kopia lustrzana https://github.com/inkstitch/inkstitch
290 wiersze
10 KiB
Python
290 wiersze
10 KiB
Python
# Authors: see git history
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#
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# Copyright (c) 2010 Authors
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# Licensed under the GNU GPL version 3.0 or later. See the file LICENSE for details.
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import math
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from math import tau
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import typing
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from copy import copy
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import numpy as np
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from shapely import geometry as shgeo
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from ..utils import prng
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from ..utils.geometry import Point
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""" Utility functions to produce running stitches. """
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def split_segment_even_n(a, b, segments: int, jitter_sigma: float = 0.0, random_seed=None) -> typing.List[shgeo.Point]:
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if segments <= 1:
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return []
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line = shgeo.LineString((a, b))
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splits = np.array(range(1, segments)) / segments
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if random_seed is not None:
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jitters = (prng.nUniformFloats(len(splits), random_seed) * 2) - 1
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splits = splits + jitters * (jitter_sigma / segments)
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# sort the splits in case a bad roll transposes any of them
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return [line.interpolate(x, normalized=True) for x in sorted(splits)]
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def split_segment_even_dist(a, b, max_length: float, jitter_sigma: float = 0.0, random_seed=None) -> typing.List[shgeo.Point]:
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distance = shgeo.Point(a).distance(shgeo.Point(b))
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segments = math.ceil(distance / max_length)
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return split_segment_even_n(a, b, segments, jitter_sigma, random_seed)
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def split_segment_random_phase(a, b, length: float, length_sigma: float, random_seed: str) -> typing.List[shgeo.Point]:
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line = shgeo.LineString([a, b])
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progress = length * prng.uniformFloats(random_seed, "phase")[0]
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splits = [progress]
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distance = line.length
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if progress >= distance:
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return []
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for x in prng.iterUniformFloats(random_seed):
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progress += length * (1 + length_sigma * (x - 0.5) * 2)
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if progress >= distance:
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break
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splits.append(progress)
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return [line.interpolate(x, normalized=False) for x in splits]
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class AngleInterval():
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# Modular interval containing either the entire circle or less than half of it
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# partially based on https://fgiesen.wordpress.com/2015/09/24/intervals-in-modular-arithmetic/
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def __init__(self, a: float, b: float, all: bool = False):
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self.all = all
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self.a = a
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self.b = b
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@staticmethod
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def all():
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return AngleInterval(0, math.tau, True)
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@staticmethod
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def fromBall(p: Point, epsilon: float):
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d = p.length()
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if d <= epsilon:
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return AngleInterval.all()
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center = p.angle()
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delta = math.asin(epsilon / d)
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return AngleInterval(center - delta, center + delta)
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@staticmethod
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def fromSegment(a: Point, b: Point):
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angleA = a.angle()
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angleB = b.angle()
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diff = (angleB - angleA) % tau
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if diff == 0 or diff == math.pi:
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return None
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elif diff < math.pi:
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return AngleInterval(angleA - 1e-6, angleB + 1e-6)
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# slightly larger than normal to avoid rounding error when this method is used in cutSegment
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else:
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return AngleInterval(angleB - 1e-6, angleA + 1e-6)
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def containsAngle(self, angle: float):
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if self.all:
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return True
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return (angle - self.a) % tau <= (self.b - self.a) % tau
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def containsPoint(self, p: Point):
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return self.containsAngle(math.atan2(p.y, p.x))
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def intersect(self, other):
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# assume that each interval contains less than half the circle (or all of it)
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if other is None:
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return None
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elif self.all:
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return other
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elif other.all:
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return self
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elif self.containsAngle(other.a):
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if other.containsAngle(self.b):
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return AngleInterval(other.a, self.b)
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else:
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return AngleInterval(other.a, other.b)
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elif other.containsAngle(self.a):
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if self.containsAngle(other.b):
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return AngleInterval(self.a, other.b)
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else:
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return AngleInterval(self.a, self.b)
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else:
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return None
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def cutSegment(self, origin: Point, a: Point, b: Point):
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if self.all:
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return None
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segArc = AngleInterval.fromSegment(a - origin, b - origin)
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if segArc is None:
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return a # b is exactly behind origin from a
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if segArc.containsAngle(self.a):
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return cut_segment_with_angle(origin, self.a, a, b)
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elif segArc.containsAngle(self.b):
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return cut_segment_with_angle(origin, self.b, a, b)
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else:
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return None
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def cut_segment_with_angle(origin: Point, angle: float, a: Point, b: Point) -> Point:
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# Assumes the crossing is inside the segment
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p = a - origin
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d = b - a
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c = Point(math.cos(angle), math.sin(angle))
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t = (p.y*c.x - p.x*c.y) / (d.x*c.y - d.y*c.x)
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if t < -0.000001 or t > 1.000001:
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raise Exception("cut_segment_with_angle returned a parameter of {0} with points {1} {2} and cut line {3} ".format(t, p, b-origin, c))
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return a + d*t
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def cut_segment_with_circle(origin: Point, r: float, a: Point, b: Point) -> Point:
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# assumes that a is inside the circle and b is outside
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p = a - origin
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d = b - a
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# inner products
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p2 = p * p
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d2 = d * d
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r2 = r * r
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pd = p * d
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# r2 = p2 + 2*pd*t + d2*t*t, quadratic formula
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t = (math.sqrt(pd*pd + r2*d2 - p2*d2) - pd) / d2
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if t < -0.000001 or t > 1.000001:
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raise Exception("cut_segment_with_circle returned a parameter of {0}".format(t))
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return a + d*t
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def take_stitch(start: Point, points: typing.Sequence[Point], idx: int, stitch_length: float, tolerance: float):
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# Based on a single step of the Zhao-Saalfeld curve simplification algorithm.
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# https://cartogis.org/docs/proceedings/archive/auto-carto-13/pdf/linear-time-sleeve-fitting-polyline-simplification-algorithms.pdf
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# Adds early termination condition based on stitch length.
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if idx >= len(points):
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return None, None
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sleeve = AngleInterval.all()
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last = start
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for i in range(idx, len(points)):
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p = points[i]
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if sleeve.containsPoint(p - start):
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if start.distance(p) < stitch_length:
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sleeve = sleeve.intersect(AngleInterval.fromBall(p - start, tolerance))
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last = p
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continue
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else:
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cut = cut_segment_with_circle(start, stitch_length, last, p)
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return cut, i
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else:
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cut = sleeve.cutSegment(start, last, p)
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if start.distance(cut) > stitch_length:
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cut = cut_segment_with_circle(start, stitch_length, last, p)
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return cut, i
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return points[-1], None
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def stitch_curve_evenly(points: typing.Sequence[Point], stitch_length: float, tolerance: float):
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# Will split a straight line into even-length stitches while still handling curves correctly.
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# Includes end point but not start point.
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if len(points) < 2:
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return []
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distLeft = [0] * len(points)
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for i in reversed(range(0, len(points) - 1)):
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distLeft[i] = distLeft[i + 1] + points[i].distance(points[i+1])
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i = 1
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last = points[0]
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stitches = []
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while i is not None and i < len(points):
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d = last.distance(points[i]) + distLeft[i]
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if d == 0:
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return stitches
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stitch_len = d / math.ceil(d / stitch_length) + 0.000001 # correction for rounding error
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stitch, newidx = take_stitch(last, points, i, stitch_len, tolerance)
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i = newidx
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if stitch is not None:
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stitches.append(stitch)
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last = stitch
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return stitches
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def path_to_curves(points: typing.List[Point], min_len: float):
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# split a path at obvious corner points so that they get stitched exactly
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# min_len controls the minimum length after splitting for which it won't split again,
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# which is used to avoid creating large numbers of corner points when encouintering micro-messes.
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if len(points) < 3:
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return [points]
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curves = []
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last = 0
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last_seg = points[1] - points[0]
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seg_len = last_seg.length()
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for i in range(1, len(points) - 1):
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# vectors of the last and next segments
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a = last_seg
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b = points[i + 1] - points[i]
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aabb = (a * a) * (b * b)
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abab = (a * b) * abs(a * b)
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# Test if the turn angle from vectors a to b is more than 45 degrees.
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# Optimized version of checking if cos(angle(a,b)) <= sqrt(0.5) and is defined
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if aabb > 0 and abab <= 0.5 * aabb:
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if seg_len >= min_len:
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curves.append(points[last: i + 1])
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last = i
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seg_len = 0
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if b * b > 0:
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last_seg = b
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seg_len += b.length()
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curves.append(points[last:])
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return curves
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def running_stitch(points, stitch_length, tolerance):
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# Turn a continuous path into a running stitch.
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stitches = [points[0]]
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for curve in path_to_curves(points, 2 * tolerance):
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# segments longer than twice the tollerance will usually be forced by it, so set that as the minimum for corner detection
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stitches.extend(stitch_curve_evenly(curve, stitch_length, tolerance))
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return stitches
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def bean_stitch(stitches, repeats):
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"""Generate bean stitch from a set of stitches.
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"Bean" stitch is made by backtracking each stitch to make it heavier. A
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simple bean stitch would be two stitches forward, one stitch back, two
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stitches forward, etc. This would result in each stitch being tripled.
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We'll say that the above counts as 1 repeat. Backtracking each stitch
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repeatedly will result in a heavier bean stitch. There will always be
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an odd number of threads piled up for each stitch.
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Repeats is a list of a repeated pattern e.g. [0, 1, 3] doesn't repeat the first stitch,
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goes back and forth on the second stitch, goes goes 3 times back and forth on the third stitch,
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and starts the pattern again by not repeating the fourth stitch, etc.
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"""
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if len(stitches) < 2:
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return stitches
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repeat_list_length = len(repeats)
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repeat_list_pos = 0
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new_stitches = [stitches[0]]
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for stitch in stitches:
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new_stitches.append(stitch)
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for i in range(repeats[repeat_list_pos]):
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new_stitches.extend(copy(new_stitches[-2:]))
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repeat_list_pos += 1
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if repeat_list_pos == repeat_list_length:
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repeat_list_pos = 0
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return new_stitches
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