/
svg_paths.py
174 lines (146 loc) · 5.8 KB
/
svg_paths.py
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
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
import re
def main():
path = "M 262.85714,266.6479 C 339.86994,315.42528 317.14286,172.36218 411.42857,258.07647"
path = 'M 23.128643,300.00104 L 74.827962,315.64688 C 74.827962,315.64688 79.589741,238.77816 103.39864,277.55265 C 127.20754,316.32714 127.88779,357.14239 157.81897,274.15138'
path = 'M 469.3754,192.52087 L 519.03396,139.46104 C 519.03396,139.46104 575.49506,120.41392 567.33201,182.99731 C 559.16895,245.5807 488.42252,244.90044 488.42252,244.90044 L 455.09006,228.57434 C 455.09006,228.57434 463.25311,220.41129 469.3754,192.52087 z'
path = 'M 92.099638,57.108572 C 92.099638,57.108572 96.525478,51.628959 102.4266,51.418205 C 108.32772,51.207451 107.90621,58.162343 113.80733,58.373097 C 119.70845,58.583852 131.29994,54.790274 134.88276,60.902149 C 138.46559,67.014025 142.04841,75.444197 133.82899,80.713055 C 125.60957,85.981913 120.55147,69.332322 113.80733,72.704391 C 107.06319,76.07646 108.74923,83.663616 102.21584,80.291547 C 95.682461,76.919478 79.454378,67.435533 79.454378,67.435533'
#print linearize_path(path)
# Polygon to triangulate
path = 'M 193.47779,368.65544 L 278.70015,486.1241 L 439.93164,352.53229 L 541.27715,437.75465 L 690.99211,258.0967 L 511.33416,299.55623 L 359.3159,156.75119 L 345.49605,366.35213 L 241.84724,350.22898 L 255.66708,198.21072 z'
#path = reverse_path(path)
print triangulate_path(path)
def point_in_triangle(p1, p2, p3, p):
for a, b in [(p1, p2), (p2, p3), (p3, p1)]:
if polygon_area(a, b, p) < 0:
return False
return True
def triangulate_path(path):
points = path_points(path)
if points[0] == points[-1]:
points = points[:-1]
triangles = []
while len(points) > 2:
n = len(points)
for i in xrange(n):
tri = points[(i-1) % n], points[i], points[(i+1) % n]
lp, cp, rp = tri
is_convex_vertice = polygon_area(lp, cp, rp) < 0
if is_convex_vertice and all(not point_in_triangle(rp, cp, lp, p)
for p in points
if p not in tri):
del points[i]
triangles.append((lp, cp, rp, lp))
break
return ' '.join(points_path(t, closed=True) for t in triangles)
def linearize_path(path):
"""
Creates a path with only M and L.
In path can contain M, L and C.
"""
new_path = []
for type, cs in get_path(path):
if type == 'M':
last_p = cs.next()
new_path.append('M %f,%f' % (last_p))
elif type == 'L':
last_p = cs.next()
new_path.append('L %f,%f' % (last_p))
elif type == 'C':
control_points = [last_p] + list(cs)
for p in bezier_points(control_points):
new_path.append('L %f,%f' % (p))
last_p = control_points[-1]
elif type == 'z':
new_path.append('z')
return ' '.join(new_path)
def bezier_points(p, steps = 10):
class SimpleVector(object):
def __init__(self, x, y):
self.x = x
self.y = y
def __add__(self, other):
return self.__class__(self.x + other.x, self.y + other.y)
def __sub__(self, other):
return self.__class__(self.x - other.x, self.y - other.y)
def __mul__(self, k):
return self.__class__(k * self.x, k * self.y)
def __iadd__(self, other):
self.x += other.x
self.y += other.y
return self
def __isub__(self, other):
self.x -= other.x
self.y -= other.y
return self
__rmul__ = __mul__
def bezier_iter(p, steps):
"""
http://www.niksula.cs.hut.fi/~hkankaan/Homepages/bezierfast.html
"""
t = 1.0 / steps
t2 = t*t
p0, p1, p2, p3 = p
f = p0
fd = 3 * (p1 - p0) * t
fdd_per_2 = 3 * (p0 - 2 * p1 + p2) * t2
fddd_per_2 = 3 * (3 * (p1 - p2) + p3 - p0) * t2 * t
fddd = fddd_per_2 + fddd_per_2
fdd = fdd_per_2 + fdd_per_2
fddd_per_6 = fddd_per_2 * (1.0 / 3)
for x in xrange(steps):
f += fd + fdd_per_2 + fddd_per_6
yield f
fd += fdd + fddd_per_2
fdd += fddd
fdd_per_2 += fddd_per_2
p = [SimpleVector(*t) for t in p]
return ((p.x, p.y) for p in bezier_iter(p, steps))
def path_points(path):
points = [tuple(map(float, e.split(',')))
for e in path.split() if len(e) > 1]
return points
def points_path(points, closed=False):
path = ['M %f,%f' % (points[0])]
for point in points[1:]:
path.append('L %f,%f' % point)
if closed:
path.append('z')
return ' '.join(path)
def get_path(path):
regex = re.compile('([MLCz])([-\d., ]*)')
return ((match.group(1),
(tuple(float(c) for c in p.split(','))
for p in match.group(2).split()))
for match in regex.finditer(path))
def split_paths(jumping_path):
return ['M%s' % p for p in jumping_path.split('M')[1:]]
def reverse_path(path):
new_type = 'M'
closed = False
new_path = []
for type, cs in reversed(list(get_path(path))):
if type == 'z':
closed = True
else:
x, y = cs.next()
new_path.append('%s %f,%f' % (new_type, x, y))
new_type = 'L'
if closed:
new_path.append('z')
return ' '.join(new_path)
def polygon_area(*points):
"""
http://local.wasp.uwa.edu.au/~pbourke/geometry/clockwise/
"""
n = len(points)
a = 0
for i in xrange(n):
j = (i + 1) % n
x, y = points[i]
nx, ny = points[j]
a += x * ny - nx * y
return a / 2.0
def path_area(path):
return polygon_area(*path_points(path))
if __name__ == '__main__':
main()