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from typing import Optional, Tuple
import numpy as np
import torch
import torch.nn as nn
from jaxtyping import Float, Integer
from torch import Tensor
from .mesh import Mesh
class IsosurfaceHelper(nn.Module):
points_range: Tuple[float, float] = (0, 1)
@property
def grid_vertices(self) -> Float[Tensor, "N 3"]:
raise NotImplementedError
@property
def requires_instance_per_batch(self) -> bool:
return False
class MarchingTetrahedraHelper(IsosurfaceHelper):
def __init__(self, resolution: int, tets_path: str):
super().__init__()
self.resolution = resolution
self.tets_path = tets_path
self.triangle_table: Float[Tensor, "..."]
self.register_buffer(
"triangle_table",
torch.as_tensor(
[
[-1, -1, -1, -1, -1, -1],
[1, 0, 2, -1, -1, -1],
[4, 0, 3, -1, -1, -1],
[1, 4, 2, 1, 3, 4],
[3, 1, 5, -1, -1, -1],
[2, 3, 0, 2, 5, 3],
[1, 4, 0, 1, 5, 4],
[4, 2, 5, -1, -1, -1],
[4, 5, 2, -1, -1, -1],
[4, 1, 0, 4, 5, 1],
[3, 2, 0, 3, 5, 2],
[1, 3, 5, -1, -1, -1],
[4, 1, 2, 4, 3, 1],
[3, 0, 4, -1, -1, -1],
[2, 0, 1, -1, -1, -1],
[-1, -1, -1, -1, -1, -1],
],
dtype=torch.long,
),
persistent=False,
)
self.num_triangles_table: Integer[Tensor, "..."]
self.register_buffer(
"num_triangles_table",
torch.as_tensor(
[0, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 0], dtype=torch.long
),
persistent=False,
)
self.base_tet_edges: Integer[Tensor, "..."]
self.register_buffer(
"base_tet_edges",
torch.as_tensor([0, 1, 0, 2, 0, 3, 1, 2, 1, 3, 2, 3], dtype=torch.long),
persistent=False,
)
tets = np.load(self.tets_path)
self._grid_vertices: Float[Tensor, "..."]
self.register_buffer(
"_grid_vertices",
torch.from_numpy(tets["vertices"]).float(),
persistent=False,
)
self.indices: Integer[Tensor, "..."]
self.register_buffer(
"indices", torch.from_numpy(tets["indices"]).long(), persistent=False
)
self._all_edges: Optional[Integer[Tensor, "Ne 2"]] = None
center_indices, boundary_indices = self.get_center_boundary_index(
self._grid_vertices
)
self.center_indices: Integer[Tensor, "..."]
self.register_buffer("center_indices", center_indices, persistent=False)
self.boundary_indices: Integer[Tensor, "..."]
self.register_buffer("boundary_indices", boundary_indices, persistent=False)
def get_center_boundary_index(self, verts):
magn = torch.sum(verts**2, dim=-1)
center_idx = torch.argmin(magn)
boundary_neg = verts == verts.max()
boundary_pos = verts == verts.min()
boundary = torch.bitwise_or(boundary_pos, boundary_neg)
boundary = torch.sum(boundary.float(), dim=-1)
boundary_idx = torch.nonzero(boundary)
return center_idx, boundary_idx.squeeze(dim=-1)
def normalize_grid_deformation(
self, grid_vertex_offsets: Float[Tensor, "Nv 3"]
) -> Float[Tensor, "Nv 3"]:
return (
(self.points_range[1] - self.points_range[0])
/ self.resolution # half tet size is approximately 1 / self.resolution
* torch.tanh(grid_vertex_offsets)
) # FIXME: hard-coded activation
@property
def grid_vertices(self) -> Float[Tensor, "Nv 3"]:
return self._grid_vertices
@property
def all_edges(self) -> Integer[Tensor, "Ne 2"]:
if self._all_edges is None:
# compute edges on GPU, or it would be VERY SLOW (basically due to the unique operation)
edges = torch.tensor(
[0, 1, 0, 2, 0, 3, 1, 2, 1, 3, 2, 3],
dtype=torch.long,
device=self.indices.device,
)
_all_edges = self.indices[:, edges].reshape(-1, 2)
_all_edges_sorted = torch.sort(_all_edges, dim=1)[0]
_all_edges = torch.unique(_all_edges_sorted, dim=0)
self._all_edges = _all_edges
return self._all_edges
def sort_edges(self, edges_ex2):
with torch.no_grad():
order = (edges_ex2[:, 0] > edges_ex2[:, 1]).long()
order = order.unsqueeze(dim=1)
a = torch.gather(input=edges_ex2, index=order, dim=1)
b = torch.gather(input=edges_ex2, index=1 - order, dim=1)
return torch.stack([a, b], -1)
def _forward(self, pos_nx3, sdf_n, tet_fx4):
with torch.no_grad():
occ_n = sdf_n > 0
occ_fx4 = occ_n[tet_fx4.reshape(-1)].reshape(-1, 4)
occ_sum = torch.sum(occ_fx4, -1)
valid_tets = (occ_sum > 0) & (occ_sum < 4)
occ_sum = occ_sum[valid_tets]
# find all vertices
all_edges = tet_fx4[valid_tets][:, self.base_tet_edges].reshape(-1, 2)
all_edges = self.sort_edges(all_edges)
unique_edges, idx_map = torch.unique(all_edges, dim=0, return_inverse=True)
unique_edges = unique_edges.long()
mask_edges = occ_n[unique_edges.reshape(-1)].reshape(-1, 2).sum(-1) == 1
mapping = (
torch.ones(
(unique_edges.shape[0]), dtype=torch.long, device=pos_nx3.device
)
* -1
)
mapping[mask_edges] = torch.arange(
mask_edges.sum(), dtype=torch.long, device=pos_nx3.device
)
idx_map = mapping[idx_map] # map edges to verts
interp_v = unique_edges[mask_edges]
edges_to_interp = pos_nx3[interp_v.reshape(-1)].reshape(-1, 2, 3)
edges_to_interp_sdf = sdf_n[interp_v.reshape(-1)].reshape(-1, 2, 1)
edges_to_interp_sdf[:, -1] *= -1
denominator = edges_to_interp_sdf.sum(1, keepdim=True)
edges_to_interp_sdf = torch.flip(edges_to_interp_sdf, [1]) / denominator
verts = (edges_to_interp * edges_to_interp_sdf).sum(1)
idx_map = idx_map.reshape(-1, 6)
v_id = torch.pow(2, torch.arange(4, dtype=torch.long, device=pos_nx3.device))
tetindex = (occ_fx4[valid_tets] * v_id.unsqueeze(0)).sum(-1)
num_triangles = self.num_triangles_table[tetindex]
# Generate triangle indices
faces = torch.cat(
(
torch.gather(
input=idx_map[num_triangles == 1],
dim=1,
index=self.triangle_table[tetindex[num_triangles == 1]][:, :3],
).reshape(-1, 3),
torch.gather(
input=idx_map[num_triangles == 2],
dim=1,
index=self.triangle_table[tetindex[num_triangles == 2]][:, :6],
).reshape(-1, 3),
),
dim=0,
)
return verts, faces
def forward(
self,
level: Float[Tensor, "N3 1"],
deformation: Optional[Float[Tensor, "N3 3"]] = None,
) -> Mesh:
if deformation is not None:
grid_vertices = self.grid_vertices + self.normalize_grid_deformation(
deformation
)
else:
grid_vertices = self.grid_vertices
v_pos, t_pos_idx = self._forward(grid_vertices, level, self.indices)
mesh = Mesh(
v_pos=v_pos,
t_pos_idx=t_pos_idx,
# extras
grid_vertices=grid_vertices,
tet_edges=self.all_edges,
grid_level=level,
grid_deformation=deformation,
)
return mesh
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