def plate_with_hole(size=.05):
fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1),
dm.dcircle(p,0,0,0.5))
fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5)
p, t = dm.distmesh2d(fd, fh, size, (-1,-1,1,1),
[(-1,-1),(-1,1),(1,-1),(1,1)])
return p, t
def plate_with_hole(size=.05):
fd = lambda p: dm.ddiff(dm.drectangle(p, -1, 1, -1, 1),
dm.dcircle(p, 0, 0, 0.5))
fh = lambda p: 0.05 + 0.3 * dm.dcircle(p, 0, 0, 0.5)
p, t = dm.distmesh2d(fd, fh, size, (-1, -1, 1, 1), [(-1, -1), (-1, 1),
(1, -1), (1, 1)])
return p, t
def naca0012_airfoil():
"""NACA0012 airfoil"""
hlead = 0.01
htrail = 0.04
hmax = 2
circx = 2
circr = 4
a = .12 / .2 * np.array([0.2969, -0.1260, -0.3516, 0.2843, -0.1036])
a0 = a[0]
a1 = np.hstack((a[5:0:-1], 0.0))
fd = lambda p: dm.ddiff(dm.dcircle(p, circx, 0, circr), (abs(
p[:, 1]) - np.polyval(a1, p[:, 0]))**2 - a0**2 * p[:, 0])
fh = lambda p: np.minimum(
np.minimum(hlead + 0.3 * dm.dcircle(p, 0, 0, 0), htrail + 0.3 * dm.
dcircle(p, 1, 0, 0)), hmax)
fixx = 1.0 - htrail * np.cumsum(1.3**np.arange(5))
fixy = a0 * np.sqrt(fixx) + np.polyval(a1, fixx)
fix = np.vstack(
(np.array([(circx - circr, 0), (circx + circr, 0), (circx, -circr),
(circx, circr), (0, 0), (1, 0)]), np.vstack(
(fixx, fixy)).T, np.vstack((fixx, -fixy)).T))
box = (circx - circr, -circr, circx + circr, circr)
h0 = min(hlead, htrail, hmax)
return dm.distmesh2d(fd, fh, h0, box, fix)
def rectangle_with_circular_hole():
"""Rectangle with circular hole, refined at circle boundary"""
fd = lambda p: dm.ddiff(dm.drectangle(p, -1, 1, -1, 1),
dm.dcircle(p, 0, 0, 0.5))
fh = lambda p: 0.05 + 0.3 * dm.dcircle(p, 0, 0, 0.5)
return dm.distmesh2d(fd, fh, 0.05, (-1, -1, 1, 1), [(-1, -1), (-1, 1),
(1, -1), (1, 1)])
def fd10(p):
r = np.sqrt(p[:,0]**2 + p[:,1]**2)
z = p[:,2]
d1 = r-1.0
d2 = z-1.0
d3 = -z-1.0
d4 = np.sqrt(d1**2+d2**2)
d5 = np.sqrt(d1**2+d3**2)
d = dm.dintersect(dm.dintersect(d1, d2), d3)
ix = (d1>0)*(d2>0)
d[ix] = d4[ix]
ix = (d1>0)*(d3>0)
d[ix] = d5[ix]
return dm.ddiff(d, dm.dsphere(p, 0,0,0, 0.5))
def fd10(p):
r = np.sqrt(p[:, 0]**2 + p[:, 1]**2)
z = p[:, 2]
d1 = r - 1.0
d2 = z - 1.0
d3 = -z - 1.0
d4 = np.sqrt(d1**2 + d2**2)
d5 = np.sqrt(d1**2 + d3**2)
d = dm.dintersect(dm.dintersect(d1, d2), d3)
ix = (d1 > 0) * (d2 > 0)
d[ix] = d4[ix]
ix = (d1 > 0) * (d3 > 0)
d[ix] = d5[ix]
return dm.ddiff(d, dm.dsphere(p, 0, 0, 0, 0.5))
def naca0012_airfoil():
"""NACA0012 airfoil"""
hlead=0.01; htrail=0.04; hmax=2; circx=2; circr=4
a=.12/.2*np.array([0.2969,-0.1260,-0.3516,0.2843,-0.1036])
a0=a[0]; a1=np.hstack((a[5:0:-1], 0.0))
fd = lambda p: dm.ddiff(
dm.dcircle(p,circx,0,circr),
(abs(p[:,1])-np.polyval(a1, p[:,0]))**2-a0**2*p[:,0])
fh = lambda p: np.minimum(np.minimum(
hlead+0.3*dm.dcircle(p,0,0,0),
htrail+0.3*dm.dcircle(p,1,0,0)),hmax)
fixx = 1.0-htrail*np.cumsum(1.3**np.arange(5))
fixy = a0*np.sqrt(fixx)+np.polyval(a1, fixx)
fix = np.vstack((
np.array([(circx-circr,0),(circx+circr,0),
(circx,-circr),(circx,circr),
(0,0),(1,0)]),
np.vstack((fixx, fixy)).T,
np.vstack((fixx, -fixy)).T))
box = (circx-circr,-circr, circx+circr,circr)
h0 = min(hlead, htrail, hmax)
return dm.distmesh2d(fd, fh, h0, box, fix)
def fd(p):
return dm.ddiff(dm.ddiff(fdout(p), dm.dcircle(p,0,0,vfr)), dm.dcircle(p,2*rad,0,vfr))
def __init__(self, lx, ly, cx, cy, r): fd = lambda p: dm.ddiff(dm.drectangle(p,-lx,lx,-ly,ly), dm.dcircle(p,cx,cx,r)) fh = lambda p: 0.05+0.03*dm.dcircle(p,cx,cy,r) p, t = dm.distmeshnd(fd, fh, 0.5, (-lx,-ly,lx,ly),[(-lx,-ly),(-lx,ly),(lx,-ly),(lx,ly)]) self.nodes = p self.conn = t
def rectangle_with_circle_at_corner():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p, 0, 10, 0, 6),
dm.dcircle(p, 10, 0, 4))
return dm.distmesh2d(fd, dm.huniform, 0.9, (0, 0, 10, 6))
import distmesh as dm fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1), dm.dcircle(p,0,0,0.5)) fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5) p, t = dm.distmesh2d(fd, fh, 0.05, (-1,-1,1,1), [(-1,-1),(-1,1),(1,-1),(1,1)])
def findObjectThreshold(img, threshold=7):
"""Find object within image using simple thresholding
Input:
-img: input image object
-threshold: threshold intensity to apply (can be chosen from looking at
histograms)
Output:
-mask: mask containing object
-contours: contours outlining mask
-hierarchy: hierarchy of contours
"""
#Test code:
#img = cv2.imread('./video/testcontours.jpg')
#Just try simple thresholding instead: (quick!, seems to work fine)
if len(img.shape) == 3:
frame_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
else:
frame_gray = img
frame_gray = cv2.blur(frame_gray, (5, 5))
frame_gray = cv2.blur(frame_gray, (5, 5))
frame_gray = cv2.blur(frame_gray, (5, 5))
#Global threshold
ret1, mask = cv2.threshold(frame_gray, threshold, 255, cv2.THRESH_TOZERO)
mask2 = np.where((mask == 2) | (mask == 0), 0, 1).astype('uint8')
#Find contours of mask
if is_cv3():
im2, c, h = cv2.findContours(mask2.copy(), cv2.RETR_TREE,
cv2.CHAIN_APPROX_SIMPLE)
else:
c, h = cv2.findContours(mask2.copy(), cv2.RETR_TREE,
cv2.CHAIN_APPROX_SIMPLE)
ctrs = Contours(c, h)
#Remove contours that are smaller than 40 square pixels, or that are above
#level one
changed = True
maxarea = 0
for (ct, level) in ctrs.traverse():
maxarea = max(maxarea, cv2.contourArea(ct))
while changed:
changed = False
#print 'length: %d' % len(ctrs.contours)
for idx, (ct, level) in enumerate(ctrs.traverse()):
area = cv2.contourArea(ct)
if area < maxarea and level == 0:
ctrs.remove(idx)
changed = True
break
if area < 40:
ctrs.remove(idx)
changed = True
break
if level > 1:
ctrs.remove(idx)
changed = True
break
#Make the signed diff function
#All of them
if len(ctrs.contours) > 1:
fd = lambda p: dm.ddiff(ppt(ctrs.contours[0], p, True),
ddunion(ctrs.contours[1:], p, True))
else:
fd = lambda p: ppt(ctrs.contours[0], p, True)
#Two of them
#fd = lambda p: dm.dunion(ppt(ctrs.contours[2], p, True), ppt(ctrs.contours[1], p, True))
#One of them
#fd = lambda p: ppt(ctrs.contours[0], p, True)
#Diff of two of them
#fd = lambda p: dm.ddiff(ppt(ctrs.contours[0], p, True), ppt(ctrs.contours[1], p, True))
#Draw contours
#cv2.drawContours(grid, ctrs.contours[0:2], -1, (0,255,0), 3)
#cv2.imshow('image', grid)
#cv2.waitKey(0)
return (mask2, ctrs, fd)
def rectangle_with_circle_at_corner():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p,0,10,0,6), dm.dcircle(p,10,0,4))
return dm.distmesh2d(fd, dm.huniform, 0.9, (0, 0, 10, 6))
def rectangle_with_circle_at_centre():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p,0,20,0,12), dm.dcircle(p,10,6,4))
return dm.distmesh2d(fd, dm.huniform, 0.5, (0, 0, 20, 12), max_iter=100)
def rectangle_with_circular_hole():
"""Rectangle with circular hole, refined at circle boundary"""
fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1), dm.dcircle(p,0,0,0.5))
fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5)
return dm.distmesh2d(fd, fh, 0.05, (-1,-1,1,1),
[(-1,-1),(-1,1),(1,-1),(1,1)])
def findObjectThreshold(img, threshold = 7):
"""Find object within image using simple thresholding
Input:
-img: input image object
-threshold: threshold intensity to apply (can be chosen from looking at
histograms)
Output:
-mask: mask containing object
-contours: contours outlining mask
-hierarchy: hierarchy of contours
"""
#Test code:
#img = cv2.imread('./video/testcontours.jpg')
#Just try simple thresholding instead: (quick!, seems to work fine)
if len(img.shape) == 3:
frame_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
else:
frame_gray = img
#Global threshold
ret1, mask = cv2.threshold(frame_gray, threshold, 255, cv2.THRESH_TOZERO)
mask2 = np.where((mask==2)|(mask==0),0,1).astype('uint8')
#Find contours of mask
if is_cv3():
im2, c, h = cv2.findContours(mask2.copy(),cv2.RETR_TREE,cv2.CHAIN_APPROX_SIMPLE)
else:
c, h = cv2.findContours(mask2.copy(),cv2.RETR_TREE,cv2.CHAIN_APPROX_SIMPLE)
ctrs = Contours(c, h)
#Remove contours that are smaller than 40 square pixels, or that are above
#level one
changed = True
maxarea = 0
for (ct, level) in ctrs.traverse():
maxarea = max(maxarea, cv2.contourArea(ct))
while changed:
changed = False
for idx, (ct, level) in enumerate(ctrs.traverse()):
area = cv2.contourArea(ct)
if area < maxarea and level == 0:
ctrs.remove(idx)
changed = True
break
if area < 40:
ctrs.remove(idx)
changed = True
break
if level > 1:
ctrs.remove(idx)
changed = True
break
#Make the signed diff function
#All of them
if len(ctrs.contours) > 1:
fd = lambda p: dm.ddiff(ppt(ctrs.contours[0], p, True), ddunion(ctrs.contours[1:], p, True))
else:
fd = lambda p: ppt(ctrs.contours[0], p, True)
#Two of them
#fd = lambda p: dm.dunion(ppt(ctrs.contours[2], p, True), ppt(ctrs.contours[1], p, True))
#One of them
#fd = lambda p: ppt(ctrs.contours[0], p, True)
#Diff of two of them
#fd = lambda p: dm.ddiff(ppt(ctrs.contours[0], p, True), ppt(ctrs.contours[1], p, True))
#Draw contours
#cv2.drawContours(grid, ctrs.contours[0:2], -1, (0,255,0), 3)
#cv2.imshow('image', grid)
#cv2.waitKey(0)
return (mask2, ctrs, fd)
def rectangle_with_circle_at_centre():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p, 0, 20, 0, 12),
dm.dcircle(p, 10, 6, 4))
return dm.distmesh2d(fd, dm.huniform, 0.5, (0, 0, 20, 12), max_iter=100)
