def createMesh(self, ctrs, fd, frame, plot=False):
self.frame = frame
pfix = None
# Extract bounding box
xmin, ymin, xmax, ymax = self.bbox
if pfix is not None:
pfix = np.array(pfix, dtype='d')
#1. Set up initial points
x, y = np.mgrid[xmin:(xmax + self.h0):self.h0,
ymin:(ymax + self.h0 * np.sqrt(3) / 2):self.h0 *
np.sqrt(3) / 2]
x[:, 1::2] += self.h0 / 2 # Shift even rows
p = np.vstack((x.flat, y.flat)).T # List of node coordinates
# 2. Remove points outside the region, apply the rejection method
a = fd(p)
p = p[np.where(a < self.geps)] # Keep only d<0 points
r0 = 1 / self.fh(p)**2 # Probability to keep point
p = p[np.random.random(p.shape[0]) < r0 / r0.max()] # Rejection method
if pfix is not None:
p = ml.setdiff_rows(p, pfix) # Remove duplicated nodes
pfix = ml.unique_rows(pfix)
nfix = pfix.shape[0]
p = np.vstack((pfix, p)) # Prepend fix points
else:
nfix = 0
N = p.shape[0] # Number of points N
self.N = N
count = 0
pold = float('inf') # For first iteration
################################################################################
#Mesh creation
################################################################################
while count < self.maxiter:
print 'DistMesh create count: %d/%d' % (count, self.maxiter)
count += 1
# 3. Retriangulation by the Delaunay algorithm
dist = lambda p1, p2: np.sqrt(((p1 - p2)**2).sum(1))
if (dist(p, pold) /
self.h0).max() > self.ttol: # Any large movement?
pold = p.copy() # Save current positions
self.delaunay = spspatial.Delaunay(p)
t = self.delaunay.vertices # List of triangles
pmid = p[t].sum(1) / 3 # Compute centroids
t = t[fd(pmid) < -self.geps] # Keep interior triangles
# 4. Describe each bar by a unique pair of nodes
bars = np.vstack((t[:, [0, 1]], t[:, [1, 2]],
t[:, [2, 0]])) # Interior bars duplicated
bars.sort(axis=1)
bars = ml.unique_rows(bars) # Bars as node pairs
#Plot
fc = frame.copy()
if frame is not None:
drawGrid(fc, p, bars)
if plot:
cv2.imshow('Initial mesh', fc)
k = cv2.waitKey(30) & 0xff
if k == 27:
break
# 6. Move mesh points based on bar lengths L and forces F
barvec = p[bars[:, 0]] - p[bars[:, 1]] # List of bar vectors
L = np.sqrt((barvec**2).sum(1)) # L = Bar lengths
hbars = self.fh(p[bars].sum(1) / 2)
L0 = 1.5 * self.h0 * np.ones_like(L)
#(hbars*Fscale
#*np.sqrt((L**2).sum()/(hbars**2).sum())) # L0 = Desired lengths
F = self.k * (L0 - L)
F[F <
0] = 0 #F[F<0]*.5#0 # Bar forces (scalars)
Fvec = F[:, None] / L[:, None].dot(
[[1, 1]]) * barvec # Bar forces (x,y components)
Ftot = ml.dense(bars[:, [0, 0, 1, 1]],
np.repeat([[0, 1, 0, 1]], len(F), axis=0),
np.hstack((Fvec, -Fvec)),
shape=(N, 2))
Ftot[:nfix] = 0 # Force = 0 at fixed points
p += self.deltat * Ftot # Update node positions
# 7. Bring outside points back to the boundary
d = fd(p)
ix = d > 0 # Find points outside (d>0)
ddeps = 1e-1
for idx in range(10):
if ix.any():
dgradx = (fd(p[ix] + [ddeps, 0]) -
d[ix]) / ddeps # Numerical
dgrady = (fd(p[ix] + [0, ddeps]) -
d[ix]) / ddeps # gradient
dgrad2 = dgradx**2 + dgrady**2
p[ix] -= (d[ix] * np.vstack(
(dgradx, dgrady)) / dgrad2).T # Project
# 8. Termination criterion: All interior nodes move less than dptol (scaled)
if (np.sqrt((self.deltat * Ftot[d < -self.geps]**2).sum(1)) /
self.h0).max() < self.dptol:
break
self.p = p
self.t = t
self.bars = bars
self.L = L
def createMesh(self, ctrs, fd, frame, plot = False):
self.frame = frame
pfix = None
# Extract bounding box
xmin, ymin, xmax, ymax = self.bbox
if pfix is not None:
pfix = np.array(pfix, dtype='d')
#1. Set up initial points
x, y = np.mgrid[xmin:(xmax+self.h0):self.h0,
ymin:(ymax+self.h0*np.sqrt(3)/2):self.h0*np.sqrt(3)/2]
x[:, 1::2] += self.h0/2 # Shift even rows
p = np.vstack((x.flat, y.flat)).T # List of node coordinates
# 2. Remove points outside the region, apply the rejection method
a = fd(p)
p = p[np.where(a<self.geps)] # Keep only d<0 points
r0 = 1/self.fh(p)**2 # Probability to keep point
p = p[np.random.random(p.shape[0])<r0/r0.max()] # Rejection method
if pfix is not None:
p = ml.setdiff_rows(p, pfix) # Remove duplicated nodes
pfix = ml.unique_rows(pfix); nfix = pfix.shape[0]
p = np.vstack((pfix, p)) # Prepend fix points
else:
nfix = 0
N = p.shape[0] # Number of points N
self.N = N
count = 0
pold = float('inf') # For first iteration
################################################################################
#Mesh creation
################################################################################
while count < self.maxiter:
#print count
count += 1
# 3. Retriangulation by the Delaunay algorithm
dist = lambda p1, p2: np.sqrt(((p1-p2)**2).sum(1))
if (dist(p, pold)/self.h0).max() > self.ttol: # Any large movement?
pold = p.copy() # Save current positions
self.delaunay = spspatial.Delaunay(p)
t = self.delaunay.vertices # List of triangles
pmid = p[t].sum(1)/3 # Compute centroids
t = t[fd(pmid) < -self.geps] # Keep interior triangles
# 4. Describe each bar by a unique pair of nodes
bars = np.vstack((t[:, [0,1]],
t[:, [1,2]],
t[:, [2,0]])) # Interior bars duplicated
bars.sort(axis=1)
bars = ml.unique_rows(bars) # Bars as node pairs
#Plot
fc = frame.copy()
if frame is not None:
drawGrid(fc, p, bars)
if plot:
cv2.imshow('Initial mesh',fc)
k = cv2.waitKey(30) & 0xff
if k == 27:
break
# 6. Move mesh points based on bar lengths L and forces F
barvec = p[bars[:,0]] - p[bars[:,1]] # List of bar vectors
L = np.sqrt((barvec**2).sum(1)) # L = Bar lengths
hbars = self.fh(p[bars].sum(1)/2)
L0 = 1.5*self.h0*np.ones_like(L); #(hbars*Fscale
#*np.sqrt((L**2).sum()/(hbars**2).sum())) # L0 = Desired lengths
F = self.k*(L0-L)
F[F<0] = 0#F[F<0]*.5#0 # Bar forces (scalars)
Fvec = F[:,None]/L[:,None].dot([[1,1]])*barvec # Bar forces (x,y components)
Ftot = ml.dense(bars[:,[0,0,1,1]],
np.repeat([[0,1,0,1]], len(F), axis=0),
np.hstack((Fvec, -Fvec)),
shape=(N, 2))
Ftot[:nfix] = 0 # Force = 0 at fixed points
p += self.deltat*Ftot # Update node positions
# 7. Bring outside points back to the boundary
d = fd(p); ix = d>0 # Find points outside (d>0)
ddeps = 1e-1
for idx in range(10):
if ix.any():
dgradx = (fd(p[ix]+[ddeps,0])-d[ix])/ddeps # Numerical
dgrady = (fd(p[ix]+[0,ddeps])-d[ix])/ddeps # gradient
dgrad2 = dgradx**2 + dgrady**2
p[ix] -= (d[ix]*np.vstack((dgradx, dgrady))/dgrad2).T # Project
# 8. Termination criterion: All interior nodes move less than dptol (scaled)
if (np.sqrt((self.deltat*Ftot[d<-self.geps]**2).sum(1))/self.h0).max() < self.dptol:
break
self.p = p
self.t = t
self.bars = bars
self.L = L
def plot(self):
fc = self.frame.copy()
if self.bars is not None:
drawGrid(fc, self.p, self.bars)
cv2.imshow('Current mesh', fc)
k = cv2.waitKey(30) & 0xff
def plot(self):
fc = self.frame.copy()
if self.bars is not None:
drawGrid(fc, self.p, self.bars)
cv2.imshow('Current mesh',fc)
k = cv2.waitKey(30) & 0xff
