-
Notifications
You must be signed in to change notification settings - Fork 0
/
MazeSimple.py
388 lines (319 loc) · 12.2 KB
/
MazeSimple.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
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
import concurrent.futures as cf
import math
import sys
import timeit
import matplotlib.cm as cm
import matplotlib.pyplot as plt
import numpy as np
from numba import jit
import AttractRepel
import Hilbert
import Quantization
import Segments
import TSPopt
@jit
def _ptlen_local(a, b):
return math.hypot(a[0] - b[0], a[1] - b[1])
@jit
def _ptlen2_local(a, b):
return (a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2
@jit
def _repulse(r):
force = (r ** 12)
return force
class MazeSimple:
K0 = 0.1 # [0.1;0.3]
K1 = 0.15 # [1.5*K0; 2.5*K0]
D = 10 # dimensional adjustment?
KMIN = 0.25
KMAX = 0.7
Ff = 0.1 # [0.005; 0.3]
Fb = 0.03 # [0; 0.2]
Fa = 1. # [0; 10]
Fo = 1.
R0 = 2.
R1_R0 = 2.5
R0_B = 10.
TAKEN_SAMPLE_SIZE = 20
CHUNK = 4000
PROCESSORS = 4
def delta(self, i):
d = self.maze_path[i]
v = self.imin[d[0], d[1]]
assert v >= 0
assert v < 256
return float(v + 1) / 256.
@jit(cache=True)
def brownian(self):
mean = [0., 0.]
cov = [[1., 0.], [0., 1.]]
size = len(self.maze_path)
x, y = np.random.multivariate_normal(mean, cov, size).T
z = list(zip(x, y))
brownA = np.empty([size, 2])
for i, zi in enumerate(z):
n = np.array(zi)
n = np.multiply(n, self.Fb)
brownA[i] = n
return brownA
@staticmethod
@jit
def density(pixel_val):
x = 256 / (256 - pixel_val)
# x = 1. + math.log(pixel_val + 1, 2.)
return x
@jit
def R0_val(self, i_pt):
i_pt0 = max(min(round(i_pt[0]), self.imin.shape[0] - 1), 0)
i_pt1 = max(min(round(i_pt[1]), self.imin.shape[1] - 1), 0)
r0 = self.R0 * self.density(self.imin[i_pt0][i_pt1])
return r0, self.R1_R0 * r0
def attract_repel_serial(self):
"""
This is the brute force version
Returns:
attract repel vector
"""
fi_l = AttractRepel.attract_repel_global(im=self.imin, maze_path=self.maze_path,
R0=self.R0, R1_R0=self.R1_R0,
Fa=self.Fa)
return np.array(fi_l)
@jit
def boundary_slow(self):
"""
This is the brute force version
Returns:
boundary vector
"""
returnA = np.empty([len(self.maze_path), 2])
R1 = 2.0 * self.R0_B
for i in range(0,
len(self.maze_path)):
fi = np.array([0., 0.])
pi = np.array(self.maze_path[i])
for j in range(0,
len(self.boundary_seg) - 1):
j_pt = self.boundary_seg[j]
jp1_pt = self.boundary_seg[j + 1]
pi2xij, xij = TSPopt.distABtoP(j_pt, jp1_pt, pi)
self.minDist = min(self.minDist, pi2xij)
if pi2xij < R1:
fij = (pi - xij) / max(0.00001, pi2xij)
fij *= _repulse(self.R0_B / pi2xij) * self.Fo
fi += fij
returnA[i] = fi
return returnA
def resampling(self):
tmp3 = []
ptA = self.maze_path[0]
tmp3.append(ptA)
r0_a, _ = self.R0_val(ptA)
skip = False
for ptB in self.maze_path[1:]:
skip = False
r0_b, _ = self.R0_val(ptB)
d = _ptlen_local(ptA, ptB)
r0_ab = (r0_a + r0_b) / 2
if d > self.KMAX * r0_ab:
ptAB = np.multiply(np.add(ptA, ptB), 0.5)
tmp3.append(ptAB)
tmp3.append(ptB)
elif d < self.KMIN * r0_ab:
skip = True
else:
tmp3.append(ptB)
ptA = ptB
r0_a = r0_b
# if the last value was skipped, reattach it.
if skip:
tmp3.append(ptB)
self.maze_path = tmp3
self.lenList.append(len(self.maze_path))
def optimize_loop2(self, loop_bound=1000, img_dump=100, equil=1.025, tsp=10):
# Main optimize loop
# keep running until stopping criteria met
loop_count = 0
start_time = timeit.default_timer()
while True:
# compute force on each node
brownian = self.brownian()
attract_repel = self.attract_repel_serial()
boundary = self.boundary_slow()
# move each node
netforce = np.add(boundary, attract_repel)
deltaforce = np.array([np.hypot(a[0], a[1]) for a in netforce])
maxdelta = deltaforce.max()
if maxdelta > 0.1:
ceil_force = np.multiply(netforce,0.1 / maxdelta)
#for nf, df in zip(netforce, deltaforce):
# ceil_force.append(np.multiply(nf, 0.1 / (maxdelta)))
#ceil_force = np.array(ceil_force)
else:
ceil_force = np.array(netforce)
netmove = np.add(ceil_force, brownian)
tmp2 = np.add(self.maze_path, netmove)
tmp3 = [[min(self.bndry_xmax - 1, max(self.xmin + 1, x)),
min(self.bndry_ymax - 1, max(self.ymin + 1, y))] for x, y in tmp2]
tmp3[0] = self.maze_path[0]
tmp3[-1] = self.maze_path[-1]
self.maze_path = np.array(tmp3)
# resampling
self.resampling()
# stopping criteria
if loop_count > loop_bound:
break
if loop_count % img_dump == 0:
self.plotMazeImage("img/fig" + str(loop_count).zfill(5) + ".png")
elapsed = timeit.default_timer() - start_time
start_time = timeit.default_timer()
print(str(loop_count) + " " + str(len(self.maze_path)) + " " + str(elapsed))
loop_count += 1
self.plotMazeImage("figLast.png", points=True)
def plotMazeImage(self, name, points=False,superimpose=False):
plt_x = [a[0] for a in self.maze_path]
plt_y = [a[1] for a in self.maze_path]
if superimpose:
plt.imshow(np.transpose(self.imin), cmap=cm.gray)
if points:
plt.plot(plt_x, plt_y, '.-')
else:
plt.plot(plt_x, plt_y, '-', linewidth=0.3)
plt.gca().set_aspect('equal', adjustable='box')
plt.savefig(name,dpi=600)
plt.clf()
def maze_to_segments(self):
self.segments = Segments.Segments()
self.segments.append(self.maze_path)
def __init__(self, image_matrix, white=1, levels=4, init_shape=3):
"""
:param image_matrix:
"""
self.dnCount = 0
self.dnSum = 0.
self.upCount = 0
self.upSum = 0.
self.lenList = list()
self.imin = image_matrix
self.xmin = 0
self.ymin = 0
self.xmax = self.imin.shape[0] - 1
self.ymax = self.imin.shape[1] - 1
# whiten
self.imin /= white
self.imin += 255 - (255 // white)
# quantize
self.centroids = Quantization.measCentroid(self.imin, levels)
print(self.centroids)
levels = min(levels, len(self.centroids))
levels = max(2, levels)
nq = np.array([[x * 255 / (levels - 1)] for x in range(0, levels)])
self.imin = Quantization.quantMatrix(self.imin, nq, self.centroids)
plt.imshow(self.imin, cmap=cm.gray)
plt.savefig("figStartOrig.png")
plt.clf()
# self.R0_B = self.density(nq[-1][0])
# Initial segment
if init_shape == 1:
moore = []
m = []
n = 1 << 7
for i in range(0, n ** 2):
x, y = Hilbert.d2xy(n, i, True)
m.append((x, y))
moore.append(((self.imin.shape[0] * x) / (n - 1),
(self.imin.shape[1] * y) / (n - 1)))
'''
Rotate the moore graph to start in the middle
'''
m2q = len(moore) // 4
moore2 = moore[m2q:]
moore2.extend(moore[:m2q])
'''
Add the first and last point to return to start
'''
ptAlpha = np.multiply(np.array(self.imin.shape), 0.5)
moore2.append(tuple(ptAlpha))
moore2.insert(0, tuple(ptAlpha))
moore3 = [(0.95 * x + 0.025 * self.imin.shape[0], 0.95 * y + 0.025 * self.imin.shape[1]) for x, y in moore2]
self.maze_path = np.array(moore3)
self.plotMazeImage("figStart0.png")
self.maze_path = TSPopt.simplify(self.maze_path)
for i in range(10):
self.resampling()
self.plotMazeImage("figStart1.png")
self.maze_path = TSPopt.simplify(self.maze_path)
while True:
delta, seg1 = TSPopt.threeOptLocal(self.maze_path, 40)
self.maze_path = seg1
if delta == 0.:
break
self.plotMazeImage("figStart2.png")
for i in range(10):
self.resampling()
'''
Have to add a brownian to thois because when you do the resample, you could end up with points
on the same line, which will lead to a divb0 issue.
'''
brownian = self.brownian()
self.maze_path = np.add(self.maze_path, brownian)
self.plotMazeImage("figStart3.png")
elif init_shape == 2:
import LSystem
gosper = LSystem.LSystem(axiom='B',
rules=[('A', 'A-B--B+A++AA+B-'),
('B', '+A-BB--B-A++A+B')],
angle=60.0)
gosper.iterate(5)
self.maze_path = np.array(gosper.segment(initialpt=[200.0, 600.0], d=4.0))
self.plotMazeImage("figStartGosper0.png")
elif init_shape == 3:
import LSystem
fass2 = LSystem.LSystem(axiom="FX",
rules=[('X','Y-LFL-FRF-LFLFL-FRFR+F'),
('Y','X+RFR+FLF+RFRFR+FLFL-F'),
('L','LF+RFR+FL-F-LFLFL-FRFR+'),
('R','-LFLF+RFRFR+F+RF-LFL-FR')],
angle = 90)
fass2.iterate(5)
path1=np.array(fass2.segment(initialpt=[0.0,0.0], d=1.0))
dim = path1.max() - path1.min()
path2 = list()
path1min = path1.min()
for pt in path1:
path2.append(((self.imin.shape[0] * (pt[0]-path1min)) / (dim - 1),
(self.imin.shape[1] * (pt[1]-path1min)) / (dim - 1)))
path3 = [(0.95 * x + 0.025 * self.imin.shape[0], 0.95 * y + 0.025 * self.imin.shape[1]) for x, y in path2]
self.maze_path = path3
self.plotMazeImage("figFass2_0.png")
self.maze_path = TSPopt.simplify(self.maze_path)
for i in range(10):
self.resampling()
self.plotMazeImage("figFass2_1.png")
self.maze_path = TSPopt.simplify(self.maze_path)
while True:
delta, seg1 = TSPopt.threeOptLocal(self.maze_path, 40)
self.maze_path = seg1
if delta == 0.:
break
self.plotMazeImage("figFass2_2.png")
for i in range(10):
self.resampling()
else:
self.maze_path = [(0., 0.)]
segListEnd = tuple([x - 1 for x in self.imin.shape])
self.maze_path.append(segListEnd)
self.maze_path = np.array(self.maze_path)
self.seg = Segments.Segments()
factor = 0.5
delta = 0.0
self.bndry_xmax = self.xmax + factor * self.R0_B - delta
self.bndry_ymax = self.ymax + factor * self.R0_B - delta
self.bndry_xmin = self.xmin - factor * self.R0_B + delta
self.bndry_ymin = self.ymin - factor * self.R0_B + delta
pt_00 = (self.bndry_xmin, self.bndry_ymin)
pt_01 = (self.bndry_xmin, self.bndry_ymax)
pt_11 = (self.bndry_xmax, self.bndry_ymax)
pt_10 = (self.bndry_xmax, self.bndry_ymin)
self.boundary_seg = [pt_00, pt_01, pt_11, pt_10, pt_00]
self.minDist = sys.float_info.max
# self.seg.scale(1.0) # fix the types. Hygiene