File size: 16,559 Bytes
434b0b0 | 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 | import torch
import torch.nn.functional as tfunc
import torch_scatter
def prepend_dummies(
vertices: torch.Tensor, # V,D
faces: torch.Tensor, # F,3 long
) -> tuple[torch.Tensor, torch.Tensor]:
"""prepend dummy elements to vertices and faces to enable "masked" scatter operations"""
V, D = vertices.shape
vertices = torch.concat(
(torch.full((1, D), fill_value=torch.nan, device=vertices.device), vertices),
dim=0,
)
faces = torch.concat(
(torch.zeros((1, 3), dtype=torch.long, device=faces.device), faces + 1), dim=0
)
return vertices, faces
def remove_dummies(
vertices: torch.Tensor, # V,D - first vertex all nan and unreferenced
faces: torch.Tensor, # F,3 long - first face all zeros
) -> tuple[torch.Tensor, torch.Tensor]:
"""remove dummy elements added with prepend_dummies()"""
return vertices[1:], faces[1:] - 1
def calc_edges(
faces: torch.Tensor, # F,3 long - first face may be dummy with all zeros
with_edge_to_face: bool = False,
) -> tuple[torch.Tensor, ...]:
"""
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
"""
F = faces.shape[0]
# make full edges, lower vertex index first
face_edges = torch.stack((faces, faces.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
edges, full_to_unique = torch.unique(
input=sorted_edges, sorted=True, return_inverse=True, dim=0
) # (E,2),(F*3)
E = edges.shape[0]
face_to_edge = full_to_unique.reshape(F, 3) # F,3
if not with_edge_to_face:
return edges, face_to_edge
is_right = full_edges[:, 0] != sorted_edges[:, 0] # F*3
edge_to_face = torch.zeros(
(E, 2, 2), dtype=torch.long, device=faces.device
) # E,LR=2,S=2
scatter_src = torch.cartesian_prod(
torch.arange(0, F, device=faces.device), torch.arange(0, 3, device=faces.device)
) # F*3,2
edge_to_face.reshape(2 * E, 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
return edges, face_to_edge, edge_to_face
def calc_edge_length(
vertices: torch.Tensor, # V,3 first may be dummy
edges: torch.Tensor, # E,2 long, lower vertex index first, (0,0) for unused
) -> torch.Tensor: # E
full_vertices = vertices[edges] # E,2,3
a, b = full_vertices.unbind(dim=1) # E,3
return torch.norm(a - b, p=2, dim=-1)
def calc_face_normals(
vertices: torch.Tensor, # V,3 first vertex may be unreferenced
faces: torch.Tensor, # F,3 long, first face may be all zero
normalize: bool = False,
) -> torch.Tensor: # F,3
"""
n
|
c0 corners ordered counterclockwise when
/ \ looking onto surface (in neg normal direction)
c1---c2
"""
full_vertices = vertices[faces] # F,C=3,3
v0, v1, v2 = full_vertices.unbind(dim=1) # F,3
face_normals = torch.cross(v1 - v0, v2 - v0, dim=1) # F,3
if normalize:
face_normals = tfunc.normalize(face_normals, eps=1e-6, dim=1) # TODO inplace?
return face_normals # F,3
def calc_vertex_normals(
vertices: torch.Tensor, # V,3 first vertex may be unreferenced
faces: torch.Tensor, # F,3 long, first face may be all zero
face_normals: torch.Tensor = None, # F,3, not normalized
) -> torch.Tensor: # F,3
F = faces.shape[0]
if face_normals is None:
face_normals = calc_face_normals(vertices, faces)
vertex_normals = torch.zeros(
(vertices.shape[0], 3, 3), dtype=vertices.dtype, device=vertices.device
) # V,C=3,3
vertex_normals.scatter_add_(
dim=0,
index=faces[:, :, None].expand(F, 3, 3),
src=face_normals[:, None, :].expand(F, 3, 3),
)
vertex_normals = vertex_normals.sum(dim=1) # V,3
return tfunc.normalize(vertex_normals, eps=1e-6, dim=1)
def calc_face_ref_normals(
faces: torch.Tensor, # F,3 long, 0 for unused
vertex_normals: torch.Tensor, # V,3 first unused
normalize: bool = False,
) -> torch.Tensor: # F,3
"""calculate reference normals for face flip detection"""
full_normals = vertex_normals[faces] # F,C=3,3
ref_normals = full_normals.sum(dim=1) # F,3
if normalize:
ref_normals = tfunc.normalize(ref_normals, eps=1e-6, dim=1)
return ref_normals
def pack(
vertices: torch.Tensor, # V,3 first unused and nan
faces: torch.Tensor, # F,3 long, 0 for unused
) -> tuple[torch.Tensor, torch.Tensor]: # (vertices,faces), keeps first vertex unused
"""removes unused elements in vertices and faces"""
V = vertices.shape[0]
# remove unused faces
used_faces = faces[:, 0] != 0
used_faces[0] = True
faces = faces[used_faces] # sync
# remove unused vertices
used_vertices = torch.zeros(V, 3, dtype=torch.bool, device=vertices.device)
used_vertices.scatter_(
dim=0, index=faces, value=True, reduce="add"
) # TODO int faster?
used_vertices = used_vertices.any(dim=1)
used_vertices[0] = True
vertices = vertices[used_vertices] # sync
# update used faces
ind = torch.zeros(V, dtype=torch.long, device=vertices.device)
V1 = used_vertices.sum()
ind[used_vertices] = torch.arange(0, V1, device=vertices.device) # sync
faces = ind[faces]
return vertices, faces
def split_edges(
vertices: torch.Tensor, # V,3 first unused
faces: torch.Tensor, # F,3 long, 0 for unused
edges: torch.Tensor, # E,2 long 0 for unused, lower vertex index first
face_to_edge: torch.Tensor, # F,3 long 0 for unused
splits, # E bool
pack_faces: bool = True,
) -> tuple[torch.Tensor, torch.Tensor]: # (vertices,faces)
# c2 c2 c...corners = faces
# . . . . s...side_vert, 0 means no split
# . . .N2 . S...shrunk_face
# . . . . Ni...new_faces
# s2 s1 s2|c2...s1|c1
# . . . . .
# . . . S . .
# . . . . N1 .
# c0...(s0=0)....c1 s0|c0...........c1
#
# pseudo-code:
# S = [s0|c0,s1|c1,s2|c2] example:[c0,s1,s2]
# split = side_vert!=0 example:[False,True,True]
# N0 = split[0]*[c0,s0,s2|c2] example:[0,0,0]
# N1 = split[1]*[c1,s1,s0|c0] example:[c1,s1,c0]
# N2 = split[2]*[c2,s2,s1|c1] example:[c2,s2,s1]
V = vertices.shape[0]
F = faces.shape[0]
S = splits.sum().item() # sync
if S == 0:
return vertices, faces
edge_vert = torch.zeros_like(splits, dtype=torch.long) # E
edge_vert[splits] = torch.arange(
V, V + S, dtype=torch.long, device=vertices.device
) # E 0 for no split, sync
side_vert = edge_vert[face_to_edge] # F,3 long, 0 for no split
split_edges = edges[splits] # S sync
# vertices
split_vertices = vertices[split_edges].mean(dim=1) # S,3
vertices = torch.concat((vertices, split_vertices), dim=0)
# faces
side_split = side_vert != 0 # F,3
shrunk_faces = torch.where(side_split, side_vert, faces) # F,3 long, 0 for no split
new_faces = side_split[:, :, None] * torch.stack(
(faces, side_vert, shrunk_faces.roll(1, dims=-1)), dim=-1
) # F,N=3,C=3
faces = torch.concat((shrunk_faces, new_faces.reshape(F * 3, 3))) # 4F,3
if pack_faces:
mask = faces[:, 0] != 0
mask[0] = True
faces = faces[mask] # F',3 sync
return vertices, faces
def collapse_edges(
vertices: torch.Tensor, # V,3 first unused
faces: torch.Tensor, # F,3 long 0 for unused
edges: torch.Tensor, # E,2 long 0 for unused, lower vertex index first
priorities: torch.Tensor, # E float
stable: bool = False, # only for unit testing
) -> tuple[torch.Tensor, torch.Tensor]: # (vertices,faces)
V = vertices.shape[0]
# check spacing
_, order = priorities.sort(stable=stable) # E
rank = torch.zeros_like(order)
rank[order] = torch.arange(0, len(rank), device=rank.device)
vert_rank = torch.zeros(V, dtype=torch.long, device=vertices.device) # V
edge_rank = rank # E
for i in range(3):
torch_scatter.scatter_max(
src=edge_rank[:, None].expand(-1, 2).reshape(-1),
index=edges.reshape(-1),
dim=0,
out=vert_rank,
)
edge_rank, _ = vert_rank[edges].max(dim=-1) # E
candidates = edges[(edge_rank == rank).logical_and_(priorities > 0)] # E',2
# check connectivity
vert_connections = torch.zeros(V, dtype=torch.long, device=vertices.device) # V
vert_connections[candidates[:, 0]] = 1 # start
edge_connections = vert_connections[edges].sum(dim=-1) # E, edge connected to start
vert_connections.scatter_add_(
dim=0,
index=edges.reshape(-1),
src=edge_connections[:, None].expand(-1, 2).reshape(-1),
) # one edge from start
vert_connections[candidates] = 0 # clear start and end
edge_connections = vert_connections[edges].sum(
dim=-1
) # E, one or two edges from start
vert_connections.scatter_add_(
dim=0,
index=edges.reshape(-1),
src=edge_connections[:, None].expand(-1, 2).reshape(-1),
) # one or two edges from start
collapses = candidates[
vert_connections[candidates[:, 1]] <= 2
] # E" not more than two connections between start and end
# mean vertices
vertices[collapses[:, 0]] = vertices[collapses].mean(dim=1) # TODO dim?
# update faces
dest = torch.arange(0, V, dtype=torch.long, device=vertices.device) # V
dest[collapses[:, 1]] = dest[collapses[:, 0]]
faces = dest[faces] # F,3 TODO optimize?
c0, c1, c2 = faces.unbind(dim=-1)
collapsed = (c0 == c1).logical_or_(c1 == c2).logical_or_(c0 == c2)
faces[collapsed] = 0
return vertices, faces
def calc_face_collapses(
vertices: torch.Tensor, # V,3 first unused
faces: torch.Tensor, # F,3 long, 0 for unused
edges: torch.Tensor, # E,2 long 0 for unused, lower vertex index first
face_to_edge: torch.Tensor, # F,3 long 0 for unused
edge_length: torch.Tensor, # E
face_normals: torch.Tensor, # F,3
vertex_normals: torch.Tensor, # V,3 first unused
min_edge_length: torch.Tensor = None, # V
area_ratio=0.5, # collapse if area < min_edge_length**2 * area_ratio
shortest_probability=0.8,
) -> torch.Tensor: # E edges to collapse
E = edges.shape[0]
F = faces.shape[0]
# face flips
ref_normals = calc_face_ref_normals(faces, vertex_normals, normalize=False) # F,3
face_collapses = (face_normals * ref_normals).sum(dim=-1) < 0 # F
# small faces
if min_edge_length is not None:
min_face_length = min_edge_length[faces].mean(dim=-1) # F
min_area = min_face_length**2 * area_ratio # F
face_collapses.logical_or_(face_normals.norm(dim=-1) < min_area * 2) # F
face_collapses[0] = False
# faces to edges
face_length = edge_length[face_to_edge] # F,3
if shortest_probability < 1:
# select shortest edge with shortest_probability chance
randlim = round(2 / (1 - shortest_probability))
rand_ind = torch.randint(0, randlim, size=(F,), device=faces.device).clamp_max_(
2
) # selected edge local index in face
sort_ind = torch.argsort(face_length, dim=-1, descending=True) # F,3
local_ind = sort_ind.gather(dim=-1, index=rand_ind[:, None])
else:
local_ind = torch.argmin(face_length, dim=-1)[
:, None
] # F,1 0...2 shortest edge local index in face
edge_ind = face_to_edge.gather(dim=1, index=local_ind)[
:, 0
] # F 0...E selected edge global index
edge_collapses = torch.zeros(E, dtype=torch.long, device=vertices.device)
edge_collapses.scatter_add_(
dim=0, index=edge_ind, src=face_collapses.long()
) # TODO legal for bool?
return edge_collapses.bool()
def flip_edges(
vertices: torch.Tensor, # V,3 first unused
faces: torch.Tensor, # F,3 long, first must be 0, 0 for unused
edges: torch.Tensor, # E,2 long, first must be 0, 0 for unused, lower vertex index first
edge_to_face: torch.Tensor, # E,[left,right],[face,side]
with_border: bool = True, # handle border edges (D=4 instead of D=6)
with_normal_check: bool = True, # check face normal flips
stable: bool = False, # only for unit testing
):
V = vertices.shape[0]
E = edges.shape[0]
device = vertices.device
vertex_degree = torch.zeros(V, dtype=torch.long, device=device) # V long
vertex_degree.scatter_(dim=0, index=edges.reshape(E * 2), value=1, reduce="add")
neighbor_corner = (edge_to_face[:, :, 1] + 2) % 3 # go from side to corner
neighbors = faces[edge_to_face[:, :, 0], neighbor_corner] # E,LR=2
edge_is_inside = neighbors.all(dim=-1) # E
if with_border:
# inside vertices should have D=6, border edges D=4, so we subtract 2 for all inside vertices
# need to use float for masks in order to use scatter(reduce='multiply')
vertex_is_inside = torch.ones(
V, 2, dtype=torch.float32, device=vertices.device
) # V,2 float
src = edge_is_inside.type(torch.float32)[:, None].expand(E, 2) # E,2 float
vertex_is_inside.scatter_(dim=0, index=edges, src=src, reduce="multiply")
vertex_is_inside = vertex_is_inside.prod(dim=-1, dtype=torch.long) # V long
vertex_degree -= 2 * vertex_is_inside # V long
neighbor_degrees = vertex_degree[neighbors] # E,LR=2
edge_degrees = vertex_degree[edges] # E,2
#
# loss = Sum_over_affected_vertices((new_degree-6)**2)
# loss_change = Sum_over_neighbor_vertices((degree+1-6)**2-(degree-6)**2)
# + Sum_over_edge_vertices((degree-1-6)**2-(degree-6)**2)
# = 2 * (2 + Sum_over_neighbor_vertices(degree) - Sum_over_edge_vertices(degree))
#
loss_change = 2 + neighbor_degrees.sum(dim=-1) - edge_degrees.sum(dim=-1) # E
candidates = torch.logical_and(loss_change < 0, edge_is_inside) # E
loss_change = loss_change[candidates] # E'
if loss_change.shape[0] == 0:
return
edges_neighbors = torch.concat(
(edges[candidates], neighbors[candidates]), dim=-1
) # E',4
_, order = loss_change.sort(descending=True, stable=stable) # E'
rank = torch.zeros_like(order)
rank[order] = torch.arange(0, len(rank), device=rank.device)
vertex_rank = torch.zeros((V, 4), dtype=torch.long, device=device) # V,4
torch_scatter.scatter_max(
src=rank[:, None].expand(-1, 4), index=edges_neighbors, dim=0, out=vertex_rank
)
vertex_rank, _ = vertex_rank.max(dim=-1) # V
neighborhood_rank, _ = vertex_rank[edges_neighbors].max(dim=-1) # E'
flip = rank == neighborhood_rank # E'
if with_normal_check:
# cl-<-----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---->-cr
v = vertices[edges_neighbors] # E",4,3
v = v - v[:, 0:1] # make relative to e0
e1 = v[:, 1]
cl = v[:, 2]
cr = v[:, 3]
n = torch.cross(e1, cl) + torch.cross(cr, e1) # sum of old normal vectors
flip.logical_and_(
torch.sum(n * torch.cross(cr, cl), dim=-1) > 0
) # first new face
flip.logical_and_(
torch.sum(n * torch.cross(cl - e1, cr - e1), dim=-1) > 0
) # second new face
flip_edges_neighbors = edges_neighbors[flip] # E",4
flip_edge_to_face = edge_to_face[candidates, :, 0][flip] # E",2
flip_faces = flip_edges_neighbors[:, [[0, 3, 2], [1, 2, 3]]] # E",2,3
faces.scatter_(
dim=0,
index=flip_edge_to_face.reshape(-1, 1).expand(-1, 3),
src=flip_faces.reshape(-1, 3),
)
|