def plot_path(segs, nodes, tol = 1.0, show_cpts = False):
if show_cpts:
cpts = []
j = 0
cmd = 'moveto'
for i in range(len(segs)):
i1 = (i + 1) % len(nodes)
n0 = nodes[i]
n1 = nodes[i1]
x0, y0, t0 = n0.x, n0.y, n0.ty
x1, y1, t1 = n1.x, n1.y, n1.ty
ks = segs[i].ks
abs_ks = abs(ks[0]) + abs(ks[1] / 2) + abs(ks[2] / 8) + abs(ks[3] / 48)
n_subdiv = int(ceil(.001 + tol * abs_ks))
n_subhalf = (n_subdiv + 1) / 2
if n_subdiv > 1:
n_subdiv = n_subhalf * 2
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, n_subhalf)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, n_subhalf)
mside.reverse()
for j in range(len(mside)):
mside[j] = (-mside[j][0], -mside[j][1])
if n_subdiv > 1:
pts = mside + pside[1:]
else:
pts = mside[:1] + pside[1:]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
rot = chord_th - atan2(pts[-1][1] - pts[0][1], pts[-1][0] - pts[0][0])
scale = chord_len / hypot(pts[-1][1] - pts[0][1], pts[-1][0] - pts[0][0])
u, v = scale * cos(rot), scale * sin(rot)
xt = x0 - u * pts[0][0] + v * pts[0][1]
yt = y0 - u * pts[0][1] - v * pts[0][0]
s = -.5
for x, y in pts:
xp, yp = xt + u * x - v * y, yt + u * y + v * x
thp = (((ks[3]/24 * s + ks[2]/6) * s + ks[1] / 2) * s + ks[0]) * s + rot
up, vp = scale / (1.5 * n_subdiv) * cos(thp), scale / (1.5 * n_subdiv) * sin(thp)
if s == -.5:
if cmd == 'moveto':
print xp, yp, 'moveto'
cmd = 'curveto'
else:
if show_cpts:
cpts.append((xlast + ulast, ylast + vlast))
cpts.append((xp - up, yp - vp))
print xlast + ulast, ylast + vlast, xp - up, yp - vp, xp, yp, 'curveto'
xlast, ylast, ulast, vlast = xp, yp, up, vp
s += 1. / n_subdiv
if t1 == 'v':
j += 2
else:
j += 1
print 'stroke'
if show_cpts:
for x, y in cpts:
print 'gsave 0 0 1 setrgbcolor', x, y, 'translate circle fill grestore'
def make_error_vec(path, th, k):
if path[0][2] == '{': closed = 0
else: closed = 1
n = len(path)
v = zeros(n * 2, Float)
j = 0
for i in range(len(path) + closed - 1):
i1 = (i + 1) % len(path)
x0, y0, t0 = path[i]
x1, y1, t1 = path[i1]
j1 = (j + 1) % len(th)
th0 = th[j]
k0 = k[j]
th1 = th[j1]
k1 = k[j1]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
ks = poly3.solve_3spiro(mod_2pi(chord_th - th0),
mod_2pi(th1 - chord_th), k0 * chord_len,
k1 * chord_len)
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, 64)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, 64)
l = chord_len / hypot(pside[-1][0] + mside[-1][0],
pside[-1][1] + mside[-1][1])
k1l = (ks[1] - .5 * ks[2] + .125 * ks[3]) / (l * l)
k1r = (ks[1] + .5 * ks[2] + .125 * ks[3]) / (l * l)
k2l = (ks[2] - .5 * ks[3]) / (l * l * l)
k2r = (ks[2] + .5 * ks[3]) / (l * l * l)
if t0 == 'o' or t0 == '[' or t0 == 'v':
v[2 * j] -= k1l
v[2 * j + 1] -= k2l
elif t0 == 'c':
v[2 * j + 1] += k2l
if t1 == 'o' or t1 == ']' or t1 == 'v':
v[2 * j1] += k1r
v[2 * j1 + 1] += k2r
elif t1 == 'c':
v[2 * j1] += k2r
print "% left k'", k1l, "k''", k2l, "right k'", k1r, "k''", k2r
if t1 == 'v':
j += 2
else:
j += 1
print '% error vector:'
for i in range(n):
print '% ', v[2 * i], v[2 * i + 1]
return v
def make_error_vec(path, th, k):
if path[0][2] == '{': closed = 0
else: closed = 1
n = len(path)
v = zeros(n * 2, Float)
j = 0
for i in range(len(path) + closed - 1):
i1 = (i + 1) % len(path)
x0, y0, t0 = path[i]
x1, y1, t1 = path[i1]
j1 = (j + 1) % len(th)
th0 = th[j]
k0 = k[j]
th1 = th[j1]
k1 = k[j1]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
ks = poly3.solve_3spiro(mod_2pi(chord_th - th0),
mod_2pi(th1 - chord_th),
k0 * chord_len, k1 * chord_len)
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, 64)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, 64)
l = chord_len / hypot(pside[-1][0] + mside[-1][0], pside[-1][1] + mside[-1][1])
k1l = (ks[1] - .5 * ks[2] + .125 * ks[3]) / (l * l)
k1r = (ks[1] + .5 * ks[2] + .125 * ks[3]) / (l * l)
k2l = (ks[2] - .5 * ks[3]) / (l * l * l)
k2r = (ks[2] + .5 * ks[3]) / (l * l * l)
if t0 == 'o' or t0 == '[' or t0 == 'v':
v[2 * j] -= k1l
v[2 * j + 1] -= k2l
elif t0 == 'c':
v[2 * j + 1] += k2l
if t1 == 'o' or t1 == ']' or t1 == 'v':
v[2 * j1] += k1r
v[2 * j1 + 1] += k2r
elif t1 == 'c':
v[2 * j1] += k2r
print "% left k'", k1l, "k''", k2l, "right k'", k1r, "k''", k2r
if t1 == 'v':
j += 2
else:
j += 1
print '% error vector:'
for i in range(n):
print '% ', v[2 * i], v[2 * i + 1]
return v
def plot_path(path, th, k):
if path[0][2] == '{': closed = 0
else: closed = 1
j = 0
cmd = 'moveto'
for i in range(len(path) + closed - 1):
i1 = (i + 1) % len(path)
x0, y0, t0 = path[i]
x1, y1, t1 = path[i1]
j1 = (j + 1) % len(th)
th0 = th[j]
k0 = k[j]
th1 = th[j1]
k1 = k[j1]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
ks = poly3.solve_3spiro(mod_2pi(chord_th - th0),
mod_2pi(th1 - chord_th), k0 * chord_len,
k1 * chord_len)
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, 64)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, 64)
mside.reverse()
for i in range(len(mside)):
mside[i] = (-mside[i][0], -mside[i][1])
pts = mside + pside[1:]
rot = chord_th - atan2(pts[-1][1] - pts[0][1], pts[-1][0] - pts[0][0])
scale = hypot(x1 - x0, y1 - y0) / hypot(pts[-1][1] - pts[0][1],
pts[-1][0] - pts[0][0])
u, v = scale * cos(rot), scale * sin(rot)
xt = x0 - u * pts[0][0] + v * pts[0][1]
yt = y0 - u * pts[0][1] - v * pts[0][0]
for x, y in pts:
print xt + u * x - v * y, yt + u * y + v * x, cmd
cmd = 'lineto'
if t1 == 'v':
j += 2
else:
j += 1
print 'stroke'
if 0:
j = 0
for i in range(len(path)):
x0, y0, t0 = path[i]
print 'gsave', x0, y0, 'translate'
print ' ', th[j] * 180 / pi, 'rotate'
print ' -50 0 moveto 50 0 lineto stroke'
print 'grestore'
j += 1
def plot_path(path, th, k):
if path[0][2] == '{': closed = 0
else: closed = 1
j = 0
cmd = 'moveto'
for i in range(len(path) + closed - 1):
i1 = (i + 1) % len(path)
x0, y0, t0 = path[i]
x1, y1, t1 = path[i1]
j1 = (j + 1) % len(th)
th0 = th[j]
k0 = k[j]
th1 = th[j1]
k1 = k[j1]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
ks = poly3.solve_3spiro(mod_2pi(chord_th - th0),
mod_2pi(th1 - chord_th),
k0 * chord_len, k1 * chord_len)
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, 64)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, 64)
mside.reverse()
for i in range(len(mside)):
mside[i] = (-mside[i][0], -mside[i][1])
pts = mside + pside[1:]
rot = chord_th - atan2(pts[-1][1] - pts[0][1], pts[-1][0] - pts[0][0])
scale = hypot(x1 - x0, y1 - y0) / hypot(pts[-1][1] - pts[0][1], pts[-1][0] - pts[0][0])
u, v = scale * cos(rot), scale * sin(rot)
xt = x0 - u * pts[0][0] + v * pts[0][1]
yt = y0 - u * pts[0][1] - v * pts[0][0]
for x, y in pts:
print xt + u * x - v * y, yt + u * y + v * x, cmd
cmd = 'lineto'
if t1 == 'v':
j += 2
else:
j += 1
print 'stroke'
if 0:
j = 0
for i in range(len(path)):
x0, y0, t0 = path[i]
print 'gsave', x0, y0, 'translate'
print ' ', th[j] * 180 / pi, 'rotate'
print ' -50 0 moveto 50 0 lineto stroke'
print 'grestore'
j += 1
def plot_ks(path, th, k):
if path[0][2] == '{': closed = 0
else: closed = 1
j = 0
cmd = 'moveto'
xo = 36
yo = 550
xscale = .5
yscale = 2000
x = xo
for i in range(len(path) + closed - 1):
i1 = (i + 1) % len(path)
x0, y0, t0 = path[i]
x1, y1, t1 = path[i1]
j1 = (j + 1) % len(th)
th0 = th[j]
k0 = k[j]
th1 = th[j1]
k1 = k[j1]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
ks = poly3.solve_3spiro(mod_2pi(chord_th - th0),
mod_2pi(th1 - chord_th), k0 * chord_len,
k1 * chord_len)
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, 64)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, 64)
print '%', x0, y0, k0, k1
print "% ks = ", ks
l = 2 * chord_len / hypot(pside[-1][0] + mside[-1][0],
pside[-1][1] + mside[-1][1])
for i in range(100):
s = .01 * i - 0.5
kp = poly3.eval_cubic(ks[0], ks[1], .5 * ks[2], 1. / 6 * ks[3], s)
kp /= l
print x + xscale * l * (s + .5), yo + yscale * kp, cmd
cmd = 'lineto'
x += xscale * l
if t1 == 'v':
j += 2
else:
j += 1
print 'stroke'
print xo, yo, 'moveto', x, yo, 'lineto stroke'
def make_matrix(path, th, k):
if path[0][2] == '{': closed = 0
else: closed = 1
n = len(path)
m = zeros((n * 2, n * 2), Float)
j = 0
for i in range(len(path) + closed - 1):
i1 = (i + 1) % len(path)
x0, y0, t0 = path[i]
x1, y1, t1 = path[i1]
j1 = (j + 1) % len(th)
th0 = th[j]
k0 = k[j]
th1 = th[j1]
k1 = k[j1]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
ks = poly3.solve_3spiro(mod_2pi(chord_th - th0),
mod_2pi(th1 - chord_th), k0 * chord_len,
k1 * chord_len)
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, 64)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, 64)
l = chord_len / hypot(pside[-1][0] + mside[-1][0],
pside[-1][1] + mside[-1][1])
if t0 == 'o' or t0 == '[' or t0 == 'v':
add_k1l(m, 2 * j, j, j1, l, -1)
add_k2l(m, 2 * j + 1, j, j1, l, -1)
elif t0 == 'c':
add_k2l(m, 2 * j + 1, j, j1, l, 1)
if t1 == 'o' or t1 == ']' or t1 == 'v':
add_k1r(m, 2 * j1, j, j1, l, 1)
add_k2r(m, 2 * j1 + 1, j, j1, l, 1)
elif t1 == 'c':
add_k2r(m, 2 * j1, j, j1, l, 1)
if t1 == 'v':
j += 2
else:
j += 1
return m
def plot_ks(path, th, k):
if path[0][2] == '{': closed = 0
else: closed = 1
j = 0
cmd = 'moveto'
xo = 36
yo = 550
xscale = .5
yscale = 2000
x = xo
for i in range(len(path) + closed - 1):
i1 = (i + 1) % len(path)
x0, y0, t0 = path[i]
x1, y1, t1 = path[i1]
j1 = (j + 1) % len(th)
th0 = th[j]
k0 = k[j]
th1 = th[j1]
k1 = k[j1]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
ks = poly3.solve_3spiro(mod_2pi(chord_th - th0),
mod_2pi(th1 - chord_th),
k0 * chord_len, k1 * chord_len)
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, 64)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, 64)
print '%', x0, y0, k0, k1
print "% ks = ", ks
l = 2 * chord_len / hypot(pside[-1][0] + mside[-1][0], pside[-1][1] + mside[-1][1])
for i in range(100):
s = .01 * i - 0.5
kp = poly3.eval_cubic(ks[0], ks[1], .5 * ks[2], 1./6 * ks[3], s)
kp /= l
print x + xscale * l * (s + .5), yo + yscale * kp, cmd
cmd = 'lineto'
x += xscale * l
if t1 == 'v':
j += 2
else:
j += 1
print 'stroke'
print xo, yo, 'moveto', x, yo, 'lineto stroke'
def make_matrix(path, th, k):
if path[0][2] == '{': closed = 0
else: closed = 1
n = len(path)
m = zeros((n * 2, n * 2), Float)
j = 0
for i in range(len(path) + closed - 1):
i1 = (i + 1) % len(path)
x0, y0, t0 = path[i]
x1, y1, t1 = path[i1]
j1 = (j + 1) % len(th)
th0 = th[j]
k0 = k[j]
th1 = th[j1]
k1 = k[j1]
chord_th = atan2(y1 - y0, x1 - x0)
chord_len = hypot(y1 - y0, x1 - x0)
ks = poly3.solve_3spiro(mod_2pi(chord_th - th0),
mod_2pi(th1 - chord_th),
k0 * chord_len, k1 * chord_len)
ksp = (ks[0] * .5, ks[1] * .25, ks[2] * .125, ks[3] * .0625)
pside = poly3.int_3spiro_poly(ksp, 64)
ksm = (ks[0] * -.5, ks[1] * .25, ks[2] * -.125, ks[3] * .0625)
mside = poly3.int_3spiro_poly(ksm, 64)
l = chord_len / hypot(pside[-1][0] + mside[-1][0], pside[-1][1] + mside[-1][1])
if t0 == 'o' or t0 == '[' or t0 == 'v':
add_k1l(m, 2 * j, j, j1, l, -1)
add_k2l(m, 2 * j + 1, j, j1, l, -1)
elif t0 == 'c':
add_k2l(m, 2 * j + 1, j, j1, l, 1)
if t1 == 'o' or t1 == ']' or t1 == 'v':
add_k1r(m, 2 * j1, j, j1, l, 1)
add_k2r(m, 2 * j1 + 1, j, j1, l, 1)
elif t1 == 'c':
add_k2r(m, 2 * j1, j, j1, l, 1)
if t1 == 'v':
j += 2
else:
j += 1
return m
