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mightyscape-1.1-deprecated/extensions/svgpathtools/smoothing.py

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2020-07-30 01:16:18 +02:00
"""This submodule contains functions related to smoothing paths of Bezier
curves."""
# External Dependencies
from __future__ import division, absolute_import, print_function
# Internal Dependencies
from .path import Path, CubicBezier, Line
from .misctools import isclose
from .paths2svg import disvg
def is_differentiable(path, tol=1e-8):
for idx in range(len(path)):
u = path[(idx-1) % len(path)].unit_tangent(1)
v = path[idx].unit_tangent(0)
u_dot_v = u.real*v.real + u.imag*v.imag
if abs(u_dot_v - 1) > tol:
return False
return True
def kinks(path, tol=1e-8):
"""returns indices of segments that start on a non-differentiable joint."""
kink_list = []
for idx in range(len(path)):
if idx == 0 and not path.isclosed():
continue
try:
u = path[(idx - 1) % len(path)].unit_tangent(1)
v = path[idx].unit_tangent(0)
u_dot_v = u.real*v.real + u.imag*v.imag
flag = False
except ValueError:
flag = True
if flag or abs(u_dot_v - 1) > tol:
kink_list.append(idx)
return kink_list
def _report_unfixable_kinks(_path, _kink_list):
mes = ("\n%s kinks have been detected at that cannot be smoothed.\n"
"To ignore these kinks and fix all others, run this function "
"again with the second argument 'ignore_unfixable_kinks=True' "
"The locations of the unfixable kinks are at the beginnings of "
"segments: %s" % (len(_kink_list), _kink_list))
disvg(_path, nodes=[_path[idx].start for idx in _kink_list])
raise Exception(mes)
def smoothed_joint(seg0, seg1, maxjointsize=3, tightness=1.99):
""" See Andy's notes on
Smoothing Bezier Paths for an explanation of the method.
Input: two segments seg0, seg1 such that seg0.end==seg1.start, and
jointsize, a positive number
Output: seg0_trimmed, elbow, seg1_trimmed, where elbow is a cubic bezier
object that smoothly connects seg0_trimmed and seg1_trimmed.
"""
assert seg0.end == seg1.start
assert 0 < maxjointsize
assert 0 < tightness < 2
# sgn = lambda x:x/abs(x)
q = seg0.end
try: v = seg0.unit_tangent(1)
except: v = seg0.unit_tangent(1 - 1e-4)
try: w = seg1.unit_tangent(0)
except: w = seg1.unit_tangent(1e-4)
max_a = maxjointsize / 2
a = min(max_a, min(seg1.length(), seg0.length()) / 20)
if isinstance(seg0, Line) and isinstance(seg1, Line):
'''
Note: Letting
c(t) = elbow.point(t), v= the unit tangent of seg0 at 1, w = the
unit tangent vector of seg1 at 0,
Q = seg0.point(1) = seg1.point(0), and a,b>0 some constants.
The elbow will be the unique CubicBezier, c, such that
c(0)= Q-av, c(1)=Q+aw, c'(0) = bv, and c'(1) = bw
where a and b are derived above/below from tightness and
maxjointsize.
'''
# det = v.imag*w.real-v.real*w.imag
# Note:
# If det is negative, the curvature of elbow is negative for all
# real t if and only if b/a > 6
# If det is positive, the curvature of elbow is negative for all
# real t if and only if b/a < 2
# if det < 0:
# b = (6+tightness)*a
# elif det > 0:
# b = (2-tightness)*a
# else:
# raise Exception("seg0 and seg1 are parallel lines.")
b = (2 - tightness)*a
elbow = CubicBezier(q - a*v, q - (a - b/3)*v, q + (a - b/3)*w, q + a*w)
seg0_trimmed = Line(seg0.start, elbow.start)
seg1_trimmed = Line(elbow.end, seg1.end)
return seg0_trimmed, [elbow], seg1_trimmed
elif isinstance(seg0, Line):
'''
Note: Letting
c(t) = elbow.point(t), v= the unit tangent of seg0 at 1,
w = the unit tangent vector of seg1 at 0,
Q = seg0.point(1) = seg1.point(0), and a,b>0 some constants.
The elbow will be the unique CubicBezier, c, such that
c(0)= Q-av, c(1)=Q, c'(0) = bv, and c'(1) = bw
where a and b are derived above/below from tightness and
maxjointsize.
'''
# det = v.imag*w.real-v.real*w.imag
# Note: If g has the same sign as det, then the curvature of elbow is
# negative for all real t if and only if b/a < 4
b = (4 - tightness)*a
# g = sgn(det)*b
elbow = CubicBezier(q - a*v, q + (b/3 - a)*v, q - b/3*w, q)
seg0_trimmed = Line(seg0.start, elbow.start)
return seg0_trimmed, [elbow], seg1
elif isinstance(seg1, Line):
args = (seg1.reversed(), seg0.reversed(), maxjointsize, tightness)
rseg1_trimmed, relbow, rseg0 = smoothed_joint(*args)
elbow = relbow[0].reversed()
return seg0, [elbow], rseg1_trimmed.reversed()
else:
# find a point on each seg that is about a/2 away from joint. Make
# line between them.
t0 = seg0.ilength(seg0.length() - a/2)
t1 = seg1.ilength(a/2)
seg0_trimmed = seg0.cropped(0, t0)
seg1_trimmed = seg1.cropped(t1, 1)
seg0_line = Line(seg0_trimmed.end, q)
seg1_line = Line(q, seg1_trimmed.start)
args = (seg0_trimmed, seg0_line, maxjointsize, tightness)
dummy, elbow0, seg0_line_trimmed = smoothed_joint(*args)
args = (seg1_line, seg1_trimmed, maxjointsize, tightness)
seg1_line_trimmed, elbow1, dummy = smoothed_joint(*args)
args = (seg0_line_trimmed, seg1_line_trimmed, maxjointsize, tightness)
seg0_line_trimmed, elbowq, seg1_line_trimmed = smoothed_joint(*args)
elbow = elbow0 + [seg0_line_trimmed] + elbowq + [seg1_line_trimmed] + elbow1
return seg0_trimmed, elbow, seg1_trimmed
def smoothed_path(path, maxjointsize=3, tightness=1.99, ignore_unfixable_kinks=False):
"""returns a path with no non-differentiable joints."""
if len(path) == 1:
return path
assert path.iscontinuous()
sharp_kinks = []
new_path = [path[0]]
for idx in range(len(path)):
if idx == len(path)-1:
if not path.isclosed():
continue
else:
seg1 = new_path[0]
else:
seg1 = path[idx + 1]
seg0 = new_path[-1]
try:
unit_tangent0 = seg0.unit_tangent(1)
unit_tangent1 = seg1.unit_tangent(0)
flag = False
except ValueError:
flag = True # unit tangent not well-defined
if not flag and isclose(unit_tangent0, unit_tangent1): # joint is already smooth
if idx != len(path)-1:
new_path.append(seg1)
continue
else:
kink_idx = (idx + 1) % len(path) # kink at start of this seg
if not flag and isclose(-unit_tangent0, unit_tangent1):
# joint is sharp 180 deg (must be fixed manually)
new_path.append(seg1)
sharp_kinks.append(kink_idx)
else: # joint is not smooth, let's smooth it.
args = (seg0, seg1, maxjointsize, tightness)
new_seg0, elbow_segs, new_seg1 = smoothed_joint(*args)
new_path[-1] = new_seg0
new_path += elbow_segs
if idx == len(path) - 1:
new_path[0] = new_seg1
else:
new_path.append(new_seg1)
# If unfixable kinks were found, let the user know
if sharp_kinks and not ignore_unfixable_kinks:
_report_unfixable_kinks(path, sharp_kinks)
return Path(*new_path)