = arrayutil.toArray(num.vstack((x,y,z)))
nVectors = getMem((3, coords_sph.shape[1]))
nVectors[0, :] = x
nVectors[1, :] = y
nVectors[2, :] = z
return nVectors
def sph2n(coords_sph):
'''convert from chi/eta spherical coordinates to normal vectors;
can use with coords from femODF.FemHemisphere
'''
assert coords_sph.shape[0] == 2, 'shape[0] not 2'
z = num.cos(coords_sph[0,:])
rho = num.sin(coords_sph[0,:])
x = rho * num.cos(coords_sph[1,:])
y = rho * num.sin(coords_sph[1,:])
# nVectors = arrayutil.toArray(num.vstack((x,y,z)))
nVectors = getMem((3,coords_sph.shape[1]))
nVectors[0,:] = x
nVectors[1,:] = y
nVectors[2,:] = z
return nVectors