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 drawLines(pw, pointLists=[],
netStyle = None, netNDiv = 12, netAlpha = 0.5, rMat=None,
southern=False, invertFromSouthern=True,
origin=(0.,0.), r=1.0):
x0, y0 = origin
lines = pw.a.get_lines()
for line in lines:
line.remove()
ringAngs = num.linspace(0,num.pi*2.,181)
if netStyle:
arcAngsM = num.linspace(-num.pi/2.,num.pi/2.,91)
arcAngsL = num.linspace(0, num.pi, 181)
rMat_yDiv = ors.RotInv(-num.pi/netNDiv, [0,1,0]).toMatrix()
pw(r*num.cos(ringAngs)+x0,r*num.sin(ringAngs)+y0,style='k-')
if netStyle:
nVMerid = num.vstack( ( num.cos(arcAngsM), num.sin(arcAngsM), num.zeros(len(arcAngsM)) ) )
for iDiv in range(netNDiv-1):
nVMerid = num.dot(rMat_yDiv, nVMerid)
eaProj = n2eap(nVMerid, flip=False)
pw(r*eaProj[0,:]+x0, r*eaProj[1,:]+y0, alpha=netAlpha, style=netStyle)
for latAng in num.pi/netNDiv*num.arange(1,netNDiv):
polZ = num.cos(latAng)
polR = num.sin(latAng)
nVLat = num.vstack( ( polR*num.cos(arcAngsL), polZ*num.ones(len(arcAngsL)), polR*num.sin(arcAngsL)) )
eaProj = n2eap(nVLat, flip=False)
pw(r*eaProj[0,:]+x0, r*eaProj[1,:]+y0, alpha=netAlpha, style=netStyle)
'done with drawing net'
for points, pwKWArgs in pointLists:
nVecs = matrixutil.unitVector(points)
if rMat is not None:
'rotate as did elsewhere'
nVecs = num.dot(rMat, nVecs)
bNVecsS = nVecs[2,:] < 0
if southern:
nVecsS = nVecs[:,bNVecsS]
nVecsS = fromSouthern(nVecsS, invertFromSouthern)
eaProj = n2eap(nVecsS, flip=False)
pw(r*eaProj[0,:]+x0, r*eaProj[1,:]+y0, **pwKWArgs)
else:
nVecsN = nVecs[:,num.logical_not(bNVecsS)]
eaProj = n2eap(nVecsN, flip=False)
pw(r*eaProj[0,:]+x0, r*eaProj[1,:]+x0, **pwKWArgs)
'done with pointLists'
return
def drawLines(pw,
pointLists=[],
netStyle=None,
netNDiv=12,
netAlpha=0.5,
rMat=None,
southern=False,
invertFromSouthern=True,
origin=(0., 0.),
r=1.0):
x0, y0 = origin
lines = pw.a.get_lines()
for line in lines:
line.remove()
ringAngs = num.linspace(0, num.pi * 2., 181)
if netStyle:
arcAngsM = num.linspace(-num.pi / 2., num.pi / 2., 91)
arcAngsL = num.linspace(0, num.pi, 181)
rMat_yDiv = ors.RotInv(-num.pi / netNDiv, [0, 1, 0]).toMatrix()
pw(r * num.cos(ringAngs) + x0, r * num.sin(ringAngs) + y0, style='k-')
if netStyle:
nVMerid = num.vstack(
(num.cos(arcAngsM), num.sin(arcAngsM), num.zeros(len(arcAngsM))))
for iDiv in range(netNDiv - 1):
nVMerid = num.dot(rMat_yDiv, nVMerid)
eaProj = n2eap(nVMerid, flip=False)
pw(r * eaProj[0, :] + x0,
r * eaProj[1, :] + y0,
alpha=netAlpha,
style=netStyle)
for latAng in num.pi / netNDiv * num.arange(1, netNDiv):
polZ = num.cos(latAng)
polR = num.sin(latAng)
nVLat = num.vstack(
(polR * num.cos(arcAngsL), polZ * num.ones(len(arcAngsL)),
polR * num.sin(arcAngsL)))
eaProj = n2eap(nVLat, flip=False)
pw(r * eaProj[0, :] + x0,
r * eaProj[1, :] + y0,
alpha=netAlpha,
style=netStyle)
'done with drawing net'
for points, pwKWArgs in pointLists:
nVecs = matrixutil.unitVector(points)
if rMat is not None:
'rotate as did elsewhere'
nVecs = num.dot(rMat, nVecs)
bNVecsS = nVecs[2, :] < 0
if southern:
nVecsS = nVecs[:, bNVecsS]
nVecsS = fromSouthern(nVecsS, invertFromSouthern)
eaProj = n2eap(nVecsS, flip=False)
pw(r * eaProj[0, :] + x0, r * eaProj[1, :] + y0, **pwKWArgs)
else:
nVecsN = nVecs[:, num.logical_not(bNVecsS)]
eaProj = n2eap(nVecsN, flip=False)
pw(r * eaProj[0, :] + x0, r * eaProj[1, :] + x0, **pwKWArgs)
'done with pointLists'
return