def endOfIteration(self):
self.iter += 1
if self.iter % self.saveRate == 0:
(obj1, self.xt, self.at, self.yt, self.vt) = self.objectiveFunDef(self.rhot, withTrajectory=True)
for k in range(self.nTarg):
self.fvDef[k].updateVertices(np.squeeze(self.xt[(k + 1) * self.Tsize1, :, :]))
(xt, at, yt, vt, zt, Jt) = evol.secondOrderFiberEvolution(
self.x0,
self.a0,
self.y0,
self.v0,
self.rhot,
self.param.KparDiff,
withPointSet=self.fv0Fine.vertices,
withJacobian=True,
)
fvDef = surfaces.Surface(surf=self.fv0Fine)
for kk in range(self.Tsize + 1):
fvDef.updateVertices(np.squeeze(zt[kk, :, :]))
fvDef.saveVTK(
self.outputDir + "/" + self.saveFile + str(kk) + ".vtk", scalars=Jt[kk, :], scal_name="Jacobian"
)
vn = np.squeeze(vt[kk, ...])
vn = vn / np.sqrt((vn ** 2).sum(axis=1))[:, np.newaxis]
savePoints(self.outputDir + "/fiber_" + self.saveFile + str(kk) + ".vtk", yt[kk, ...], vector=vn)
# self.fvDef.saveVTK(self.outputDir +'/'+ self.saveFile+str(kk)+'.vtk', scalars = self.idx, scal_name='Labels')
else:
(obj1, self.xt, self.at, self.yt, self.vt) = self.objectiveFunDef(self.rhot, withTrajectory=True)
for k in range(self.nTarg):
self.fvDef[k].updateVertices(np.squeeze(self.xt[(k + 1) * self.Tsize1, :, :]))
def objectiveFunDef(self, rhot, withTrajectory=False, withJacobian=False, Init=None):
if Init == None:
x0 = self.x0
y0 = self.y0
v0 = self.v0
a0 = self.a0
else:
x0 = Init[0]
y0 = Init[2]
v0 = Init[3]
a0 = Init[1]
param = self.param
timeStep = 1.0 / self.Tsize
dim2 = self.dim ** 2
# print a0.shape
if withJacobian:
(xt, at, yt, vt, Jt) = evol.secondOrderFiberEvolution(
x0, a0, y0, v0, rhot, param.KparDiff, withJacobian=True
)
else:
(xt, at, yt, vt) = evol.secondOrderFiberEvolution(x0, a0, y0, v0, rhot, param.KparDiff)
# print xt[-1, :, :]
# print obj
obj = 0
for t in range(self.Tsize):
v = np.squeeze(vt[t, :, :])
rho = np.squeeze(rhot[t, :])
obj = obj + timeStep * ((rho ** 2) * (v ** 2).sum(axis=1)).sum() / 2
# print xt.sum(), at.sum(), obj
if withJacobian:
return obj, xt, at, yt, vt, Jt
elif withTrajectory:
return obj, xt, at, yt, vt
else:
return obj
def compute(createSurfaces=True):
if createSurfaces:
[x,y,z] = np.mgrid[0:200, 0:200, 0:200]/100.
ay = np.fabs(y-1)
az = np.fabs(z-1)
ax = np.fabs(x-0.5)
s2 = np.sqrt(2)
c1 = np.sqrt(0.06)
c2 = np.sqrt(0.045)
c3 = 0.1
I1 = np.minimum(c1**2 - (ax**2 + 0.5*ay**2 + az**2), np.minimum((ax**2 + 0.5*ay**2 + az**2)-c2**2, 1+c3-y))
fv1 = Surface() ;
fv1.Isosurface(I1, value = 0, target=1000, scales=[1, 1, 1], smooth=0.01)
#return fv1
#s1 = 1.375
#s2 = 2
s1 = 1.1
s2 = 1.2
p = 1.75
I1 = np.minimum(c1**p/s1 - ((ax**p + 0.5*ay**p + az**p)), np.minimum((s2*ax**p + s2*0.5*ay**p + s2*az**p)-c2**p/s1, 1+c3/s1-y))
fv2 = Surface() ;
fv2.Isosurface(I1, value = 0, target=1000, scales=[1, 1, 1], smooth=0.01)
fv2.vertices[:,1] += 15 - 15/s1
s1 *= 1.1
s2 *= 1.2
I1 = np.minimum(c1**p/s1 - ((ax**p + 0.5*ay**p + az**p)), np.minimum((s2*ax**p + s2*0.5*ay**p + s2*az**p)-c2**p/s1, 1+c3/s1-y))
fv3 = Surface() ;
fv3.Isosurface(I1, value = 0, target=1000, scales=[1, 1, 1], smooth=0.01)
fv3.vertices[:,1] += 15 - 15/s1
fv1.saveVTK('/Users/younes/Development/Results/Fibers/fv1.vtk')
fv2.saveVTK('/Users/younes/Development/Results/Fibers/fv2.vtk')
fv3.saveVTK('/Users/younes/Development/Results/Fibers/fv3.vtk')
else:
fv1 = Surface(filename='/Users/younes/Development/Results/Fibers/fv1.vtk')
fv2 = Surface(filename='/Users/younes/Development/Results/Fibers/fv2.vtk')
fv3 = Surface(filename='/Users/younes/Development/Results/Fibers/fv3.vtk')
## Long axis is 0y
V1 = fv1.vertices/100 - [0,1,1]
N1 = fv1.computeVertexNormals()
sel0 = V1[:,1] < 0.95*V1[:,1].max()
I0 = np.nonzero(sel0)
I0 = I0[0]
V1 = V1[I0, :]
N1 = N1[I0, :]
QNN = (N1[:,0]-0.5)**2 + 0.5*N1[:,1]**2 + N1[:,2]**2
QVV = (V1[:,0]-0.5)**2 + 0.5*V1[:,1]**2 + V1[:,2]**2
QNV = (N1[:,0]-0.5)*(V1[:,0]-0.5) + 0.5*N1[:,1]*V1[:,1] + N1[:,2]*V1[:,2]
#exterior wall
sel1 = np.logical_and(np.fabs(QVV-0.06) < 0.01, (np.fabs(N1[:,1]) < 0.8))
I1 = np.nonzero(sel1)
I1= I1[0]
V11 = V1[I1, :]
N11 = N1[I1, :]
a = np.zeros(len(I1))
a = (-QNV[I1] - np.sqrt(QNV[I1]**2 - QNN[I1]*(QVV[I1]-0.0525)))/QNN[I1]
N = V1.shape[0]
M = V1.shape[0] + len(I1)
#M = M1 + len(I1)
y0 = np.zeros([M,3])
v0 = np.zeros([M,3])
nz = np.zeros([N, 3])
nz2 = np.zeros([N, 3])
y0[0:N, :] = V1
#y0[N:M1, :] = V11 + 0.5*a[:,np.newaxis]*N11
y0[N:M, :] = V11 + a[:,np.newaxis]*N11
nz[:, 0] = -N1[:, 2]
nz[:, 2] = N1[:, 0]
nz2[:,0] = N1[:,0]*N1[:,1]
nz2[:,1] = -(N1[:,0]**2 + N1[:,2]**2)
nz2[:,2] = N1[:,2]*N1[:,1]
nz = nz / (1e-5 + np.sqrt((nz**2).sum(axis=1)[:,np.newaxis]))
nz2 = nz2 / (1e-5 + np.sqrt((nz2**2).sum(axis=1)[:,np.newaxis]))
theta = 2*np.pi/3
psi = 0 #np.pi/12
c = np.cos(theta)
s = np.sin(theta)
c0 = np.cos(psi)
s0 = np.sin(psi)
v0[0:N, :] = -c*nz - s*nz2
v0[I1,:] *= -1
#v0[I1, :] += 2*s*nz2[I1,:]
v0[N:M, :] = nz[I1, :]
#v0[M1:M, :] = -c*nz[I1,:] + s*nz2[I1,:]
v0[0:N,:] = c0*v0[0:N, :] - s0*N1
K1 = Kernel(name='laplacian', sigma = 10.0)
y0 = 100*(y0+[0,1,1])
pointSets.savePoints('/Users/younes/Development/Results/Fibers/Ellipses/fibers.vtk', y0, vector=v0)
sm = SurfaceMatchingParam(timeStep=0.1, KparDiff=K1, sigmaDist=5, sigmaError=1., errorType='measure')
f = SurfaceMatching(Template=fv1, Target=[fv2,fv3], Fiber=(y0,v0), outputDir='/Users/younes/Development/Results/Fibers/Ellipses',param=sm, testGradient=False,
#subsampleTargetSize = 500,
maxIter=1000)
xt, at, yt, vt = pointEvolution.secondOrderFiberEvolution(fv1.vertices, np.zeros(y0.shape), y0, v0, -10*np.ones([10, y0.shape[0]]), K1)
fvDef = Surface(surf=fv1)
for k in range(xt.shape[0]):
fvDef.updateVertices(xt[k, ...])
fvDef.saveVTK('/Users/younes/Development/Results/Fibers/fvDef'+str(k)+'.vtk')
#return
f.optimizeMatching()
return f, f23
def __init__(
self,
Template=None,
Target=None,
Fiber=None,
fileTempl=None,
fileTarg=None,
fileFiber=None,
param=None,
initialMomentum=None,
maxIter=1000,
regWeight=1.0,
verb=True,
subsampleTargetSize=-1,
testGradient=True,
saveFile="evolution",
outputDir=".",
):
if Template == None:
if fileTempl == None:
print "Please provide a template surface"
return
else:
self.fv0 = surfaces.Surface(filename=fileTempl)
else:
self.fv0 = surfaces.Surface(surf=Template)
if Target == None:
if fileTarg == None:
print "Please provide a list of target surfaces"
return
else:
self.fv1 = []
for f in fileTarg:
self.fv1.append(surfaces.Surface(filename=f))
else:
self.fv1 = []
for s in Target:
self.fv1.append(surfaces.Surface(surf=s))
if Fiber == None:
if fileFiber == None:
print "Please provide fiber structure"
return
else:
(self.y0, self.v0) = read3DVectorField(fileFiber)
else:
self.y0 = np.copy(Fiber[0])
self.v0 = np.copy(Fiber[1])
# print np.fabs(self.fv1.surfel-self.fv0.surfel).max()
self.nTarg = len(self.fv1)
self.saveRate = 10
self.iter = 0
self.outputDir = outputDir
if not os.access(outputDir, os.W_OK):
if os.access(outputDir, os.F_OK):
print "Cannot save in " + outputDir
return
else:
os.mkdir(outputDir)
self.dim = self.fv0.vertices.shape[1]
self.maxIter = maxIter
self.verb = verb
self.testGradient = testGradient
self.regweight = regWeight
if param == None:
self.param = SurfaceMatchingParam()
else:
self.param = param
self.fv0Fine = surfaces.Surface(surf=self.fv0)
if subsampleTargetSize > 0:
self.fv0.Simplify(subsampleTargetSize)
v0 = self.fv0.surfVolume()
for s in self.fv1:
v1 = s.surfVolume()
if v0 * v1 < 0:
s.flipFaces()
print "simplified template", self.fv0.vertices.shape[0]
self.x0 = self.fv0.vertices
self.fvDef = []
for k in range(self.nTarg):
self.fvDef.append(surfaces.Surface(surf=self.fv0))
self.npt = self.y0.shape[0]
self.Tsize1 = int(round(1.0 / self.param.timeStep))
self.Tsize = self.nTarg * self.Tsize1
self.rhot = np.zeros([self.Tsize, self.y0.shape[0]])
self.rhotTry = np.zeros([self.Tsize, self.y0.shape[0]])
if initialMomentum == None:
self.xt = np.tile(self.x0, [self.Tsize + 1, 1, 1])
self.a0 = np.zeros([self.y0.shape[0], self.x0.shape[1]])
self.at = np.tile(self.a0, [self.Tsize + 1, 1, 1])
self.yt = np.tile(self.y0, [self.Tsize + 1, 1, 1])
self.vt = np.tile(self.v0, [self.Tsize + 1, 1, 1])
else:
self.a0 = initialMomentum
(self.xt, self.at, self.yt, self.vt) = evol.secondOrderFiberEvolution(
self.x0, self.a0, self.y0, self.v0, self.rhot, self.param.KparDiff
)
self.obj = None
self.objTry = None
self.gradCoeff = self.fv0.vertices.shape[0]
self.saveFile = saveFile
self.fv0.saveVTK(self.outputDir + "/Template.vtk")
for k, s in enumerate(self.fv1):
s.saveVTK(self.outputDir + "/Target" + str(k) + ".vtk")
