def cubic_bezier_t_of_s_dynamic(p0,p1,p2,p3, initial_step = 50):
'''
returns a dictionary mapping of arclen values ot t values
approximated at steps along the curve. Dumber method than
the decastelejue subdivision.
'''
s_t_map = {}
s_t_map[0] = 0
pi0 = p0
cumul_length = 0
iters = 0
dt = 1/initial_step
t = dt
while t < 1 and iters < 1000:
iters += 1
weights = cubic_bezier_weights(t)
pi1 = cubic_bezier_blend_weights(p0, p1, p2, p3, weights)
cumul_length += (pi1 - pi0).length
v_num = (pi1 - pi0).length/dt
v_cls = cubic_bezier_derivative(p0, p1, p2, p3, t).length
s_t_map[cumul_length] = t
pi0 = pi1
dt *= v_cls/v_num
t += dt
if iters == 1000:
print('maxed iters')
#take care of the last point
weights = cubic_bezier_weights(1)
pi1 = cubic_bezier_blend_weights(p0, p1, p2, p3, weights)
cumul_length += (pi1 - pi0).length
s_t_map[cumul_length] = 1
dprint('initial dt %f, final dt %f' % (1/initial_step, dt), l=4)
return s_t_map
def cubic_bezier_t_of_s_dynamic(p0, p1, p2, p3, initial_step=50):
'''
returns a dictionary mapping of arclen values ot t values
approximated at steps along the curve. Dumber method than
the decastelejue subdivision.
'''
s_t_map = {}
s_t_map[0] = 0
pi0 = p0
cumul_length = 0
iters = 0
dt = 1 / initial_step
t = dt
while t < 1 and iters < 1000:
iters += 1
weights = cubic_bezier_weights(t)
pi1 = cubic_bezier_blend_weights(p0, p1, p2, p3, weights)
cumul_length += (pi1 - pi0).length
v_num = (pi1 - pi0).length / dt
v_cls = cubic_bezier_derivative(p0, p1, p2, p3, t).length
s_t_map[cumul_length] = t
pi0 = pi1
dt *= v_cls / v_num
t += dt
if iters == 1000:
print('maxed iters')
#take care of the last point
weights = cubic_bezier_weights(1)
pi1 = cubic_bezier_blend_weights(p0, p1, p2, p3, weights)
cumul_length += (pi1 - pi0).length
s_t_map[cumul_length] = 1
dprint('initial dt %f, final dt %f' % (1 / initial_step, dt), l=4)
return s_t_map
def cubic_bezier_fit_points(l_co, error_scale, depth=0, t0=0, t3=1, allow_split=True, force_split=False):
'''
fits cubic bezier to given points
returns list of tuples of (t0,t3,p0,p1,p2,p3)
that best fits the given points l_co
where t0 and t3 are the passed-in t0 and t3
and p0,p1,p2,p3 are the control points of bezier
'''
assert l_co
if len(l_co)<3:
p0,p3 = l_co[0],l_co[-1]
p12 = (p0+p3)/2
return [(t0,t3,p0,p12,p12,p3)]
l_d = [0] + [(v0-v1).length for v0,v1 in zip(l_co[:-1],l_co[1:])]
l_ad = [s for d,s in common_utilities.iter_running_sum(l_d)]
dist = sum(l_d)
if dist <= 0:
print('cubic_bezier_fit_points: returning []')
return [] #[(t0,t3,l_co[0],l_co[0],l_co[0],l_co[0])]
l_t = [ad/dist for ad in l_ad]
ex,x0,x1,x2,x3 = cubic_bezier_fit_value([co[0] for co in l_co], l_t)
ey,y0,y1,y2,y3 = cubic_bezier_fit_value([co[1] for co in l_co], l_t)
ez,z0,z1,z2,z3 = cubic_bezier_fit_value([co[2] for co in l_co], l_t)
tot_error = ex+ey+ez
dprint('total error = %f (%f)' % (tot_error,error_scale), l=4)
if not force_split:
if tot_error < error_scale or depth == 4 or len(l_co)<=15 or not allow_split:
p0,p1,p2,p3 = Vector((x0,y0,z0)),Vector((x1,y1,z1)),Vector((x2,y2,z2)),Vector((x3,y3,z3))
return [(t0,t3,p0,p1,p2,p3)]
# too much error in fit. split sequence in two, and fit each sub-sequence
# find a good split point
ind_split = -1
mindot = 1.0
for ind in range(5,len(l_co)-5):
if l_t[ind] < 0.4: continue
if l_t[ind] > 0.6: break
#if l_ad[ind] < 0.1: continue
#if l_ad[ind] > dist-0.1: break
v0 = l_co[ind-4]
v1 = l_co[ind+0]
v2 = l_co[ind+4]
d0 = (v1-v0).normalized()
d1 = (v2-v1).normalized()
dot01 = d0.dot(d1)
if ind_split==-1 or dot01 < mindot:
ind_split = ind
mindot = dot01
if ind_split == -1:
# did not find a good splitting point!
p0,p1,p2,p3 = Vector((x0,y0,z0)),Vector((x1,y1,z1)),Vector((x2,y2,z2)),Vector((x3,y3,z3))
return [(t0,t3,p0,p1,p2,p3)]
l_co_left = l_co[:ind_split]
l_co_right = l_co[ind_split:]
tsplit = ind_split / (len(l_co)-1)
return cubic_bezier_fit_points(l_co_left, error_scale, depth=depth+1, t0=t0, t3=tsplit) + cubic_bezier_fit_points(l_co_right, error_scale, depth=depth+1, t0=tsplit, t3=t3)
def cubic_bezier_fit_points(l_co,
error_scale,
depth=0,
t0=0,
t3=1,
allow_split=True,
force_split=False):
'''
fits cubic bezier to given points
returns list of tuples of (t0,t3,p0,p1,p2,p3)
that best fits the given points l_co
where t0 and t3 are the passed-in t0 and t3
and p0,p1,p2,p3 are the control points of bezier
'''
assert l_co
if len(l_co) < 3:
p0, p3 = l_co[0], l_co[-1]
p12 = (p0 + p3) / 2
return [(t0, t3, p0, p12, p12, p3)]
l_d = [0] + [(v0 - v1).length for v0, v1 in zip(l_co[:-1], l_co[1:])]
l_ad = [s for d, s in common_utilities.iter_running_sum(l_d)]
dist = sum(l_d)
if dist <= 0:
print('cubic_bezier_fit_points: returning []')
return [] #[(t0,t3,l_co[0],l_co[0],l_co[0],l_co[0])]
l_t = [ad / dist for ad in l_ad]
ex, x0, x1, x2, x3 = cubic_bezier_fit_value([co[0] for co in l_co], l_t)
ey, y0, y1, y2, y3 = cubic_bezier_fit_value([co[1] for co in l_co], l_t)
ez, z0, z1, z2, z3 = cubic_bezier_fit_value([co[2] for co in l_co], l_t)
tot_error = ex + ey + ez
dprint('total error = %f (%f)' % (tot_error, error_scale), l=4)
if not force_split:
if tot_error < error_scale or depth == 4 or len(
l_co) <= 15 or not allow_split:
p0, p1, p2, p3 = Vector((x0, y0, z0)), Vector(
(x1, y1, z1)), Vector((x2, y2, z2)), Vector((x3, y3, z3))
return [(t0, t3, p0, p1, p2, p3)]
# too much error in fit. split sequence in two, and fit each sub-sequence
# find a good split point
ind_split = -1
mindot = 1.0
for ind in range(5, len(l_co) - 5):
if l_t[ind] < 0.4: continue
if l_t[ind] > 0.6: break
#if l_ad[ind] < 0.1: continue
#if l_ad[ind] > dist-0.1: break
v0 = l_co[ind - 4]
v1 = l_co[ind + 0]
v2 = l_co[ind + 4]
d0 = (v1 - v0).normalized()
d1 = (v2 - v1).normalized()
dot01 = d0.dot(d1)
if ind_split == -1 or dot01 < mindot:
ind_split = ind
mindot = dot01
if ind_split == -1:
# did not find a good splitting point!
p0, p1, p2, p3 = Vector((x0, y0, z0)), Vector((x1, y1, z1)), Vector(
(x2, y2, z2)), Vector((x3, y3, z3))
return [(t0, t3, p0, p1, p2, p3)]
l_co_left = l_co[:ind_split]
l_co_right = l_co[ind_split:]
tsplit = ind_split / (len(l_co) - 1)
return cubic_bezier_fit_points(
l_co_left, error_scale, depth=depth + 1, t0=t0,
t3=tsplit) + cubic_bezier_fit_points(
l_co_right, error_scale, depth=depth + 1, t0=tsplit, t3=t3)
