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from typing import *
import numpy as np
import torch
from .. import _C
from flex_gemm.kernels import cuda as flexgemm_kernels
__all__ = [
"mesh_to_flexible_dual_grid",
"flexible_dual_grid_to_mesh",
]
@torch.no_grad()
def mesh_to_flexible_dual_grid(
vertices: torch.Tensor,
faces: torch.Tensor,
voxel_size: Union[float, list, tuple, np.ndarray, torch.Tensor] = None,
grid_size: Union[int, list, tuple, np.ndarray, torch.Tensor] = None,
aabb: Union[list, tuple, np.ndarray, torch.Tensor] = None,
face_weight: float = 1.0,
boundary_weight: float = 1.0,
regularization_weight: float = 0.1,
timing: bool = False,
) -> Union[torch.Tensor, torch.Tensor, torch.Tensor]:
"""
Voxelize a mesh into a sparse voxel grid.
Args:
vertices (torch.Tensor): The vertices of the mesh.
faces (torch.Tensor): The faces of the mesh.
voxel_size (float, list, tuple, np.ndarray, torch.Tensor): The size of each voxel.
grid_size (int, list, tuple, np.ndarray, torch.Tensor): The size of the grid.
NOTE: One of voxel_size and grid_size must be provided.
aabb (list, tuple, np.ndarray, torch.Tensor): The axis-aligned bounding box of the mesh.
If not provided, it will be computed automatically.
face_weight (float): The weight of the face term in the dual contouring algorithm.
boundary_weight (float): The weight of the boundary term in the dual contouring algorithm.
regularization_weight (float): The weight of the regularization term in the dual contouring algorithm.
timing (bool): Whether to time the voxelization process.
Returns:
torch.Tensor: The indices of the voxels that are occupied by the mesh.
The shape of the tensor is (N, 3), where N is the number of occupied voxels.
torch.Tensor: The dual vertices of the mesh.
torch.Tensor: The intersected flag of each voxel.
"""
# Load mesh
vertices = vertices.float()
faces = faces.int()
# Voxelize settings
assert voxel_size is not None or grid_size is not None, "Either voxel_size or grid_size must be provided"
if voxel_size is not None:
if isinstance(voxel_size, float):
voxel_size = [voxel_size, voxel_size, voxel_size]
if isinstance(voxel_size, (list, tuple)):
voxel_size = np.array(voxel_size)
if isinstance(voxel_size, np.ndarray):
voxel_size = torch.tensor(voxel_size, dtype=torch.float32)
assert isinstance(voxel_size, torch.Tensor), f"voxel_size must be a float, list, tuple, np.ndarray, or torch.Tensor, but got {type(voxel_size)}"
assert voxel_size.dim() == 1, f"voxel_size must be a 1D tensor, but got {voxel_size.shape}"
assert voxel_size.size(0) == 3, f"voxel_size must have 3 elements, but got {voxel_size.size(0)}"
if grid_size is not None:
if isinstance(grid_size, int):
grid_size = [grid_size, grid_size, grid_size]
if isinstance(grid_size, (list, tuple)):
grid_size = np.array(grid_size)
if isinstance(grid_size, np.ndarray):
grid_size = torch.tensor(grid_size, dtype=torch.int32)
assert isinstance(grid_size, torch.Tensor), f"grid_size must be an int, list, tuple, np.ndarray, or torch.Tensor, but got {type(grid_size)}"
assert grid_size.dim() == 1, f"grid_size must be a 1D tensor, but got {grid_size.shape}"
assert grid_size.size(0) == 3, f"grid_size must have 3 elements, but got {grid_size.size(0)}"
if aabb is not None:
if isinstance(aabb, (list, tuple)):
aabb = np.array(aabb)
if isinstance(aabb, np.ndarray):
aabb = torch.tensor(aabb, dtype=torch.float32)
assert isinstance(aabb, torch.Tensor), f"aabb must be a list, tuple, np.ndarray, or torch.Tensor, but got {type(aabb)}"
assert aabb.dim() == 2, f"aabb must be a 2D tensor, but got {aabb.shape}"
assert aabb.size(0) == 2, f"aabb must have 2 rows, but got {aabb.size(0)}"
assert aabb.size(1) == 3, f"aabb must have 3 columns, but got {aabb.size(1)}"
# Auto adjust aabb
if aabb is None:
min_xyz = vertices.min(dim=0).values
max_xyz = vertices.max(dim=0).values
if voxel_size is not None:
padding = torch.ceil((max_xyz - min_xyz) / voxel_size) * voxel_size - (max_xyz - min_xyz)
min_xyz -= padding * 0.5
max_xyz += padding * 0.5
if grid_size is not None:
padding = (max_xyz - min_xyz) / (grid_size - 1)
min_xyz -= padding * 0.5
max_xyz += padding * 0.5
aabb = torch.stack([min_xyz, max_xyz], dim=0).float().cuda()
# Fill voxel size or grid size
if voxel_size is None:
voxel_size = (aabb[1] - aabb[0]) / grid_size
if grid_size is None:
grid_size = ((aabb[1] - aabb[0]) / voxel_size).round().int()
# subdivide mesh
vertices = vertices - aabb[0].reshape(1, 3)
grid_range = torch.stack([torch.zeros_like(grid_size), grid_size], dim=0).int()
ret = _C.mesh_to_flexible_dual_grid_cpu(
vertices,
faces,
voxel_size,
grid_range,
face_weight,
boundary_weight,
regularization_weight,
timing,
)
return ret
def flexible_dual_grid_to_mesh(
coords: torch.Tensor,
dual_vertices: torch.Tensor,
intersected_flag: torch.Tensor,
split_weight: Union[torch.Tensor, None],
aabb: Union[list, tuple, np.ndarray, torch.Tensor],
voxel_size: Union[float, list, tuple, np.ndarray, torch.Tensor] = None,
grid_size: Union[int, list, tuple, np.ndarray, torch.Tensor] = None,
train: bool = False,
):
"""
Extract mesh from sparse voxel structures using flexible dual grid.
Args:
coords (torch.Tensor): The coordinates of the voxels.
dual_vertices (torch.Tensor): The dual vertices.
intersected_flag (torch.Tensor): The intersected flag.
split_weight (torch.Tensor): The split weight of each dual quad. If None, the algorithm
will split based on minimum angle.
aabb (list, tuple, np.ndarray, torch.Tensor): The axis-aligned bounding box of the mesh.
voxel_size (float, list, tuple, np.ndarray, torch.Tensor): The size of each voxel.
grid_size (int, list, tuple, np.ndarray, torch.Tensor): The size of the grid.
NOTE: One of voxel_size and grid_size must be provided.
train (bool): Whether to use training mode.
Returns:
vertices (torch.Tensor): The vertices of the mesh.
faces (torch.Tensor): The faces of the mesh.
"""
# Static variables
if not hasattr(flexible_dual_grid_to_mesh, "edge_neighbor_voxel_offset"):
flexible_dual_grid_to_mesh.edge_neighbor_voxel_offset = torch.tensor([
[[0, 0, 0], [0, 0, 1], [0, 1, 1], [0, 1, 0]], # x-axis
[[0, 0, 0], [1, 0, 0], [1, 0, 1], [0, 0, 1]], # y-axis
[[0, 0, 0], [0, 1, 0], [1, 1, 0], [1, 0, 0]], # z-axis
], dtype=torch.int, device=coords.device).unsqueeze(0)
if not hasattr(flexible_dual_grid_to_mesh, "quad_split_1"):
flexible_dual_grid_to_mesh.quad_split_1 = torch.tensor([0, 1, 2, 0, 2, 3], dtype=torch.long, device=coords.device, requires_grad=False)
if not hasattr(flexible_dual_grid_to_mesh, "quad_split_2"):
flexible_dual_grid_to_mesh.quad_split_2 = torch.tensor([0, 1, 3, 3, 1, 2], dtype=torch.long, device=coords.device, requires_grad=False)
if not hasattr(flexible_dual_grid_to_mesh, "quad_split_train"):
flexible_dual_grid_to_mesh.quad_split_train = torch.tensor([0, 1, 4, 1, 2, 4, 2, 3, 4, 3, 0, 4], dtype=torch.long, device=coords.device, requires_grad=False)
# AABB
if isinstance(aabb, (list, tuple)):
aabb = np.array(aabb)
if isinstance(aabb, np.ndarray):
aabb = torch.tensor(aabb, dtype=torch.float32, device=coords.device)
assert isinstance(aabb, torch.Tensor), f"aabb must be a list, tuple, np.ndarray, or torch.Tensor, but got {type(aabb)}"
assert aabb.dim() == 2, f"aabb must be a 2D tensor, but got {aabb.shape}"
assert aabb.size(0) == 2, f"aabb must have 2 rows, but got {aabb.size(0)}"
assert aabb.size(1) == 3, f"aabb must have 3 columns, but got {aabb.size(1)}"
# Voxel size
if voxel_size is not None:
if isinstance(voxel_size, float):
voxel_size = [voxel_size, voxel_size, voxel_size]
if isinstance(voxel_size, (list, tuple)):
voxel_size = np.array(voxel_size)
if isinstance(voxel_size, np.ndarray):
voxel_size = torch.tensor(voxel_size, dtype=torch.float32, device=coords.device)
grid_size = ((aabb[1] - aabb[0]) / voxel_size).round().int()
else:
assert grid_size is not None, "Either voxel_size or grid_size must be provided"
if isinstance(grid_size, int):
grid_size = [grid_size, grid_size, grid_size]
if isinstance(grid_size, (list, tuple)):
grid_size = np.array(grid_size)
if isinstance(grid_size, np.ndarray):
grid_size = torch.tensor(grid_size, dtype=torch.int32, device=coords.device)
voxel_size = (aabb[1] - aabb[0]) / grid_size
assert isinstance(voxel_size, torch.Tensor), f"voxel_size must be a float, list, tuple, np.ndarray, or torch.Tensor, but got {type(voxel_size)}"
assert voxel_size.dim() == 1, f"voxel_size must be a 1D tensor, but got {voxel_size.shape}"
assert voxel_size.size(0) == 3, f"voxel_size must have 3 elements, but got {voxel_size.size(0)}"
assert isinstance(grid_size, torch.Tensor), f"grid_size must be an int, list, tuple, np.ndarray, or torch.Tensor, but got {type(grid_size)}"
assert grid_size.dim() == 1, f"grid_size must be a 1D tensor, but got {grid_size.shape}"
assert grid_size.size(0) == 3, f"grid_size must have 3 elements, but got {grid_size.size(0)}"
# Extract mesh
N = dual_vertices.shape[0]
mesh_vertices = (coords.float() + dual_vertices) / (2 * N) - 0.5
# Store active voxels into hashmap
hashmap = torch.full((2 * int(2 * N),), 0xffffffff, dtype=torch.uint32, device=coords.device)
flexgemm_kernels.hashmap_insert_3d_idx_as_val_cuda(hashmap, torch.cat([torch.zeros_like(coords[:, :1]), coords], dim=-1), *grid_size.tolist())
# Find connected voxels
edge_neighbor_voxel = coords.reshape(N, 1, 1, 3) + flexible_dual_grid_to_mesh.edge_neighbor_voxel_offset # (N, 3, 4, 3)
connected_voxel = edge_neighbor_voxel[intersected_flag] # (M, 4, 3)
M = connected_voxel.shape[0]
connected_voxel_hash_key = torch.cat([
torch.zeros((M * 4, 1), dtype=torch.int, device=coords.device),
connected_voxel.reshape(-1, 3)
], dim=1)
connected_voxel_indices = flexgemm_kernels.hashmap_lookup_3d_cuda(hashmap, connected_voxel_hash_key, *grid_size.tolist()).reshape(M, 4).int()
connected_voxel_valid = (connected_voxel_indices != 0xffffffff).all(dim=1)
quad_indices = connected_voxel_indices[connected_voxel_valid].int() # (L, 4)
L = quad_indices.shape[0]
# Construct triangles
if not train:
mesh_vertices = (coords.float() + dual_vertices) * voxel_size + aabb[0].reshape(1, 3)
if split_weight is None:
# if split 1
atempt_triangles_0 = quad_indices[:, flexible_dual_grid_to_mesh.quad_split_1]
normals0 = torch.cross(mesh_vertices[atempt_triangles_0[:, 1]] - mesh_vertices[atempt_triangles_0[:, 0]], mesh_vertices[atempt_triangles_0[:, 2]] - mesh_vertices[atempt_triangles_0[:, 0]], dim=1)
normals1 = torch.cross(mesh_vertices[atempt_triangles_0[:, 2]] - mesh_vertices[atempt_triangles_0[:, 1]], mesh_vertices[atempt_triangles_0[:, 3]] - mesh_vertices[atempt_triangles_0[:, 1]], dim=1)
normals0 = normals0 / torch.norm(normals0, dim=1, keepdim=True)
normals1 = normals1 / torch.norm(normals1, dim=1, keepdim=True)
align0 = (normals0 * normals1).sum(dim=1, keepdim=True).abs()
# if split 2
atempt_triangles_1 = quad_indices[:, flexible_dual_grid_to_mesh.quad_split_2]
normals0 = torch.cross(mesh_vertices[atempt_triangles_1[:, 1]] - mesh_vertices[atempt_triangles_1[:, 0]], mesh_vertices[atempt_triangles_1[:, 2]] - mesh_vertices[atempt_triangles_1[:, 0]], dim=1)
normals1 = torch.cross(mesh_vertices[atempt_triangles_1[:, 2]] - mesh_vertices[atempt_triangles_1[:, 1]], mesh_vertices[atempt_triangles_1[:, 3]] - mesh_vertices[atempt_triangles_1[:, 1]], dim=1)
normals0 = normals0 / torch.norm(normals0, dim=1, keepdim=True)
normals1 = normals1 / torch.norm(normals1, dim=1, keepdim=True)
align1 = (normals0 * normals1).sum(dim=1, keepdim=True).abs()
# select split
mesh_triangles = torch.where(align0 > align1, atempt_triangles_0, atempt_triangles_1).reshape(-1, 3)
else:
split_weight_ws = split_weight[quad_indices]
split_weight_ws_02 = split_weight_ws[:, 0] * split_weight_ws[:, 2]
split_weight_ws_13 = split_weight_ws[:, 1] * split_weight_ws[:, 3]
mesh_triangles = torch.where(
split_weight_ws_02 > split_weight_ws_13,
quad_indices[:, flexible_dual_grid_to_mesh.quad_split_1],
quad_indices[:, flexible_dual_grid_to_mesh.quad_split_2]
).reshape(-1, 3)
else:
assert split_weight is not None, "split_weight must be provided in training mode"
mesh_vertices = (coords.float() + dual_vertices) * voxel_size + aabb[0].reshape(1, 3)
quad_vs = mesh_vertices[quad_indices]
mean_v02 = (quad_vs[:, 0] + quad_vs[:, 2]) / 2
mean_v13 = (quad_vs[:, 1] + quad_vs[:, 3]) / 2
split_weight_ws = split_weight[quad_indices]
split_weight_ws_02 = split_weight_ws[:, 0] * split_weight_ws[:, 2]
split_weight_ws_13 = split_weight_ws[:, 1] * split_weight_ws[:, 3]
mid_vertices = (
split_weight_ws_02 * mean_v02 +
split_weight_ws_13 * mean_v13
) / (split_weight_ws_02 + split_weight_ws_13)
mesh_vertices = torch.cat([mesh_vertices, mid_vertices], dim=0)
quad_indices = torch.cat([quad_indices, torch.arange(N, N + L, device='cuda').unsqueeze(1)], dim=1)
mesh_triangles = quad_indices[:, flexible_dual_grid_to_mesh.quad_split_train].reshape(-1, 3)
return mesh_vertices, mesh_triangles
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