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### adapted from https://github.com/NVIDIAGameWorks/kaolin/blob/master/kaolin/ops/conversions/tetmesh.py
# Copyright (c) 2021,22 NVIDIA CORPORATION & AFFILIATES.
# All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import torch
__all__ = ['marching_tetrahedra']
triangle_table = torch.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)
num_triangles_table = torch.tensor([0, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 0], dtype=torch.long)
base_tet_edges = torch.tensor([0, 1, 0, 2, 0, 3, 1, 2, 1, 3, 2, 3], dtype=torch.long)
v_id = torch.pow(2, torch.arange(4, dtype=torch.long))
def _unbatched_marching_tetrahedra(vertices, tets, sdf, scales):
"""unbatched marching tetrahedra.
Refer to :func:`marching_tetrahedra`.
"""
device = vertices.device
# call by chunk
chunk_size = 32 * 1024 * 1024
if tets.shape[0] > chunk_size:
merged_verts = None
merged_scales = None
merged_faces = None
merged_verts_ids = None
for tet_chunk in torch.chunk(tets, tets.shape[0] // chunk_size + 1):
torch.cuda.empty_cache()
verts, verts_scales, faces, verts_ids = _unbatched_marching_tetrahedra(vertices, tet_chunk, sdf, scales)
if merged_verts is None:
merged_verts = verts
merged_scales = verts_scales
merged_faces = faces
merged_verts_ids = verts_ids
else:
all_edges = torch.cat([merged_verts_ids, verts_ids], dim=0)
unique_edges, idx_map = torch.unique(all_edges, dim=0, return_inverse=True)
# merge vertices
unique_verts_0 = torch.zeros((unique_edges.shape[0], 2, 3), dtype=torch.float, device=device)
unique_verts_1 = torch.zeros((unique_edges.shape[0], 2, 1), dtype=torch.float, device=device)
unique_verts_0[idx_map[:merged_verts[0].shape[0]]] = merged_verts[0]
unique_verts_0[idx_map[merged_verts[0].shape[0]:]] = verts[0]
unique_verts_1[idx_map[:merged_verts[1].shape[0]]] = merged_verts[1]
unique_verts_1[idx_map[merged_verts[1].shape[0]:]] = verts[1]
# merge scales
unique_scales = torch.zeros((unique_edges.shape[0], 2, 1), dtype=torch.float, device=device)
unique_scales[idx_map[:merged_verts[0].shape[0]]] = merged_scales
unique_scales[idx_map[merged_verts[0].shape[0]:]] = verts_scales
# merge faces
unique_faces_0 = idx_map[merged_faces.reshape(-1)].reshape(-1, 3)
unique_faces_1 = idx_map[faces.reshape(-1) + merged_verts[0].shape[0]].reshape(-1, 3)
merged_faces = torch.cat([unique_faces_0, unique_faces_1], dim=0)
merged_verts = (unique_verts_0, unique_verts_1)
merged_scales = unique_scales
merged_verts_ids = unique_edges
torch.cuda.empty_cache()
return merged_verts, merged_scales, merged_faces, merged_verts_ids
with torch.no_grad():
occ_n = sdf > 0
occ_fx4 = occ_n[tets.reshape(-1)].reshape(-1, 4)
occ_sum = torch.sum(occ_fx4, -1)
valid_tets = (occ_sum > 0) & (occ_sum < 4)
# find all vertices
all_edges = tets[valid_tets][:, base_tet_edges.to(device)].reshape(-1, 2)
order = (all_edges[:, 0] > all_edges[:, 1]).bool()
all_edges[order] = all_edges[order][:, [1, 0]]
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=device) * -1
mapping[mask_edges] = torch.arange(mask_edges.sum(), dtype=torch.long, device=device)
idx_map = mapping[idx_map]
interp_v = unique_edges[mask_edges]
edges_to_interp = vertices[interp_v.reshape(-1)].reshape(-1, 2, 3)
edges_to_interp_sdf = sdf[interp_v.reshape(-1)].reshape(-1, 2, 1)
verts_scales = scales[interp_v.reshape(-1)].reshape(-1, 2, 1)
verts = (edges_to_interp, edges_to_interp_sdf)
idx_map = idx_map.reshape(-1, 6)
tetindex = (occ_fx4[valid_tets] * v_id.to(device).unsqueeze(0)).sum(-1)
num_triangles = num_triangles_table.to(device)[tetindex]
triangle_table_device = triangle_table.to(device)
# Generate triangle indices
faces = torch.cat((
torch.gather(input=idx_map[num_triangles == 1], dim=1,
index=triangle_table_device[tetindex[num_triangles == 1]][:, :3]).reshape(-1, 3),
torch.gather(input=idx_map[num_triangles == 2], dim=1,
index=triangle_table_device[tetindex[num_triangles == 2]][:, :6]).reshape(-1, 3),
), dim=0)
return verts, verts_scales, faces, interp_v
def marching_tetrahedra(vertices, tets, sdf, scales):
r"""Convert discrete signed distance fields encoded on tetrahedral grids to triangle
meshes using marching tetrahedra algorithm as described in `An efficient method of
triangulating equi-valued surfaces by using tetrahedral cells`_. The output surface is differentiable with respect to
input vertex positions and the SDF values. For more details and example usage in learning, see
`Deep Marching Tetrahedra\: a Hybrid Representation for High-Resolution 3D Shape Synthesis`_ NeurIPS 2021.
Args:
vertices (torch.tensor): batched vertices of tetrahedral meshes, of shape
:math:`(\text{batch_size}, \text{num_vertices}, 3)`.
tets (torch.tensor): unbatched tetrahedral mesh topology, of shape
:math:`(\text{num_tetrahedrons}, 4)`.
sdf (torch.tensor): batched SDFs which specify the SDF value of each vertex, of shape
:math:`(\text{batch_size}, \text{num_vertices})`.
Returns:
(list[torch.Tensor], list[torch.LongTensor], (optional) list[torch.LongTensor]):
- the list of vertices for mesh converted from each tetrahedral grid.
- the list of faces for mesh converted from each tetrahedral grid.
Example:
>>> vertices = torch.tensor([[[0, 0, 0],
... [1, 0, 0],
... [0, 1, 0],
... [0, 0, 1]]], dtype=torch.float)
>>> tets = torch.tensor([[0, 1, 2, 3]], dtype=torch.long)
>>> sdf = torch.tensor([[-1., -1., 0.5, 0.5]], dtype=torch.float)
>>> verts_list, faces_list, tet_idx_list = marching_tetrahedra(vertices, tets, sdf, True)
>>> verts_list[0]
tensor([[0.0000, 0.6667, 0.0000],
[0.0000, 0.0000, 0.6667],
[0.3333, 0.6667, 0.0000],
[0.3333, 0.0000, 0.6667]])
>>> faces_list[0]
tensor([[3, 0, 1],
[3, 2, 0]])
>>> tet_idx_list[0]
tensor([0, 0])
.. _An efficient method of triangulating equi-valued surfaces by using tetrahedral cells:
https://search.ieice.org/bin/summary.php?id=e74-d_1_214
.. _Deep Marching Tetrahedra\: a Hybrid Representation for High-Resolution 3D Shape Synthesis:
https://arxiv.org/abs/2111.04276
"""
list_of_outputs = [_unbatched_marching_tetrahedra(vertices[b], tets, sdf[b], scales[b]) for b in range(vertices.shape[0])]
return list(zip(*list_of_outputs)) |