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mightyscape-1.1-deprecated/extensions/fablabchemnitz/inkscape_helper/BezierCurve.py

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2020-07-30 01:16:18 +02:00
from __future__ import division
from PathSegment import *
from math import hypot
class BezierCurve(PathSegment):
nr_points = 10
def __init__(self, P): # number of points is limited to 3 or 4
if len(P) == 3: # quadratic
self.B = lambda t : (1 - t)**2 * P[0] + 2 * (1 - t) * t * P[1] + t**2 * P[2]
self.Bd = lambda t : 2 * (1 - t) * (P[1] - P[0]) + 2 * t * (P[2] - P[1])
self.Bdd = lambda t : 2 * (P[2] - 2 * P[1] + P[0])
elif len(P) == 4: #cubic
self.B = lambda t : (1 - t)**3 * P[0] + 3 * (1 - t)**2 * t * P[1] + 3 * (1 - t) * t**2 * P[2] + t**3 * P[3]
self.Bd = lambda t : 3 * (1 - t)**2 * (P[1] - P[0]) + 6 * (1 - t) * t * (P[2] - P[1]) + 3 * t**2 * (P[3] - P[2])
self.Bdd = lambda t : 6 * (1 - t) * (P[2] - 2 * P[1] + P[0]) + 6 * t * (P[3] - 2 * P[2] + P[1])
self.tangent = lambda t : self.Bd(t)
# self.curvature = lambda t : (Bd(t).x * Bdd(t).y - Bd(t).y * Bdd(t).x) / hypot(Bd(t).x, Bd(t).y)**3
self.distances = [0] # cumulative distances for each 't'
prev_pt = self.B(0)
for i in range(self.nr_points):
t = (i + 1) / self.nr_points
pt = self.B(t)
self.distances.append(self.distances[-1] + hypot(prev_pt.x - pt.x, prev_pt.y - pt.y))
prev_pt = pt
self._length = self.distances[-1]
def curvature(self, t):
n = self.Bd(t).x * self.Bdd(t).y - self.Bd(t).y * self.Bdd(t).x
d = hypot(self.Bd(t).x, self.Bd(t).y)**3
if d == 0:
return n * float('inf')
else:
return n / d
@classmethod
def quadratic(cls, start, c, end):
bezier = cls()
@classmethod
def cubic(cls, start, c1, c2, end):
bezier = cls()
def __make_eq__(self):
pass
@property
def length(self):
return self._length
def subdivide(self, part_length, start_offset=0):
nr_parts = int((self.length - start_offset) // part_length)
k_o = start_offset / self.length
k2t = lambda k : k_o + k * part_length / self.length
points = [self.pathpoint_at_t(k2t(k)) for k in range(nr_parts + 1)]
return(points, self.length - points[-1].c_dist)
def pathpoint_at_t(self, t):
"""pathpoint on the curve from t=0 to point at t."""
step = 1 / self.nr_points
pt_idx = int(t / step)
length = self.distances[pt_idx]
ip_fact = (t - pt_idx * step) / step
if ip_fact > 0 and t < 1: # not a perfect match, need to interpolate
length += ip_fact * (self.distances[pt_idx + 1] - self.distances[pt_idx])
return PathPoint(t, self.B(t), self.tangent(t), self.curvature(t), length)
def t_at_length(self, length):
"""interpolated t where the curve is at the given length"""
if length == self.length:
return 1
i_small = 0
i_big = self.nr_points + 1
while i_big - i_small > 1: # binary search
i_half = i_small + (i_big - i_small) // 2
if self.distances[i_half] <= length:
i_small = i_half
else:
i_big = i_half
small_dist = self.distances[i_small]
return i_small / self.nr_points + (length - small_dist) * (self.distances[i_big] - small_dist) # interpolated length