1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
| import matplotlib
matplotlib.use('webagg')
import numpy as np
from scipy.special import binom
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
class BezierBuilder(object):
"""Bézier curve interactive builder.
"""
def __init__(self, control_polygon, ax_bernstein):
"""Constructor.
Receives the initial control polygon of the curve.
"""
self.control_polygon = control_polygon
self.xp = list(control_polygon.get_xdata())
self.yp = list(control_polygon.get_ydata())
self.canvas = control_polygon.figure.canvas
self.ax_main = control_polygon.get_axes()
self.ax_bernstein = ax_bernstein
# Event handler for mouse clicking
self.cid = self.canvas.mpl_connect('button_press_event', self)
# Create Bézier curve
line_bezier = Line2D([], [],
c=control_polygon.get_markeredgecolor())
self.bezier_curve = self.ax_main.add_line(line_bezier)
def __call__(self, event):
# Ignore clicks outside axes
if event.inaxes != self.control_polygon.axes:
return
# Add point
self.xp.append(event.xdata)
self.yp.append(event.ydata)
self.control_polygon.set_data(self.xp, self.yp)
# Rebuild Bézier curve and update canvas
self.bezier_curve.set_data(*self._build_bezier())
self._update_bernstein()
self._update_bezier()
def _build_bezier(self):
x, y = Bezier(list(zip(self.xp, self.yp))).T
return x, y
def _update_bezier(self):
self.canvas.draw()
def _update_bernstein(self):
N = len(self.xp) - 1
t = np.linspace(0, 1, num=200)
ax = self.ax_bernstein
ax.clear()
for kk in range(N + 1):
ax.plot(t, Bernstein(N, kk)(t))
ax.set_title("Bernstein basis, N = {}".format(N))
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
def Bernstein(n, k):
"""Bernstein polynomial.
"""
coeff = binom(n, k)
def _bpoly(x):
return coeff * x ** k * (1 - x) ** (n - k)
return _bpoly
def Bezier(points, num=200):
"""Build Bézier curve from points.
"""
N = len(points)
t = np.linspace(0, 1, num=num)
curve = np.zeros((num, 2))
for ii in range(N):
curve += np.outer(Bernstein(N - 1, ii)(t), points[ii])
return curve
if __name__ == '__main__':
# Initial setup
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
# Empty line
line = Line2D([], [], ls='--', c='#666666',
marker='x', mew=2, mec='#204a87')
ax1.add_line(line)
# Canvas limits
ax1.set_xlim(0, 1)
ax1.set_ylim(0, 1)
ax1.set_title("Bézier curve")
# Bernstein plot
ax2.set_title("Bernstein basis")
# Create BezierBuilder
bezier_builder = BezierBuilder(line, ax2)
plt.show() |
