def plot_k_of_bz(bz):
dbz = tocubic.bz_deriv(bz)
ddbz = tocubic.bz_deriv(dbz)
cmd = 'moveto'
ss = [0]
def arclength_deriv(x, ss):
dx, dy = tocubic.bz_eval(dbz, x)
return [hypot(dx, dy)]
dt = 0.01
t = 0
for i in range(101):
dx, dy = tocubic.bz_eval(dbz, t)
ddx, ddy = tocubic.bz_eval(ddbz, t)
k = (ddy * dx - dy * ddx) / (dx * dx + dy * dy) ** 1.5
print 100 + 500 * ss[0], 100 + 200 * k, cmd
cmd = 'lineto'
dsdx = arclength_deriv(t, ss)
tocubic.rk4(ss, dsdx, t, .01, arclength_deriv)
t += dt
print 'stroke'
def plot_k_of_bz(bz):
dbz = tocubic.bz_deriv(bz)
ddbz = tocubic.bz_deriv(dbz)
cmd = 'moveto'
ss = [0]
def arclength_deriv(x, ss):
dx, dy = tocubic.bz_eval(dbz, x)
return [hypot(dx, dy)]
dt = 0.01
t = 0
for i in range(101):
dx, dy = tocubic.bz_eval(dbz, t)
ddx, ddy = tocubic.bz_eval(ddbz, t)
k = (ddy * dx - dy * ddx) / (dx * dx + dy * dy)**1.5
print(100 + 500 * ss[0], 100 + 200 * k, cmd)
cmd = 'lineto'
dsdx = arclength_deriv(t, ss)
tocubic.rk4(ss, dsdx, t, .01, arclength_deriv)
t += dt
print('stroke')
def measure_bz_cloth(seg, bz, n = 100):
bz_arclen = tocubic.bz_arclength_rk4(bz)
arclen_ratio = seg.arclen / bz_arclen
dbz = tocubic.bz_deriv(bz)
def measure_derivs(x, ys):
dx, dy = tocubic.bz_eval(dbz, x)
ds = hypot(dx, dy)
s = ys[0] * arclen_ratio
dscore = ds * (tocubic.mod_2pi(atan2(dy, dx) - seg.th(s)) ** 2)
#print s, atan2(dy, dx), seg.th(s)
return [ds, dscore]
dt = 1./n
t = 0
ys = [0, 0]
for i in range(n):
dydx = measure_derivs(t, ys)
tocubic.rk4(ys, dydx, t, dt, measure_derivs)
t += dt
return ys[1]
def measure_bz_cloth(seg, bz, n=100):
bz_arclen = tocubic.bz_arclength_rk4(bz)
arclen_ratio = seg.arclen / bz_arclen
dbz = tocubic.bz_deriv(bz)
def measure_derivs(x, ys):
dx, dy = tocubic.bz_eval(dbz, x)
ds = hypot(dx, dy)
s = ys[0] * arclen_ratio
dscore = ds * (tocubic.mod_2pi(atan2(dy, dx) - seg.th(s))**2)
#print s, atan2(dy, dx), seg.th(s)
return [ds, dscore]
dt = 1. / n
t = 0
ys = [0, 0]
for i in range(n):
dydx = measure_derivs(t, ys)
tocubic.rk4(ys, dydx, t, dt, measure_derivs)
t += dt
return ys[1]
