def setup_xy_fresnel(self):
k0, k1 = self.k0, self.k1
if k1 == 0: k1 = 1e-6 # hack
if k1 != 0:
sqrk1 = sqrt(2 * abs(k1))
t0 = (k0 - .5 * k1) / sqrk1
t1 = (k0 + .5 * k1) / sqrk1
(y0, x0) = cornu.eval_cornu(t0)
(y1, x1) = cornu.eval_cornu(t1)
chord_th = atan2(y1 - y0, x1 - x0)
chord = hypot(y1 - y0, x1 - x0)
scale = self.chord / chord
if k1 >= 0:
th = self.chth - chord_th
self.mxx = scale * cos(th)
self.myx = scale * sin(th)
self.mxy = -self.myx
self.myy = self.mxx
else:
th = self.chth + chord_th
self.mxx = scale * cos(th)
self.myx = scale * sin(th)
self.mxy = self.myx
self.myy = -self.mxx
# rotate -chord_th, flip top/bottom, rotate self.chth
self.x0 = self.z0[0] - (self.mxx * x0 + self.mxy * y0)
self.y0 = self.z0[1] - (self.myx * x0 + self.myy * y0)
def setup_xy_fresnel(self):
k0, k1 = self.k0, self.k1
if k1 == 0: k1 = 1e-6 # hack
if k1 != 0:
sqrk1 = sqrt(2 * abs(k1))
t0 = (k0 - .5 * k1) / sqrk1
t1 = (k0 + .5 * k1) / sqrk1
(y0, x0) = cornu.eval_cornu(t0)
(y1, x1) = cornu.eval_cornu(t1)
chord_th = atan2(y1 - y0, x1 - x0)
chord = hypot(y1 - y0, x1 - x0)
scale = self.chord / chord
if k1 >= 0:
th = self.chth - chord_th
self.mxx = scale * cos(th)
self.myx = scale * sin(th)
self.mxy = -self.myx
self.myy = self.mxx
else:
th = self.chth + chord_th
self.mxx = scale * cos(th)
self.myx = scale * sin(th)
self.mxy = self.myx
self.myy = -self.mxx
# rotate -chord_th, flip top/bottom, rotate self.chth
self.x0 = self.z0[0] - (self.mxx * x0 + self.mxy * y0)
self.y0 = self.z0[1] - (self.myx * x0 + self.myy * y0)
def cornu_to_cubic(t0, t1):
def th_fn(s):
return (s + t0)**2
y0, x0 = cornu.eval_cornu(t0)
y1, x1 = cornu.eval_cornu(t1)
bz, score = fit_cubic((x0, y0), (x1, y1), t1 - t0, th_fn, 0)
return bz, score
def cornu_to_cubic(t0, t1):
def th_fn(s):
return (s + t0) ** 2
y0, x0 = cornu.eval_cornu(t0)
y1, x1 = cornu.eval_cornu(t1)
bz, score = fit_cubic((x0, y0), (x1, y1), t1 - t0, th_fn, 0)
return bz, score
def compute_dth(k0, k1):
if k1 < 0:
return -compute_dth(k0, -k1)
elif k1 == 0:
return 0
sqrk1 = sqrt(2 * k1)
t0 = (k0 - .5 * k1) / sqrk1
t1 = (k0 + .5 * k1) / sqrk1
(y0, x0) = cornu.eval_cornu(t0)
(y1, x1) = cornu.eval_cornu(t1)
chord_th = atan2(y1 - y0, x1 - x0)
return mod_2pi(t1 * t1 - chord_th) - mod_2pi(chord_th - t0 * t0)
def compute_chord(k0, k1):
if k1 == 0:
if k0 == 0:
return 1
else:
return sin(k0 * .5) / (k0 * .5)
sqrk1 = sqrt(2 * abs(k1))
t0 = (k0 - .5 * k1) / sqrk1
t1 = (k0 + .5 * k1) / sqrk1
(y0, x0) = cornu.eval_cornu(t0)
(y1, x1) = cornu.eval_cornu(t1)
return hypot(y1 - y0, x1 - x0) / abs(t1 - t0)
def plot_errors_2d(t0, t1, as_ppm):
xs = 1024
ys = 1024
if as_ppm:
print 'P6'
print xs, ys
print 255
def th_fn(s):
return (s + t0)**2
y0, x0 = cornu.eval_cornu(t0)
y1, x1 = cornu.eval_cornu(t1)
z0 = (x0, y0)
z1 = (x1, y1)
chord = hypot(y1 - y0, x1 - x0)
arclen = t1 - t0
th0 = th_fn(0)
th1 = th_fn(arclen)
cth0, sth0 = cos(th0), sin(th0)
cth1, sth1 = -cos(th1), -sin(th1)
for y in range(ys):
b = .8 * chord * (ys - y - 1) / ys
for x in range(xs):
a = .8 * chord * x / xs
bz = [
z0, (z0[0] + cth0 * a, z0[1] + sth0 * a),
(z1[0] + cth1 * b, z1[1] + sth1 * b), z1
]
s_bz = bz_arclength(bz, 10)
def th_fn_scaled(s):
return (s * arclen / s_bz + t0)**2
score = measure_bz_rk4(bz, arclen, th_fn_scaled, 10)
if as_ppm:
ls = -log(score)
color_th = ls
darkstep = 0
if s_bz > arclen:
g0 = 128 - darkstep
else:
g0 = 128 + darkstep
sc = 127 - darkstep
rr = g0 + sc * cos(color_th)
gg = g0 + sc * cos(color_th + 2 * pi / 3)
bb = g0 + sc * cos(color_th - 2 * pi / 3)
sys.stdout.write(struct.pack('3B', rr, gg, bb))
else:
print a, b, score
if not as_ppm:
print
def plot_errors_2d(t0, t1, as_ppm):
xs = 1024
ys = 1024
if as_ppm:
print "P6"
print xs, ys
print 255
def th_fn(s):
return (s + t0) ** 2
y0, x0 = cornu.eval_cornu(t0)
y1, x1 = cornu.eval_cornu(t1)
z0 = (x0, y0)
z1 = (x1, y1)
chord = hypot(y1 - y0, x1 - x0)
arclen = t1 - t0
th0 = th_fn(0)
th1 = th_fn(arclen)
cth0, sth0 = cos(th0), sin(th0)
cth1, sth1 = -cos(th1), -sin(th1)
for y in range(ys):
b = 0.8 * chord * (ys - y - 1) / ys
for x in range(xs):
a = 0.8 * chord * x / xs
bz = [z0, (z0[0] + cth0 * a, z0[1] + sth0 * a), (z1[0] + cth1 * b, z1[1] + sth1 * b), z1]
s_bz = bz_arclength(bz, 10)
def th_fn_scaled(s):
return (s * arclen / s_bz + t0) ** 2
score = measure_bz_rk4(bz, arclen, th_fn_scaled, 10)
if as_ppm:
ls = -log(score)
color_th = ls
darkstep = 0
if s_bz > arclen:
g0 = 128 - darkstep
else:
g0 = 128 + darkstep
sc = 127 - darkstep
rr = g0 + sc * cos(color_th)
gg = g0 + sc * cos(color_th + 2 * pi / 3)
bb = g0 + sc * cos(color_th - 2 * pi / 3)
sys.stdout.write(struct.pack("3B", rr, gg, bb))
else:
print a, b, score
if not as_ppm:
print
def plot_arclen(t0, t1):
def th_fn(s):
return (s + t0)**2
y0, x0 = cornu.eval_cornu(t0)
y1, x1 = cornu.eval_cornu(t1)
z0 = (x0, y0)
z1 = (x1, y1)
chord = hypot(y1 - y0, x1 - x0)
arclen = t1 - t0
th0 = th_fn(0)
th1 = th_fn(arclen)
for i in range(101):
aab = i * .01
bz, a, b = fit_cubic_arclen_forplot(z0, z1, arclen, th0, th1, aab)
print a, b
def plot_arclen(t0, t1):
def th_fn(s):
return (s + t0) ** 2
y0, x0 = cornu.eval_cornu(t0)
y1, x1 = cornu.eval_cornu(t1)
z0 = (x0, y0)
z1 = (x1, y1)
chord = hypot(y1 - y0, x1 - x0)
arclen = t1 - t0
th0 = th_fn(0)
th1 = th_fn(arclen)
for i in range(101):
aab = i * 0.01
bz, a, b = fit_cubic_arclen_forplot(z0, z1, arclen, th0, th1, aab)
print a, b
def xy(self, s):
# using fresnel integrals; polynomial approx might be better
u = s / self.arclen - 0.5
k0, k1 = self.k0, self.k1
if k1 == 0: k1 = 1e-6 # hack
if k1 != 0:
sqrk1 = sqrt(2 * abs(k1))
t = (k0 + u * k1) / sqrk1
(y, x) = cornu.eval_cornu(t)
return [self.x0 + self.mxx * x + self.mxy * y,
self.y0 + self.myx * x + self.myy * y]
def cornu_to_cubic(t0, t1, figno):
if figno == 1:
aabmin = 0
aabmax = 0.4
elif figno == 2:
aabmin = 0.5
aabmax = 1.
else:
aabmin = 0
aabmax = 1.
fast = 0
if figno == 3:
fast = 1
elif figno == 4:
fast = 2
def th_fn(s):
return (s + t0) ** 2
y0, x0 = cornu.eval_cornu(t0)
y1, x1 = cornu.eval_cornu(t1)
bz, score = fit_cubic((x0, y0), (x1, y1), t1 - t0, th_fn, fast, aabmin, aabmax)
return bz, score
def xy(self, s):
# using fresnel integrals; polynomial approx might be better
u = s / self.arclen - 0.5
k0, k1 = self.k0, self.k1
if k1 == 0:
k1 = 1e-6 # hack
if k1 != 0:
sqrk1 = sqrt(2 * abs(k1))
t = (k0 + u * k1) / sqrk1
(y, x) = cornu.eval_cornu(t)
return [self.x0 + self.mxx * x + self.mxy * y,
self.y0 + self.myx * x + self.myy * y]
def cornu_to_cubic(t0, t1, figno):
if figno == 1:
aabmin = 0
aabmax = 0.4
elif figno == 2:
aabmin = 0.5
aabmax = 1.
else:
aabmin = 0
aabmax = 1.
fast = 0
if figno == 3:
fast = 1
elif figno == 4:
fast = 2
def th_fn(s):
return (s + t0)**2
y0, x0 = cornu.eval_cornu(t0)
y1, x1 = cornu.eval_cornu(t1)
bz, score = fit_cubic((x0, y0), (x1, y1), t1 - t0, th_fn, fast, aabmin,
aabmax)
return bz, score