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import time
from copy import deepcopy
import torch
import torch_scatter
from .remesh import (
calc_edge_length,
calc_edges,
calc_face_collapses,
calc_face_normals,
calc_vertex_normals,
collapse_edges,
flip_edges,
pack,
prepend_dummies,
remove_dummies,
split_edges,
)
@torch.no_grad()
def remesh(
vertices_etc: torch.Tensor, # V,D
faces: torch.Tensor, # F,3 long
min_edgelen: torch.Tensor, # V
max_edgelen: torch.Tensor, # V
flip: bool,
max_vertices=1e6,
):
# dummies
vertices_etc, faces = prepend_dummies(vertices_etc, faces)
vertices = vertices_etc[:, :3] # V,3
nan_tensor = torch.tensor([torch.nan], device=min_edgelen.device)
min_edgelen = torch.concat((nan_tensor, min_edgelen))
max_edgelen = torch.concat((nan_tensor, max_edgelen))
# collapse
edges, face_to_edge = calc_edges(faces) # E,2 F,3
edge_length = calc_edge_length(vertices, edges) # E
face_normals = calc_face_normals(vertices, faces, normalize=False) # F,3
vertex_normals = calc_vertex_normals(vertices, faces, face_normals) # V,3
face_collapse = calc_face_collapses(
vertices,
faces,
edges,
face_to_edge,
edge_length,
face_normals,
vertex_normals,
min_edgelen,
area_ratio=0.5,
)
shortness = (1 - edge_length / min_edgelen[edges].mean(dim=-1)).clamp_min_(
0
) # e[0,1] 0...ok, 1...edgelen=0
priority = face_collapse.float() + shortness
vertices_etc, faces = collapse_edges(vertices_etc, faces, edges, priority)
# split
if vertices.shape[0] < max_vertices:
edges, face_to_edge = calc_edges(faces) # E,2 F,3
vertices = vertices_etc[:, :3] # V,3
edge_length = calc_edge_length(vertices, edges) # E
splits = edge_length > max_edgelen[edges].mean(dim=-1)
vertices_etc, faces = split_edges(
vertices_etc, faces, edges, face_to_edge, splits, pack_faces=False
)
vertices_etc, faces = pack(vertices_etc, faces)
vertices = vertices_etc[:, :3]
if flip:
edges, _, edge_to_face = calc_edges(faces, with_edge_to_face=True) # E,2 F,3
flip_edges(vertices, faces, edges, edge_to_face, with_border=False)
return remove_dummies(vertices_etc, faces)
def lerp_unbiased(a: torch.Tensor, b: torch.Tensor, weight: float, step: int):
"""lerp with adam's bias correction"""
c_prev = 1 - weight ** (step - 1)
c = 1 - weight**step
a_weight = weight * c_prev / c
b_weight = (1 - weight) / c
a.mul_(a_weight).add_(b, alpha=b_weight)
class MeshOptimizer:
"""Use this like a pytorch Optimizer, but after calling opt.step(), do vertices,faces = opt.remesh()."""
def __init__(
self,
vertices: torch.Tensor, # V,3
faces: torch.Tensor, # F,3
lr=0.3, # learning rate
betas=(
0.8,
0.8,
0,
), # betas[0:2] are the same as in Adam, betas[2] may be used to time-smooth the relative velocity nu
gammas=(
0,
0,
0,
), # optional spatial smoothing for m1,m2,nu, values between 0 (no smoothing) and 1 (max. smoothing)
nu_ref=0.3, # reference velocity for edge length controller
edge_len_lims=(
0.01,
0.15,
), # smallest and largest allowed reference edge length
edge_len_tol=0.5, # edge length tolerance for split and collapse
gain=0.2, # gain value for edge length controller
laplacian_weight=0.02, # for laplacian smoothing/regularization
ramp=1, # learning rate ramp, actual ramp width is ramp/(1-betas[0])
grad_lim=10.0, # gradients are clipped to m1.abs()*grad_lim
remesh_interval=1, # larger intervals are faster but with worse mesh quality
local_edgelen=True, # set to False to use a global scalar reference edge length instead
):
self._vertices = vertices
self._faces = faces
self._lr = lr
self._betas = betas
self._gammas = gammas
self._nu_ref = nu_ref
self._edge_len_lims = edge_len_lims
self._edge_len_tol = edge_len_tol
self._gain = gain
self._laplacian_weight = laplacian_weight
self._ramp = ramp
self._grad_lim = grad_lim
self._remesh_interval = remesh_interval
self._local_edgelen = local_edgelen
self._step = 0
self._start = time.time()
V = self._vertices.shape[0]
# prepare continuous tensor for all vertex-based data
self._vertices_etc = torch.zeros([V, 9], device=vertices.device)
self._split_vertices_etc()
self.vertices.copy_(vertices) # initialize vertices
self._vertices.requires_grad_()
self._ref_len.fill_(edge_len_lims[1])
@property
def vertices(self):
return self._vertices
@property
def faces(self):
return self._faces
def _split_vertices_etc(self):
self._vertices = self._vertices_etc[:, :3]
self._m2 = self._vertices_etc[:, 3]
self._nu = self._vertices_etc[:, 4]
self._m1 = self._vertices_etc[:, 5:8]
self._ref_len = self._vertices_etc[:, 8]
with_gammas = any(g != 0 for g in self._gammas)
self._smooth = (
self._vertices_etc[:, :8] if with_gammas else self._vertices_etc[:, :3]
)
def zero_grad(self):
self._vertices.grad = None
@torch.no_grad()
def step(self):
eps = 1e-8
self._step += 1
# spatial smoothing
edges, _ = calc_edges(self._faces) # E,2
E = edges.shape[0]
edge_smooth = self._smooth[edges] # E,2,S
neighbor_smooth = torch.zeros_like(self._smooth) # V,S
torch_scatter.scatter_mean(
src=edge_smooth.flip(dims=[1]).reshape(E * 2, -1),
index=edges.reshape(E * 2, 1),
dim=0,
out=neighbor_smooth,
)
# apply optional smoothing of m1,m2,nu
if self._gammas[0]:
self._m1.lerp_(neighbor_smooth[:, 5:8], self._gammas[0])
if self._gammas[1]:
self._m2.lerp_(neighbor_smooth[:, 3], self._gammas[1])
if self._gammas[2]:
self._nu.lerp_(neighbor_smooth[:, 4], self._gammas[2])
# add laplace smoothing to gradients
laplace = self._vertices - neighbor_smooth[:, :3]
grad = torch.addcmul(
self._vertices.grad,
laplace,
self._nu[:, None],
value=self._laplacian_weight,
)
# gradient clipping
if self._step > 1:
grad_lim = self._m1.abs().mul_(self._grad_lim)
grad.clamp_(min=-grad_lim, max=grad_lim)
# moment updates
lerp_unbiased(self._m1, grad, self._betas[0], self._step)
lerp_unbiased(self._m2, (grad**2).sum(dim=-1), self._betas[1], self._step)
velocity = self._m1 / self._m2[:, None].sqrt().add_(eps) # V,3
speed = velocity.norm(dim=-1) # V
if self._betas[2]:
lerp_unbiased(self._nu, speed, self._betas[2], self._step) # V
else:
self._nu.copy_(speed) # V
# update vertices
ramped_lr = self._lr * min(1, self._step * (1 - self._betas[0]) / self._ramp)
self._vertices.add_(velocity * self._ref_len[:, None], alpha=-ramped_lr)
# update target edge length
if self._step % self._remesh_interval == 0:
if self._local_edgelen:
len_change = 1 + (self._nu - self._nu_ref) * self._gain
else:
len_change = 1 + (self._nu.mean() - self._nu_ref) * self._gain
self._ref_len *= len_change
self._ref_len.clamp_(*self._edge_len_lims)
def remesh(self, flip: bool = True) -> tuple[torch.Tensor, torch.Tensor]:
min_edge_len = self._ref_len * (1 - self._edge_len_tol)
max_edge_len = self._ref_len * (1 + self._edge_len_tol)
self._vertices_etc, self._faces = remesh(
self._vertices_etc, self._faces, min_edge_len, max_edge_len, flip
)
self._split_vertices_etc()
self._vertices.requires_grad_()
return self._vertices, self._faces
|