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 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 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]
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]
