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# Convert piecewise cubic into piecewise clothoid representation.
from math import *
import clothoid
import pcorn
import tocubic
import offset
def read_bz(f):
result = []
for l in f.xreadlines():
s = l.split()
if len(s) > 0:
cmd = s[-1]
#print s[:-1], cmd
if cmd == 'm':
sp = []
result.append(sp)
curpt = [float(x) for x in s[0:2]]
startpt = curpt
elif cmd == 'l':
newpt = [float(x) for x in s[0:2]]
sp.append((curpt, newpt))
curpt = newpt
elif cmd == 'c':
c1 = [float(x) for x in s[0:2]]
c2 = [float(x) for x in s[2:4]]
newpt = [float(x) for x in s[4:6]]
sp.append((curpt, c1, c2, newpt))
curpt = newpt
return result
def plot_bzs(bzs, z0, scale, fancy = False):
for sp in bzs:
for i in range(len(sp)):
bz = sp[i]
tocubic.plot_bz(bz, z0, scale, i == 0)
print 'stroke'
if fancy:
for i in range(len(sp)):
bz = sp[i]
x0, y0 = z0[0] + scale * bz[0][0], z0[1] + scale * bz[0][1]
print 'gsave', x0, y0, 'translate circle fill grestore'
if len(bz) == 4:
x1, y1 = z0[0] + scale * bz[1][0], z0[1] + scale * bz[1][1]
x2, y2 = z0[0] + scale * bz[2][0], z0[1] + scale * bz[2][1]
x3, y3 = z0[0] + scale * bz[3][0], z0[1] + scale * bz[3][1]
print 'gsave 0.5 setlinewidth', x0, y0, 'moveto'
print x1, y1, 'lineto stroke'
print x2, y2, 'moveto'
print x3, y3, 'lineto stroke grestore'
print 'gsave', x1, y1, 'translate 0.75 dup scale circle fill grestore'
print 'gsave', x2, y2, 'translate 0.75 dup scale circle fill grestore'
print 'gsave', x3, y3, 'translate 0.75 dup scale circle fill grestore'
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 cubic_bz_to_pcorn(bz, thresh):
dx = bz[3][0] - bz[0][0]
dy = bz[3][1] - bz[0][1]
dx1 = bz[1][0] - bz[0][0]
dy1 = bz[1][1] - bz[0][1]
dx2 = bz[3][0] - bz[2][0]
dy2 = bz[3][1] - bz[2][1]
chth = atan2(dy, dx)
th0 = tocubic.mod_2pi(chth - atan2(dy1, dx1))
th1 = tocubic.mod_2pi(atan2(dy2, dx2) - chth)
seg = pcorn.Segment(bz[0], bz[3], th0, th1)
err = measure_bz_cloth(seg, bz)
if err < thresh:
return [seg]
else:
# de Casteljau
x01, y01 = 0.5 * (bz[0][0] + bz[1][0]), 0.5 * (bz[0][1] + bz[1][1])
x12, y12 = 0.5 * (bz[1][0] + bz[2][0]), 0.5 * (bz[1][1] + bz[2][1])
x23, y23 = 0.5 * (bz[2][0] + bz[3][0]), 0.5 * (bz[2][1] + bz[3][1])
xl2, yl2 = 0.5 * (x01 + x12), 0.5 * (y01 + y12)
xr1, yr1 = 0.5 * (x12 + x23), 0.5 * (y12 + y23)
xm, ym = 0.5 * (xl2 + xr1), 0.5 * (yl2 + yr1)
bzl = [bz[0], (x01, y01), (xl2, yl2), (xm, ym)]
bzr = [(xm, ym), (xr1, yr1), (x23, y23), bz[3]]
segs = cubic_bz_to_pcorn(bzl, 0.5 * thresh)
segs.extend(cubic_bz_to_pcorn(bzr, 0.5 * thresh))
return segs
def bzs_to_pcorn(bzs, thresh = 1e-9):
result = []
for sp in bzs:
rsp = []
for bz in sp:
if len(bz) == 2:
dx = bz[1][0] - bz[0][0]
dy = bz[1][1] - bz[0][1]
th = atan2(dy, dx)
rsp.append(pcorn.Segment(bz[0], bz[1], 0, 0))
else:
rsp.extend(cubic_bz_to_pcorn(bz, thresh))
result.append(rsp)
return result
def plot_segs(segs):
for i in range(len(segs)):
seg = segs[i]
if i == 0:
print seg.z0[0], seg.z0[1], 'moveto'
print seg.z1[0], seg.z1[1], 'lineto'
print 'stroke'
for i in range(len(segs)):
seg = segs[i]
if i == 0:
print 'gsave', seg.z0[0], seg.z0[1], 'translate circle fill grestore'
print 'gsave', seg.z1[0], seg.z1[1], 'translate circle fill grestore'
import sys
def test_to_pcorn():
C1 = 0.55228
bz = [(100, 100), (100 + 400 * C1, 100), (500, 500 - 400 * C1), (500, 500)]
for i in range(0, 13):
thresh = .1 ** i
segs = cubic_bz_to_pcorn(bz, thresh)
plot_segs(segs)
print >> sys.stderr, thresh, len(segs)
print '0 20 translate'
if __name__ == '__main__':
f = file(sys.argv[1])
bzs = read_bz(f)
rsps = bzs_to_pcorn(bzs, 1)
#print rsps
tocubic.plot_prolog()
print 'grestore'
print '1 -1 scale 0 -720 translate'
print '/ss 1.5 def'
print '/circle { ss 0 moveto currentpoint exch ss sub exch ss 0 360 arc } bind def'
tot = 0
for segs in rsps:
curve = pcorn.Curve(segs)
#curve = offset.offset(curve, 10)
print '%', curve.arclen
print '%', curve.sstarts
if 0:
print 'gsave 1 0 0 setrgbcolor'
cmd = 'moveto'
for i in range(100):
s = i * .01 * curve.arclen
x, y = curve.xy(s)
th = curve.th(s)
sth = 5 * sin(th)
cth = 5 * cos(th)
print x, y, cmd
cmd = 'lineto'
print 'closepath stroke grestore'
for i in range(100):
s = i * .01 * curve.arclen
x, y = curve.xy(s)
th = curve.th(s)
sth = 5 * sin(th)
cth = 5 * cos(th)
if 0:
print x - cth, y - sth, 'moveto'
print x + cth, y + sth, 'lineto stroke'
if 1:
for s in curve.find_breaks():
print 'gsave 0 1 0 setrgbcolor'
x, y = curve.xy(s)
print x, y, 'translate 2 dup scale circle fill'
print 'grestore'
#plot_segs(segs)
print 'gsave 0 0 0 setrgbcolor'
optim = 3
thresh = 1e-2
new_bzs = tocubic.pcorn_curve_to_bzs(curve, optim, thresh)
tot += len(new_bzs)
plot_bzs([new_bzs], (0, 0), 1, True)
print 'grestore'
print 'grestore'
print '/Helvetica 12 selectfont'
print '36 720 moveto (thresh=%g optim=%d) show' % (thresh, optim)
print '( tot segs=%d) show' % tot
print 'showpage'
#plot_bzs(bzs, (100, 100), 1)
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