forked from CGLab-GIST/awl
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathlap.py
446 lines (352 loc) · 16.4 KB
/
lap.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
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
import torch
from torch_scatter import scatter, scatter_max, scatter_min
import numpy as np
class Geometry:
def __init__(self, v, f):
'''
for the caching
'''
self._v = v
self._f = f
self._nv = v.shape[0]
self._nf = f.shape[0]
self.device = v.device
self._v_deg = None
self._vertex_dualareas = None
self._vertex_bandwidth_cotan = None
self._vertex_bandwidth_uniform = None
self._face_areas = None
self._e = None
self._ne = None
self._edge_lengths = None
self._indices = None
self._coalesce_indices = None
self._lap_uniform_values = None
self._lap_cotangent_values = None
self._lap_kernel_fix = None
self._lap_kernel_ada = None
self._lap_kernel_mix = None
self._laplacian_uniform = None
self._laplacian_cotangent = None
self._laplacian_kernel = None
self._laplacian_ada = None
self._laplacian_mix = None
self._laplacian_mixture = None
self._adj = None
self._mesh_length = None
self._shape_scale = None
self.local_min = None
self.local_max = None
self.local_scale = None
def __calc_adjacency_list__(self):
if self._adj is not None:
return
ii = self._f[:, [1, 2, 0]].flatten()
jj = self._f[:, [2, 0, 1]].flatten()
self._adj = torch.stack([torch.cat([ii, jj]), torch.cat([jj, ii])], dim=0).unique(dim=1)
def __calc_vertex_degree__(self):
if self._v_deg is not None:
return
self.__calc_adjacency_list__()
self._v_deg = torch.unique(self._adj[0], return_counts=True)[1]
def __calc_edges__(self):
"""
from Continous remeshing. Palfinger 2022 CGI
returns tuple of
- edges E,2 long, 0 for unused, lower vertex index first
- face_to_edge F,3 long
- (optional) edge_to_face shape=E,[left,right],[face,side]
o-<-----e1 e0,e1...edge, e0<e1
| /A L,R....left and right face
| L / | both triangles ordered counter clockwise
| / R | normals pointing out of screen
V/ |
e0---->-o
"""
if self._e is not None:
return
F = self._nf
# make full edges, lower vertex index first
face_edges = torch.stack((self._f, self._f.roll(-1,1)),dim=-1) #F*3,3,2
full_edges = face_edges.reshape(F*3,2)
sorted_edges,_ = full_edges.sort(dim=-1) #F*3,2 TODO min/max faster?
# make unique edges
self._e, full_to_unique = torch.unique(input=sorted_edges, sorted=True, return_inverse=True, dim=0) #(E,2),(F*3)
self._ne = self._e.shape[0]
self._face_to_edge = full_to_unique.reshape(F,3) #F,3
is_right = full_edges[:,0]!=sorted_edges[:,0] #F*3
edge_to_face = torch.zeros((self._ne,2,2), dtype=torch.long, device=self.device) #E,LR=2,S=2
scatter_src = torch.cartesian_prod(torch.arange(0,F,device=self.device),torch.arange(0,3,device=self.device)) #F*3,2
edge_to_face.reshape(2*self._ne,2).scatter_(dim=0,index=(2*full_to_unique+is_right)[:,None].expand(F*3,2),src=scatter_src) #E,LR=2,S=2
edge_to_face[0] = 0
self._edge_to_face = edge_to_face
def __calc_edge_lengths__(self):
if self._edge_lengths is not None:
return
self.__calc_edges__()
full_vertices = self._v[self._e] #E,2,3
a,b = full_vertices.unbind(dim=1) #E,3
self._edge_lengths = torch.norm(a-b,p=2,dim=-1)
def __calc_mesh_length__(self):
if self._mesh_length is not None:
return
self.__calc_edge_lengths__()
self._mesh_length = torch.sum(self._edge_lengths)/self._ne
def __calc_faces_areas__(self):
if self._face_areas is not None:
return
face_verts = self._v[self._f]
v0, v1, v2 = face_verts[:, 0], face_verts[:, 1], face_verts[:, 2]
A = (v1 - v2).norm(dim=1)
B = (v0 - v2).norm(dim=1)
C = (v0 - v1).norm(dim=1)
s = 0.5 * (A + B + C)
self._face_areas = (s * (s - A) * (s - B) * (s - C)).clamp_(min=1e-12).sqrt()
def __calc_vertex_dualareas__(self):
if self._vertex_dualareas is not None:
return
self.__calc_faces_areas__()
vertex_dualareas = torch.zeros((self._nv, 3),dtype=self._v.dtype,device=self.device) #V,C=3,3
vertex_dualareas.scatter_add_(dim=0,index=self._f,src=self._face_areas[:, None].expand(self._nf, 3))
self._vertex_dualareas = vertex_dualareas.sum(dim=1) / 3.0 #V,3
def __calc_shape_scale__(self):
if self._shape_scale is not None:
return
self.__calc_faces_areas__()
self._shape_scale = torch.sqrt(torch.sum(self._face_areas))
def __calc_sparse_coo_indices__(self):
if self._indices is not None:
return
self.__calc_adjacency_list__()
diag_idx = self._adj[0]
self._indices = torch.cat((self._adj, torch.stack((diag_idx, diag_idx), dim=0)), dim=1)
def __calc_laplacian_uniform_indices_and_values(self, normalize=True, return_matrix=True):
if self._lap_uniform_values is not None:
return
self.__calc_adjacency_list__()
self.__calc_vertex_degree__()
self.__calc_sparse_coo_indices__()
adj = self._adj
adj_values = torch.ones(adj.shape[1], dtype=torch.float, device=self.device)
# normalization
if normalize:
deg = self._v_deg
adj_values = torch.div(adj_values[adj[1]], deg[adj[0]])
# Diagonal indicess
self._lap_uniform_values = torch.cat((-adj_values, adj_values))
self._laplacian_uniform = torch.sparse_coo_tensor(self._indices, self._lap_uniform_values, (self._nv,self._nv))
if self._coalesce_indices is None:
self._coalesce_indices = self._laplacian_uniform.indices()
def __calc_laplacian_cotangent_indices_and_values__(self, normalize=True):
"""
https://pytorch3d.readthedocs.io/en/latest/_modules/pytorch3d/loss/mesh_laplacian_smoothing.html
"""
if self._laplacian_cotangent is not None:
return
face_verts = self._v[self._f]
v0, v1, v2 = face_verts[:, 0], face_verts[:, 1], face_verts[:, 2]
A = (v1 - v2).norm(dim=1)
B = (v0 - v2).norm(dim=1)
C = (v0 - v1).norm(dim=1)
A2, B2, C2 = A * A, B * B, C * C
cota = (B2 + C2 - A2)
cotb = (A2 + C2 - B2)
cotc = (A2 + B2 - C2)
cot = torch.stack([cota, cotb, cotc], dim=1)
cot /= 2.0
ii = self._f[:, [1, 2, 0]]
jj = self._f[:, [2, 0, 1]]
idx = torch.stack([ii, jj], dim=0).view(2, self._nf * 3)
L = torch.sparse.FloatTensor(idx, cot.view(-1), (self._nv, self._nv))
L += L.t()
L = L.coalesce()
values = torch.sparse.sum(L, dim=0).to_dense()
sym_indices = torch.arange(self._nv, device=self.device)
sym_indices = torch.stack([sym_indices, sym_indices], dim=0)
if normalize:
values = 1./values
L_indices = L.indices()
D = torch.sparse.FloatTensor(L_indices, L.values()*values[L_indices[0]], (self._nv, self._nv))
L = torch.sparse.FloatTensor(sym_indices, torch.ones_like(values), (self._nv, self._nv)) - D
self._laplacian_cotangent = L.coalesce()
self._lap_cotangent_values = self._laplacian_cotangent.values()
if self._coalesce_indices is None:
self._coalesce_indices = self._laplacian_cotangent.indices()
else:
L = torch.sparse.FloatTensor(sym_indices, values, (self._nv, self._nv)) - L
self._laplacian_cotangent = L.coalesce()
self._lap_cotangent_values = self._laplacian_cotangent.values()
if self._coalesce_indices is None:
self._coalesce_indices = self._laplacian_cotangent.indices()
def __calc_vertex_normalize_local__(self):
if self.local_min is not None:
return
adj_verts = self._v[self._coalesce_indices[1]]
mins, _ = scatter_min(src=adj_verts, index=self._coalesce_indices[0][:, None].expand(-1, 3), dim=0)
maxs, _ = scatter_max(src=adj_verts, index=self._coalesce_indices[0][:, None].expand(-1, 3), dim=0)
range_ = (maxs-mins)/2.0
mins = mins-range_
maxs = maxs+range_
self.local_min, self.local_max = mins, maxs
def __calc_laplacian_kernelized_indices_and_values__(self, bandwidth=None, normalize=True):
if self._laplacian_kernel is not None:
return
self.__calc_sparse_coo_indices__()
self.__calc_vertex_normalize_local__()
h = bandwidth
if h is None:
self.__calc_vertex_degree__()
self.__calc_edge_lengths__()
h = scatter(self._edge_lengths, index=self._e[:, 1], dim=0)/self._v_deg
h = torch.max(((h[self._adj[1]] + h[self._adj[0]])/2.0)**(0.4), torch.tensor([1e-8], device=self.device))
mmrange = 1.0
if normalize:
mmrange = 2.0/(self.local_max[self._adj[0]] - self.local_min[self._adj[0]])
local_v = (self._v[self._adj[0]]-self._v[self._adj[1]])*mmrange
distance = (local_v).square().sum(dim=1)
values = self.__gaussian(h, distance)/h
summ = scatter(values, index=self._adj[1], dim=0)
values = torch.div(values, summ[self._adj[1]])
values = torch.cat((-values, values))
L = torch.sparse.FloatTensor(self._indices, values, (self._nv, self._nv))
self._laplacian_kernel = L.coalesce()
self._lap_kernel_fix = self._laplacian_kernel.values()
if self._coalesce_indices is None:
self._coalesce_indices = self._laplacian_kernel.indices()
return
def __calc_asymtotic_bandwidth__(self, coeff, scale):
self.__calc_vertex_dualareas__()
self.__calc_mesh_length__()
self.__calc_laplacian_cotangent_indices_and_values__(True)
self.__calc_laplacian_kernelized_indices_and_values__(None, True)
# local normalized coordinates
g_scale = torch.norm(self.local_max-self.local_min, dim=1, p=2) * scale
h_common = 3 * coeff * self._vertex_dualareas / (torch.pi)
mmrange = 2.0/(self.local_max[self._coalesce_indices[0]] - self.local_min[self._coalesce_indices[0]])
local_v = (self._v[self._coalesce_indices[0]]-self._v[self._coalesce_indices[1]])*mmrange
# gather edge weights
Wker = self._lap_kernel_fix
Wcot = self._lap_cotangent_values
Lu = scatter(src=Wker[:, None].expand(-1, 3)*local_v, index=self._coalesce_indices[0], dim=0, reduce='sum')
Ln = scatter(src=Wcot[:, None].expand(-1, 3)*local_v, index=self._coalesce_indices[0], dim=0, reduce='sum')
Lu = torch.sum(torch.square(Lu), dim=1)
hu = h_common/torch.max(torch.tensor([1e-8], device=self.device), Lu)
hu = torch.pow(hu, 1.0/7.0)
Ln = torch.sum(torch.square(Ln), dim=1)
hn = h_common/torch.max(torch.tensor([1e-8], device=self.device), Ln)
hn = torch.pow(hn, 1.0/7.0)
self._vertex_bandwidth_uniform = hu * g_scale
self._vertex_bandwidth_cotan = hn * g_scale
def __gaussian(
self,
h:torch.tensor, # input bandwidth
dist:torch.tensor # L2 distance between two vertices
)->torch.tensor:
const = 1.0/(4*torch.pi*h);
return torch.exp(-1.0 * dist/(4.0*h)) * const
def __calc_laplacian_adaptive_indices_and_values__(self, coeff, scale_range, cotan):
'''
None mixed version
'''
if self._laplacian_ada is not None:
return
self.__calc_asymtotic_bandwidth__(coeff, scale_range)
self.__calc_sparse_coo_indices__()
if cotan == True:
h = self._vertex_bandwidth_cotan
else:
h = self._vertex_bandwidth_uniform
distance = (self._v[self._adj[0]] - self._v[self._adj[1]]).square().sum(dim=1)
w0 = self.__gaussian(h[self._adj[0]], distance)
w1 = self.__gaussian(h[self._adj[1]], distance)
val0 = w0/h[self._adj[0]]*self._vertex_dualareas[self._adj[0]]
val1 = w1/h[self._adj[1]]*self._vertex_dualareas[self._adj[1]]
adj_values = (val0*val1).sqrt()
values = adj_values
values = torch.cat((-values, values))
L = torch.sparse.FloatTensor(self._indices, values, (self._nv, self._nv))
self._laplacian_ada = L.coalesce()
self._lap_kernel_ada = self._laplacian_ada.values()
if self._coalesce_indices is None:
self._coalesce_indices = self._laplacian_ada.indices()
def __calc_laplacian_mixed_indices_and_values__(self, coeff, scale):
'''
weight mix
'''
if self._laplacian_mix is not None:
return
self.__calc_asymtotic_bandwidth__(coeff, scale)
self.__calc_sparse_coo_indices__()
h0 = self._vertex_bandwidth_cotan
h1 = self._vertex_bandwidth_uniform
distance = (self._v[self._adj[0]] - self._v[self._adj[1]]).square().sum(dim=1)
w00 = self.__gaussian(h0[self._adj[0]], distance)
w01 = self.__gaussian(h0[self._adj[1]], distance)
w10 = self.__gaussian(h1[self._adj[0]], distance)
w11 = self.__gaussian(h1[self._adj[1]], distance)
w002, w012 = w00, w01
w102, w112 = w10, w11
Wsum0, Wsum1 = w002+w102, w012+w112
val1 = (w00*w002/Wsum0/h0[self._adj[0]] + w10*w102/Wsum0/h1[self._adj[0]])*self._vertex_dualareas[self._adj[0]]
val2 = (w01*w012/Wsum1/h0[self._adj[1]] + w11*w112/Wsum1/h1[self._adj[1]])*self._vertex_dualareas[self._adj[1]]
adj_values = torch.sqrt(val1*val2)
values = adj_values
values = torch.cat((-values, values))
L = torch.sparse.FloatTensor(self._indices, values, (self._nv, self._nv))
self._laplacian_mix = L.coalesce()
self._lap_kernel_mix = self._laplacian_mix.values()
if self._coalesce_indices is None:
self._coalesce_indices = self._laplacian_mix.indices()
def __calc_sparse_coo__(self, indices, values):
return torch.sparse_coo_tensor(indices, values, (self._nv, self._nv)).coalesce()
'''
public functions for real usage
'''
def laplacian_uniform(self):
if self._laplacian_uniform is not None:
return self._laplacian_uniform
self.__calc_laplacian_uniform_indices_and_values()
return self._laplacian_uniform
def laplacian_cotangent(self):
if self._laplacian_cotangent is not None:
return self._laplacian_cotangent
self.__calc_laplacian_cotangent_indices_and_values__()
return self._laplacian_cotangent
def laplacian_adaptive(self, weight, scale):
if self._laplacian_mix is not None:
return self._laplacian_mix.coalesce()
self.__calc_laplacian_mixed_indices_and_values__(weight, scale)
return self._laplacian_mix.coalesce()
# accessing functions: use here
def vertex_dualareas(verts, faces):
geom = Geometry(verts, faces)
geom.__calc_vertex_dualareas__()
return geom._vertex_dualareas
def asymtotic_bandwidth(verts, faces, smoothing_weight):
geom = Geometry(verts, faces)
geom.__calc_asymtotic_bandwidth__(smoothing_weight)
return geom._vertex_bandwidth_cotan, geom._vertex_bandwidth_uniform
def laplacian_uniform(verts, faces):
geom = Geometry(verts, faces)
return geom.laplacian_uniform()
def laplacian_cotangent(verts, faces, weight=None):
geom = Geometry(verts, faces)
return geom.laplacian_cotangent()
def laplacian_adaptive(verts, faces, weight, scale):
geom = Geometry(verts, faces)
return geom.laplacian_adaptive(weight, scale)
def csc_cpu_to_coo_gpu(csc_cpu):
coo = csc_cpu.tocoo()
indices = np.vstack((coo.row, coo.col))
values = coo.data
ind = torch.tensor(indices, dtype=torch.long)
val = torch.tensor(values, dtype=torch.float64)
L = torch.sparse_coo_tensor(ind, val, coo.shape).cuda()
return L.coalesce()
# testing
if __name__ == "__main__":
pos = [[0.0, 0.0, 0.0], [1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]
ind = [[0, 1, 2]]
v, f = torch.tensor(pos, dtype=torch.float64), torch.tensor(ind, dtype=torch.long)
cot = laplacian_cotangent(v, f)
ada = laplacian_adaptive(v, f, 0.96, 0.1)