def Newton_bezier(t, b, ivar, val, itmax, tol):
d = lbez.diff(b)
for it in range(itmax):
f = lbez.eval_bezier_curve(b, t) - val
if abs(f[ivar]) < tol:
return t
df = lbez.eval_bezier_curve(d, t)
if abs(df[ivar]) < 1e-15:
return None
dt = -f[ivar] / df[ivar]
t += dt
return None
def Newton_intersection(curves, t, itmax=30, tol=1e-6, verbose=False):
deriv = [lbez.diff(b) for b in curves]
for it in range(itmax):
if verbose: print 'it. #%d, t = (%s, %s)' % (it, t[0], t[1])
xy = [lbez.eval_bezier_curve(curves[i], t[i]) for i in range(2)]
if verbose:
for i in range(2):
print ' xy_%d = (%s, %s)' % (i, xy[i][0], xy[i][1])
res = xy[1] - xy[0]
if verbose: print ' |res| = %s' % (numpy.hypot(res[0], res[1]))
#
if sum(res**2) < tol**2:
return t
#
dxy = [lbez.eval_bezier_curve(deriv[i], t[i]) for i in range(2)]
dxy[1] = -dxy[1]
det = dxy[0][0] * dxy[1][1] - dxy[0][1] * dxy[1][0]
if verbose: print ' |det| = %s\n' % (abs(det))
if abs(det) < 1e-15:
return None
t[0] += (res[0] * dxy[1][1] - res[1] * dxy[1][0]) / det
t[1] += (dxy[0][0] * res[1] - dxy[0][1] * res[0]) / det
return None
def bezier_extremal_values(b, ivar):
d = lbez.diff(b)
A = d[2][ivar] - 2 * d[1][ivar] + d[0][ivar]
if abs(A) < 1e-15:
return [0.5 * d[0][ivar] / (d[0][ivar] - d[1][ivar])]
else:
B = d[1][ivar] - d[0][ivar]
C = d[0][ivar]
sqrtdelta = numpy.sqrt(B**2 - A * C)
t = []
for sign in [-1, 1]:
ts = (sign * sqrtdelta - B) / A
if ts >= 0 and ts <= 1: t.append(ts)
if len(t) < 1:
fig, ax = plt.subplots()
u = numpy.linspace(0, 1, 100)
xy = lbez.eval_bezier_curve(d, u)
ax.plot(u, xy[:, ivar])
ax.plot([0, 1], [0, 0], 'k--')
ax.set_aspect('equal')
plt.show()
return t
def evald2(self, t):
return lbez.eval_bezier_curve(self.xtt, t)
def eval(self, t):
return lbez.eval_bezier_curve(self.x, t)
if False:
fig, ax = plt.subplots()
f = open('teapot_profile_bcp.dat', 'r')
j = 0
while True:
j += 1
line = f.readline()
if ("" == line): break # end of file
b[0] = [float(a) for a in line.split()]
for i in range(1, 4):
b[i] = [float(a) for a in f.readline().split()]
line = f.readline()
#
p = lbez.eval_bezier_curve(b, t)
ax.plot(p[:, 0], p[:, 1])
ax.text(p[k, 0], p[k, 1], str(j))
f.close()
ax.set_aspect('equal')
plt.show()
##############################
# READ
f = open('teapot_elems_profile_bcp.dat', 'r')
npaths = int(f.readline())
paths = []
for ipath in range(npaths):
segms = []
nsegms = int(f.readline())
"""
b = b + 0.4 * (2 * numpy.random.rand(b.shape[0], b.shape[1]) - 1)
db = lbez.diff(b)
n = 100
t = numpy.linspace(0, 1, n)
"""
p = numpy.zeros((n,2))
for i in range(n):
f, bl, br = lbez.de_casteljau(b, t[i])
for j in range(2):
p[i,j] = f[j]
"""
p = lbez.eval_bezier_curve(b, t)
dp = lbez.eval_bezier_curve(db, t)
#print dp
fig, ax = plt.subplots()
aabb = lbez.AABB_2d_bezier_curve(b)
ctr, rng, axe = lbez.OBB_2d_bezier_curve(b)
ax.plot(p[:, 0], p[:, 1], 'k-')
ax.plot(b[:, 0], b[:, 1], 'r.-')
#ax.quiver(p[:,0], p[:,1], dp[:,0], dp[:,1], color='b')
#ax.quiver(p[:,0], p[:,1], -dp[:,1], dp[:,0], color='b')
#ax.plot(dp[:,0], dp[:,1], 'b')
