Integrate & Improve FlexiCubes
Also updated the default .mtl file settings
This commit is contained in:
MrForExample
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# Copyright (c) 2023, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
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#
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# NVIDIA CORPORATION & AFFILIATES and its licensors retain all intellectual property
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# and proprietary rights in and to this software, related documentation
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# and any modifications thereto. Any use, reproduction, disclosure or
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# distribution of this software and related documentation without an express
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# license agreement from NVIDIA CORPORATION & AFFILIATES is strictly prohibited.
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import torch
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from .tables import *
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__all__ = [
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'FlexiCubes'
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]
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class FlexiCubes:
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"""
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This class implements the FlexiCubes method for extracting meshes from scalar fields.
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It maintains a series of lookup tables and indices to support the mesh extraction process.
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FlexiCubes, a differentiable variant of the Dual Marching Cubes (DMC) scheme, enhances
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the geometric fidelity and mesh quality of reconstructed meshes by dynamically adjusting
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the surface representation through gradient-based optimization.
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During instantiation, the class loads DMC tables from a file and transforms them into
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PyTorch tensors on the specified device.
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Attributes:
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device (str): Specifies the computational device (default is "cuda").
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dmc_table (torch.Tensor): Dual Marching Cubes (DMC) table that encodes the edges
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associated with each dual vertex in 256 Marching Cubes (MC) configurations.
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num_vd_table (torch.Tensor): Table holding the number of dual vertices in each of
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the 256 MC configurations.
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check_table (torch.Tensor): Table resolving ambiguity in cases C16 and C19
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of the DMC configurations.
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tet_table (torch.Tensor): Lookup table used in tetrahedralizing the isosurface.
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quad_split_1 (torch.Tensor): Indices for splitting a quad into two triangles
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along one diagonal.
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quad_split_2 (torch.Tensor): Alternative indices for splitting a quad into
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two triangles along the other diagonal.
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quad_split_train (torch.Tensor): Indices for splitting a quad into four triangles
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during training by connecting all edges to their midpoints.
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cube_corners (torch.Tensor): Defines the positions of a standard unit cube's
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eight corners in 3D space, ordered starting from the origin (0,0,0),
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moving along the x-axis, then y-axis, and finally z-axis.
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Used as a blueprint for generating a voxel grid.
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cube_corners_idx (torch.Tensor): Cube corners indexed as powers of 2, used
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to retrieve the case id.
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cube_edges (torch.Tensor): Edge connections in a cube, listed in pairs.
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Used to retrieve edge vertices in DMC.
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edge_dir_table (torch.Tensor): A mapping tensor that associates edge indices with
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their corresponding axis. For instance, edge_dir_table[0] = 0 indicates that the
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first edge is oriented along the x-axis.
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dir_faces_table (torch.Tensor): A tensor that maps the corresponding axis of shared edges
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across four adjacent cubes to the shared faces of these cubes. For instance,
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dir_faces_table[0] = [5, 4] implies that for four cubes sharing an edge along
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the x-axis, the first and second cubes share faces indexed as 5 and 4, respectively.
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This tensor is only utilized during isosurface tetrahedralization.
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adj_pairs (torch.Tensor):
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A tensor containing index pairs that correspond to neighboring cubes that share the same edge.
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qef_reg_scale (float):
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The scaling factor applied to the regularization loss to prevent issues with singularity
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when solving the QEF. This parameter is only used when a 'grad_func' is specified.
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weight_scale (float):
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The scale of weights in FlexiCubes. Should be between 0 and 1.
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"""
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def __init__(self, device="cuda", qef_reg_scale=1e-3, weight_scale=0.99):
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self.device = device
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self.dmc_table = torch.tensor(dmc_table, dtype=torch.long, device=device, requires_grad=False)
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self.num_vd_table = torch.tensor(num_vd_table,
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dtype=torch.long, device=device, requires_grad=False)
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self.check_table = torch.tensor(
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check_table,
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dtype=torch.long, device=device, requires_grad=False)
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self.tet_table = torch.tensor(tet_table, dtype=torch.long, device=device, requires_grad=False)
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self.quad_split_1 = torch.tensor([0, 1, 2, 0, 2, 3], dtype=torch.long, device=device, requires_grad=False)
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self.quad_split_2 = torch.tensor([0, 1, 3, 3, 1, 2], dtype=torch.long, device=device, requires_grad=False)
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self.quad_split_train = torch.tensor(
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[0, 1, 1, 2, 2, 3, 3, 0], dtype=torch.long, device=device, requires_grad=False)
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self.cube_corners = torch.tensor([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [
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1, 0, 1], [0, 1, 1], [1, 1, 1]], dtype=torch.float, device=device)
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self.cube_corners_idx = torch.pow(2, torch.arange(8, requires_grad=False))
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self.cube_edges = torch.tensor([0, 1, 1, 5, 4, 5, 0, 4, 2, 3, 3, 7, 6, 7, 2, 6,
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2, 0, 3, 1, 7, 5, 6, 4], dtype=torch.long, device=device, requires_grad=False)
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self.edge_dir_table = torch.tensor([0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 1, 1],
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dtype=torch.long, device=device)
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self.dir_faces_table = torch.tensor([
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[[5, 4], [3, 2], [4, 5], [2, 3]],
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[[5, 4], [1, 0], [4, 5], [0, 1]],
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[[3, 2], [1, 0], [2, 3], [0, 1]]
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], dtype=torch.long, device=device)
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self.adj_pairs = torch.tensor([0, 1, 1, 3, 3, 2, 2, 0], dtype=torch.long, device=device)
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self.qef_reg_scale = qef_reg_scale
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self.weight_scale = weight_scale
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def construct_voxel_grid(self, res):
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"""
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Generates a voxel grid based on the specified resolution.
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Args:
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res (int or list[int]): The resolution of the voxel grid. If an integer
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is provided, it is used for all three dimensions. If a list or tuple
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of 3 integers is provided, they define the resolution for the x,
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y, and z dimensions respectively.
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Returns:
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(torch.Tensor, torch.Tensor): Returns the vertices and the indices of the
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cube corners (index into vertices) of the constructed voxel grid.
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The vertices are centered at the origin, with the length of each
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dimension in the grid being one.
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"""
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base_cube_f = torch.arange(8).to(self.device)
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if isinstance(res, int):
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res = (res, res, res)
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voxel_grid_template = torch.ones(res, device=self.device)
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res = torch.tensor([res], dtype=torch.float, device=self.device)
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coords = torch.nonzero(voxel_grid_template).float() / res # N, 3
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verts = (self.cube_corners.unsqueeze(0) / res + coords.unsqueeze(1)).reshape(-1, 3)
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cubes = (base_cube_f.unsqueeze(0) +
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torch.arange(coords.shape[0], device=self.device).unsqueeze(1) * 8).reshape(-1)
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verts_rounded = torch.round(verts * 10**5) / (10**5)
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verts_unique, inverse_indices = torch.unique(verts_rounded, dim=0, return_inverse=True)
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cubes = inverse_indices[cubes.reshape(-1)].reshape(-1, 8)
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return verts_unique - 0.5, cubes
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def __call__(self, x_nx3, s_n, cube_fx8, res, beta_fx12=None, alpha_fx8=None,
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gamma_f=None, training=False, output_tetmesh=False, grad_func=None):
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r"""
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Main function for mesh extraction from scalar field using FlexiCubes. This function converts
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discrete signed distance fields, encoded on voxel grids and additional per-cube parameters,
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to triangle or tetrahedral meshes using a differentiable operation as described in
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`Flexible Isosurface Extraction for Gradient-Based Mesh Optimization`_. FlexiCubes enhances
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mesh quality and geometric fidelity by adjusting the surface representation based on gradient
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optimization. The output surface is differentiable with respect to the input vertex positions,
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scalar field values, and weight parameters.
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If you intend to extract a surface mesh from a fixed Signed Distance Field without the
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optimization of parameters, it is suggested to provide the "grad_func" which should
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return the surface gradient at any given 3D position. When grad_func is provided, the process
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to determine the dual vertex position adapts to solve a Quadratic Error Function (QEF), as
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described in the `Manifold Dual Contouring`_ paper, and employs an smart splitting strategy.
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Please note, this approach is non-differentiable.
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For more details and example usage in optimization, refer to the
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`Flexible Isosurface Extraction for Gradient-Based Mesh Optimization`_ SIGGRAPH 2023 paper.
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Args:
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x_nx3 (torch.Tensor): Coordinates of the voxel grid vertices, can be deformed.
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s_n (torch.Tensor): Scalar field values at each vertex of the voxel grid. Negative values
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denote that the corresponding vertex resides inside the isosurface. This affects
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the directions of the extracted triangle faces and volume to be tetrahedralized.
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cube_fx8 (torch.Tensor): Indices of 8 vertices for each cube in the voxel grid.
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res (int or list[int]): The resolution of the voxel grid. If an integer is provided, it
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is used for all three dimensions. If a list or tuple of 3 integers is provided, they
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specify the resolution for the x, y, and z dimensions respectively.
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beta_fx12 (torch.Tensor, optional): Weight parameters for the cube edges to adjust dual
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vertices positioning. Defaults to uniform value for all edges.
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alpha_fx8 (torch.Tensor, optional): Weight parameters for the cube corners to adjust dual
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vertices positioning. Defaults to uniform value for all vertices.
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gamma_f (torch.Tensor, optional): Weight parameters to control the splitting of
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quadrilaterals into triangles. Defaults to uniform value for all cubes.
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training (bool, optional): If set to True, applies differentiable quad splitting for
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training. Defaults to False.
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output_tetmesh (bool, optional): If set to True, outputs a tetrahedral mesh, otherwise,
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outputs a triangular mesh. Defaults to False.
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grad_func (callable, optional): A function to compute the surface gradient at specified
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3D positions (input: Nx3 positions). The function should return gradients as an Nx3
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tensor. If None, the original FlexiCubes algorithm is utilized. Defaults to None.
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Returns:
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(torch.Tensor, torch.LongTensor, torch.Tensor): Tuple containing:
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- Vertices for the extracted triangular/tetrahedral mesh.
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- Faces for the extracted triangular/tetrahedral mesh.
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- Regularizer L_dev, computed per dual vertex.
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.. _Flexible Isosurface Extraction for Gradient-Based Mesh Optimization:
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https://research.nvidia.com/labs/toronto-ai/flexicubes/
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.. _Manifold Dual Contouring:
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https://people.engr.tamu.edu/schaefer/research/dualsimp_tvcg.pdf
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"""
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surf_cubes, occ_fx8 = self._identify_surf_cubes(s_n, cube_fx8)
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if surf_cubes.sum() == 0:
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return torch.zeros(
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(0, 3),
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device=self.device), torch.zeros(
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(0, 4),
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dtype=torch.long, device=self.device) if output_tetmesh else torch.zeros(
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(0, 3),
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dtype=torch.long, device=self.device), torch.zeros(
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(0),
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device=self.device)
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beta_fx12, alpha_fx8, gamma_f = self._normalize_weights(beta_fx12, alpha_fx8, gamma_f, surf_cubes)
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case_ids = self._get_case_id(occ_fx8, surf_cubes, res)
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surf_edges, idx_map, edge_counts, surf_edges_mask = self._identify_surf_edges(s_n, cube_fx8, surf_cubes)
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vd, L_dev, vd_gamma, vd_idx_map = self._compute_vd(
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x_nx3, cube_fx8[surf_cubes], surf_edges, s_n, case_ids, beta_fx12, alpha_fx8, gamma_f, idx_map, grad_func)
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vertices, faces, s_edges, edge_indices = self._triangulate(
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s_n, surf_edges, vd, vd_gamma, edge_counts, idx_map, vd_idx_map, surf_edges_mask, training, grad_func)
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if not output_tetmesh:
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return vertices, faces, L_dev
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else:
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vertices, tets = self._tetrahedralize(
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x_nx3, s_n, cube_fx8, vertices, faces, surf_edges, s_edges, vd_idx_map, case_ids, edge_indices,
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surf_cubes, training)
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return vertices, tets, L_dev
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def _compute_reg_loss(self, vd, ue, edge_group_to_vd, vd_num_edges):
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"""
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Regularizer L_dev as in Equation 8
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"""
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dist = torch.norm(ue - torch.index_select(input=vd, index=edge_group_to_vd, dim=0), dim=-1)
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mean_l2 = torch.zeros_like(vd[:, 0])
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mean_l2 = (mean_l2).index_add_(0, edge_group_to_vd, dist) / vd_num_edges.squeeze(1).float()
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mad = (dist - torch.index_select(input=mean_l2, index=edge_group_to_vd, dim=0)).abs()
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return mad
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def _normalize_weights(self, beta_fx12, alpha_fx8, gamma_f, surf_cubes):
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"""
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Normalizes the given weights to be non-negative. If input weights are None, it creates and returns a set of weights of ones.
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"""
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n_cubes = surf_cubes.shape[0]
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if beta_fx12 is not None:
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beta_fx12 = (torch.tanh(beta_fx12) * self.weight_scale + 1)
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else:
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beta_fx12 = torch.ones((n_cubes, 12), dtype=torch.float, device=self.device)
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if alpha_fx8 is not None:
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alpha_fx8 = (torch.tanh(alpha_fx8) * self.weight_scale + 1)
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else:
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alpha_fx8 = torch.ones((n_cubes, 8), dtype=torch.float, device=self.device)
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if gamma_f is not None:
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gamma_f = torch.sigmoid(gamma_f) * self.weight_scale + (1 - self.weight_scale)/2
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else:
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gamma_f = torch.ones((n_cubes), dtype=torch.float, device=self.device)
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return beta_fx12[surf_cubes], alpha_fx8[surf_cubes], gamma_f[surf_cubes]
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@torch.no_grad()
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def _get_case_id(self, occ_fx8, surf_cubes, res):
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"""
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Obtains the ID of topology cases based on cell corner occupancy. This function resolves the
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ambiguity in the Dual Marching Cubes (DMC) configurations as described in Section 1.3 of the
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supplementary material. It should be noted that this function assumes a regular grid.
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"""
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case_ids = (occ_fx8[surf_cubes] * self.cube_corners_idx.to(self.device).unsqueeze(0)).sum(-1)
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problem_config = self.check_table.to(self.device)[case_ids]
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to_check = problem_config[..., 0] == 1
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problem_config = problem_config[to_check]
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if not isinstance(res, (list, tuple)):
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res = [res, res, res]
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# The 'problematic_configs' only contain configurations for surface cubes. Next, we construct a 3D array,
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# 'problem_config_full', to store configurations for all cubes (with default config for non-surface cubes).
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# This allows efficient checking on adjacent cubes.
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problem_config_full = torch.zeros(list(res) + [5], device=self.device, dtype=torch.long)
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vol_idx = torch.nonzero(problem_config_full[..., 0] == 0) # N, 3
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vol_idx_problem = vol_idx[surf_cubes][to_check]
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problem_config_full[vol_idx_problem[..., 0], vol_idx_problem[..., 1], vol_idx_problem[..., 2]] = problem_config
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vol_idx_problem_adj = vol_idx_problem + problem_config[..., 1:4]
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within_range = (
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vol_idx_problem_adj[..., 0] >= 0) & (
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vol_idx_problem_adj[..., 0] < res[0]) & (
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vol_idx_problem_adj[..., 1] >= 0) & (
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vol_idx_problem_adj[..., 1] < res[1]) & (
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vol_idx_problem_adj[..., 2] >= 0) & (
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vol_idx_problem_adj[..., 2] < res[2])
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vol_idx_problem = vol_idx_problem[within_range]
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vol_idx_problem_adj = vol_idx_problem_adj[within_range]
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problem_config = problem_config[within_range]
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problem_config_adj = problem_config_full[vol_idx_problem_adj[..., 0],
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vol_idx_problem_adj[..., 1], vol_idx_problem_adj[..., 2]]
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# If two cubes with cases C16 and C19 share an ambiguous face, both cases are inverted.
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to_invert = (problem_config_adj[..., 0] == 1)
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idx = torch.arange(case_ids.shape[0], device=self.device)[to_check][within_range][to_invert]
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case_ids.index_put_((idx,), problem_config[to_invert][..., -1])
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return case_ids
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@torch.no_grad()
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def _identify_surf_edges(self, s_n, cube_fx8, surf_cubes):
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"""
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Identifies grid edges that intersect with the underlying surface by checking for opposite signs. As each edge
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can be shared by multiple cubes, this function also assigns a unique index to each surface-intersecting edge
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and marks the cube edges with this index.
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"""
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occ_n = s_n < 0
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all_edges = cube_fx8[surf_cubes][:, self.cube_edges].reshape(-1, 2)
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unique_edges, _idx_map, counts = torch.unique(all_edges, dim=0, return_inverse=True, return_counts=True)
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unique_edges = unique_edges.long()
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mask_edges = occ_n[unique_edges.reshape(-1)].reshape(-1, 2).sum(-1) == 1
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surf_edges_mask = mask_edges[_idx_map]
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counts = counts[_idx_map]
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mapping = torch.ones((unique_edges.shape[0]), dtype=torch.long, device=cube_fx8.device) * -1
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mapping[mask_edges] = torch.arange(mask_edges.sum(), device=cube_fx8.device)
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# Shaped as [number of cubes x 12 edges per cube]. This is later used to map a cube edge to the unique index
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# for a surface-intersecting edge. Non-surface-intersecting edges are marked with -1.
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idx_map = mapping[_idx_map]
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surf_edges = unique_edges[mask_edges]
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return surf_edges, idx_map, counts, surf_edges_mask
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@torch.no_grad()
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def _identify_surf_cubes(self, s_n, cube_fx8):
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"""
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Identifies grid cubes that intersect with the underlying surface by checking if the signs at
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all corners are not identical.
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"""
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occ_n = s_n < 0
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occ_fx8 = occ_n[cube_fx8.reshape(-1)].reshape(-1, 8)
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_occ_sum = torch.sum(occ_fx8, -1)
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surf_cubes = (_occ_sum > 0) & (_occ_sum < 8)
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return surf_cubes, occ_fx8
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def _linear_interp(self, edges_weight, edges_x):
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"""
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Computes the location of zero-crossings on 'edges_x' using linear interpolation with 'edges_weight'.
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"""
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edge_dim = edges_weight.dim() - 2
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assert edges_weight.shape[edge_dim] == 2
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edges_weight = torch.cat([torch.index_select(input=edges_weight, index=torch.tensor(1, device=self.device), dim=edge_dim), -
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torch.index_select(input=edges_weight, index=torch.tensor(0, device=self.device), dim=edge_dim)], edge_dim)
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denominator = edges_weight.sum(edge_dim)
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ue = (edges_x * edges_weight).sum(edge_dim) / denominator
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return ue
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def _solve_vd_QEF(self, p_bxnx3, norm_bxnx3, c_bx3=None):
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p_bxnx3 = p_bxnx3.reshape(-1, 7, 3)
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norm_bxnx3 = norm_bxnx3.reshape(-1, 7, 3)
|
||||
c_bx3 = c_bx3.reshape(-1, 3)
|
||||
A = norm_bxnx3
|
||||
B = ((p_bxnx3) * norm_bxnx3).sum(-1, keepdims=True)
|
||||
|
||||
A_reg = (torch.eye(3, device=p_bxnx3.device) * self.qef_reg_scale).unsqueeze(0).repeat(p_bxnx3.shape[0], 1, 1)
|
||||
B_reg = (self.qef_reg_scale * c_bx3).unsqueeze(-1)
|
||||
A = torch.cat([A, A_reg], 1)
|
||||
B = torch.cat([B, B_reg], 1)
|
||||
dual_verts = torch.linalg.lstsq(A, B).solution.squeeze(-1)
|
||||
return dual_verts
|
||||
|
||||
def _compute_vd(self, x_nx3, surf_cubes_fx8, surf_edges, s_n, case_ids, beta_fx12, alpha_fx8, gamma_f, idx_map, grad_func):
|
||||
"""
|
||||
Computes the location of dual vertices as described in Section 4.2
|
||||
"""
|
||||
alpha_nx12x2 = torch.index_select(input=alpha_fx8, index=self.cube_edges, dim=1).reshape(-1, 12, 2)
|
||||
surf_edges_x = torch.index_select(input=x_nx3, index=surf_edges.reshape(-1), dim=0).reshape(-1, 2, 3)
|
||||
surf_edges_s = torch.index_select(input=s_n, index=surf_edges.reshape(-1), dim=0).reshape(-1, 2, 1)
|
||||
zero_crossing = self._linear_interp(surf_edges_s, surf_edges_x)
|
||||
|
||||
idx_map = idx_map.reshape(-1, 12)
|
||||
num_vd = torch.index_select(input=self.num_vd_table, index=case_ids, dim=0)
|
||||
edge_group, edge_group_to_vd, edge_group_to_cube, vd_num_edges, vd_gamma = [], [], [], [], []
|
||||
|
||||
total_num_vd = 0
|
||||
vd_idx_map = torch.zeros((case_ids.shape[0], 12), dtype=torch.long, device=self.device, requires_grad=False)
|
||||
if grad_func is not None:
|
||||
normals = torch.nn.functional.normalize(grad_func(zero_crossing), dim=-1)
|
||||
vd = []
|
||||
for num in torch.unique(num_vd):
|
||||
cur_cubes = (num_vd == num) # consider cubes with the same numbers of vd emitted (for batching)
|
||||
curr_num_vd = cur_cubes.sum() * num
|
||||
curr_edge_group = self.dmc_table[case_ids[cur_cubes], :num].reshape(-1, num * 7)
|
||||
curr_edge_group_to_vd = torch.arange(
|
||||
curr_num_vd, device=self.device).unsqueeze(-1).repeat(1, 7) + total_num_vd
|
||||
total_num_vd += curr_num_vd
|
||||
curr_edge_group_to_cube = torch.arange(idx_map.shape[0], device=self.device)[
|
||||
cur_cubes].unsqueeze(-1).repeat(1, num * 7).reshape_as(curr_edge_group)
|
||||
|
||||
curr_mask = (curr_edge_group != -1)
|
||||
edge_group.append(torch.masked_select(curr_edge_group, curr_mask))
|
||||
edge_group_to_vd.append(torch.masked_select(curr_edge_group_to_vd.reshape_as(curr_edge_group), curr_mask))
|
||||
edge_group_to_cube.append(torch.masked_select(curr_edge_group_to_cube, curr_mask))
|
||||
vd_num_edges.append(curr_mask.reshape(-1, 7).sum(-1, keepdims=True))
|
||||
vd_gamma.append(torch.masked_select(gamma_f, cur_cubes).unsqueeze(-1).repeat(1, num).reshape(-1))
|
||||
|
||||
if grad_func is not None:
|
||||
with torch.no_grad():
|
||||
cube_e_verts_idx = idx_map[cur_cubes]
|
||||
curr_edge_group[~curr_mask] = 0
|
||||
|
||||
verts_group_idx = torch.gather(input=cube_e_verts_idx, dim=1, index=curr_edge_group)
|
||||
verts_group_idx[verts_group_idx == -1] = 0
|
||||
verts_group_pos = torch.index_select(
|
||||
input=zero_crossing, index=verts_group_idx.reshape(-1), dim=0).reshape(-1, num.item(), 7, 3)
|
||||
v0 = x_nx3[surf_cubes_fx8[cur_cubes][:, 0]].reshape(-1, 1, 1, 3).repeat(1, num.item(), 1, 1)
|
||||
curr_mask = curr_mask.reshape(-1, num.item(), 7, 1)
|
||||
verts_centroid = (verts_group_pos * curr_mask).sum(2) / (curr_mask.sum(2))
|
||||
|
||||
normals_bx7x3 = torch.index_select(input=normals, index=verts_group_idx.reshape(-1), dim=0).reshape(
|
||||
-1, num.item(), 7,
|
||||
3)
|
||||
curr_mask = curr_mask.squeeze(2)
|
||||
vd.append(self._solve_vd_QEF((verts_group_pos - v0) * curr_mask, normals_bx7x3 * curr_mask,
|
||||
verts_centroid - v0.squeeze(2)) + v0.reshape(-1, 3))
|
||||
edge_group = torch.cat(edge_group)
|
||||
edge_group_to_vd = torch.cat(edge_group_to_vd)
|
||||
edge_group_to_cube = torch.cat(edge_group_to_cube)
|
||||
vd_num_edges = torch.cat(vd_num_edges)
|
||||
vd_gamma = torch.cat(vd_gamma)
|
||||
|
||||
if grad_func is not None:
|
||||
vd = torch.cat(vd)
|
||||
L_dev = torch.zeros([1], device=self.device)
|
||||
else:
|
||||
vd = torch.zeros((total_num_vd, 3), device=self.device)
|
||||
beta_sum = torch.zeros((total_num_vd, 1), device=self.device)
|
||||
|
||||
idx_group = torch.gather(input=idx_map.reshape(-1), dim=0, index=edge_group_to_cube * 12 + edge_group)
|
||||
|
||||
x_group = torch.index_select(input=surf_edges_x, index=idx_group.reshape(-1), dim=0).reshape(-1, 2, 3)
|
||||
s_group = torch.index_select(input=surf_edges_s, index=idx_group.reshape(-1), dim=0).reshape(-1, 2, 1)
|
||||
|
||||
zero_crossing_group = torch.index_select(
|
||||
input=zero_crossing, index=idx_group.reshape(-1), dim=0).reshape(-1, 3)
|
||||
|
||||
alpha_group = torch.index_select(input=alpha_nx12x2.reshape(-1, 2), dim=0,
|
||||
index=edge_group_to_cube * 12 + edge_group).reshape(-1, 2, 1)
|
||||
ue_group = self._linear_interp(s_group * alpha_group, x_group)
|
||||
|
||||
beta_group = torch.gather(input=beta_fx12.reshape(-1), dim=0,
|
||||
index=edge_group_to_cube * 12 + edge_group).reshape(-1, 1)
|
||||
beta_sum = beta_sum.index_add_(0, index=edge_group_to_vd, source=beta_group)
|
||||
vd = vd.index_add_(0, index=edge_group_to_vd, source=ue_group * beta_group) / beta_sum
|
||||
L_dev = self._compute_reg_loss(vd, zero_crossing_group, edge_group_to_vd, vd_num_edges)
|
||||
|
||||
v_idx = torch.arange(vd.shape[0], device=self.device) # + total_num_vd
|
||||
|
||||
vd_idx_map = (vd_idx_map.reshape(-1)).scatter(dim=0, index=edge_group_to_cube *
|
||||
12 + edge_group, src=v_idx[edge_group_to_vd])
|
||||
|
||||
return vd, L_dev, vd_gamma, vd_idx_map
|
||||
|
||||
def _triangulate(self, s_n, surf_edges, vd, vd_gamma, edge_counts, idx_map, vd_idx_map, surf_edges_mask, training, grad_func):
|
||||
"""
|
||||
Connects four neighboring dual vertices to form a quadrilateral. The quadrilaterals are then split into
|
||||
triangles based on the gamma parameter, as described in Section 4.3.
|
||||
"""
|
||||
with torch.no_grad():
|
||||
group_mask = (edge_counts == 4) & surf_edges_mask # surface edges shared by 4 cubes.
|
||||
group = idx_map.reshape(-1)[group_mask]
|
||||
vd_idx = vd_idx_map[group_mask]
|
||||
edge_indices, indices = torch.sort(group, stable=True)
|
||||
quad_vd_idx = vd_idx[indices].reshape(-1, 4)
|
||||
|
||||
# Ensure all face directions point towards the positive SDF to maintain consistent winding.
|
||||
s_edges = s_n[surf_edges[edge_indices.reshape(-1, 4)[:, 0]].reshape(-1)].reshape(-1, 2)
|
||||
flip_mask = s_edges[:, 0] > 0
|
||||
quad_vd_idx = torch.cat((quad_vd_idx[flip_mask][:, [0, 1, 3, 2]],
|
||||
quad_vd_idx[~flip_mask][:, [2, 3, 1, 0]]))
|
||||
if grad_func is not None:
|
||||
# when grad_func is given, split quadrilaterals along the diagonals with more consistent gradients.
|
||||
with torch.no_grad():
|
||||
vd_gamma = torch.nn.functional.normalize(grad_func(vd), dim=-1)
|
||||
quad_gamma = torch.index_select(input=vd_gamma, index=quad_vd_idx.reshape(-1), dim=0).reshape(-1, 4, 3)
|
||||
gamma_02 = (quad_gamma[:, 0] * quad_gamma[:, 2]).sum(-1, keepdims=True)
|
||||
gamma_13 = (quad_gamma[:, 1] * quad_gamma[:, 3]).sum(-1, keepdims=True)
|
||||
else:
|
||||
quad_gamma = torch.index_select(input=vd_gamma, index=quad_vd_idx.reshape(-1), dim=0).reshape(-1, 4)
|
||||
gamma_02 = torch.index_select(input=quad_gamma, index=torch.tensor(
|
||||
0, device=self.device), dim=1) * torch.index_select(input=quad_gamma, index=torch.tensor(2, device=self.device), dim=1)
|
||||
gamma_13 = torch.index_select(input=quad_gamma, index=torch.tensor(
|
||||
1, device=self.device), dim=1) * torch.index_select(input=quad_gamma, index=torch.tensor(3, device=self.device), dim=1)
|
||||
if not training:
|
||||
mask = (gamma_02 > gamma_13).squeeze(1)
|
||||
faces = torch.zeros((quad_gamma.shape[0], 6), dtype=torch.long, device=quad_vd_idx.device)
|
||||
faces[mask] = quad_vd_idx[mask][:, self.quad_split_1]
|
||||
faces[~mask] = quad_vd_idx[~mask][:, self.quad_split_2]
|
||||
faces = faces.reshape(-1, 3)
|
||||
else:
|
||||
vd_quad = torch.index_select(input=vd, index=quad_vd_idx.reshape(-1), dim=0).reshape(-1, 4, 3)
|
||||
vd_02 = (torch.index_select(input=vd_quad, index=torch.tensor(0, device=self.device), dim=1) +
|
||||
torch.index_select(input=vd_quad, index=torch.tensor(2, device=self.device), dim=1)) / 2
|
||||
vd_13 = (torch.index_select(input=vd_quad, index=torch.tensor(1, device=self.device), dim=1) +
|
||||
torch.index_select(input=vd_quad, index=torch.tensor(3, device=self.device), dim=1)) / 2
|
||||
weight_sum = (gamma_02 + gamma_13) + 1e-8
|
||||
vd_center = ((vd_02 * gamma_02.unsqueeze(-1) + vd_13 * gamma_13.unsqueeze(-1)) /
|
||||
weight_sum.unsqueeze(-1)).squeeze(1)
|
||||
vd_center_idx = torch.arange(vd_center.shape[0], device=self.device) + vd.shape[0]
|
||||
vd = torch.cat([vd, vd_center])
|
||||
faces = quad_vd_idx[:, self.quad_split_train].reshape(-1, 4, 2)
|
||||
faces = torch.cat([faces, vd_center_idx.reshape(-1, 1, 1).repeat(1, 4, 1)], -1).reshape(-1, 3)
|
||||
return vd, faces, s_edges, edge_indices
|
||||
|
||||
def _tetrahedralize(
|
||||
self, x_nx3, s_n, cube_fx8, vertices, faces, surf_edges, s_edges, vd_idx_map, case_ids, edge_indices,
|
||||
surf_cubes, training):
|
||||
"""
|
||||
Tetrahedralizes the interior volume to produce a tetrahedral mesh, as described in Section 4.5.
|
||||
"""
|
||||
occ_n = s_n < 0
|
||||
occ_fx8 = occ_n[cube_fx8.reshape(-1)].reshape(-1, 8)
|
||||
occ_sum = torch.sum(occ_fx8, -1)
|
||||
|
||||
inside_verts = x_nx3[occ_n]
|
||||
mapping_inside_verts = torch.ones((occ_n.shape[0]), dtype=torch.long, device=self.device) * -1
|
||||
mapping_inside_verts[occ_n] = torch.arange(occ_n.sum(), device=self.device) + vertices.shape[0]
|
||||
"""
|
||||
For each grid edge connecting two grid vertices with different
|
||||
signs, we first form a four-sided pyramid by connecting one
|
||||
of the grid vertices with four mesh vertices that correspond
|
||||
to the grid edge and then subdivide the pyramid into two tetrahedra
|
||||
"""
|
||||
inside_verts_idx = mapping_inside_verts[surf_edges[edge_indices.reshape(-1, 4)[:, 0]].reshape(-1, 2)[
|
||||
s_edges < 0]]
|
||||
if not training:
|
||||
inside_verts_idx = inside_verts_idx.unsqueeze(1).expand(-1, 2).reshape(-1)
|
||||
else:
|
||||
inside_verts_idx = inside_verts_idx.unsqueeze(1).expand(-1, 4).reshape(-1)
|
||||
|
||||
tets_surface = torch.cat([faces, inside_verts_idx.unsqueeze(-1)], -1)
|
||||
"""
|
||||
For each grid edge connecting two grid vertices with the
|
||||
same sign, the tetrahedron is formed by the two grid vertices
|
||||
and two vertices in consecutive adjacent cells
|
||||
"""
|
||||
inside_cubes = (occ_sum == 8)
|
||||
inside_cubes_center = x_nx3[cube_fx8[inside_cubes].reshape(-1)].reshape(-1, 8, 3).mean(1)
|
||||
inside_cubes_center_idx = torch.arange(
|
||||
inside_cubes_center.shape[0], device=inside_cubes.device) + vertices.shape[0] + inside_verts.shape[0]
|
||||
|
||||
surface_n_inside_cubes = surf_cubes | inside_cubes
|
||||
edge_center_vertex_idx = torch.ones(((surface_n_inside_cubes).sum(), 13),
|
||||
dtype=torch.long, device=x_nx3.device) * -1
|
||||
surf_cubes = surf_cubes[surface_n_inside_cubes]
|
||||
inside_cubes = inside_cubes[surface_n_inside_cubes]
|
||||
edge_center_vertex_idx[surf_cubes, :12] = vd_idx_map.reshape(-1, 12)
|
||||
edge_center_vertex_idx[inside_cubes, 12] = inside_cubes_center_idx
|
||||
|
||||
all_edges = cube_fx8[surface_n_inside_cubes][:, self.cube_edges].reshape(-1, 2)
|
||||
unique_edges, _idx_map, counts = torch.unique(all_edges, dim=0, return_inverse=True, return_counts=True)
|
||||
unique_edges = unique_edges.long()
|
||||
mask_edges = occ_n[unique_edges.reshape(-1)].reshape(-1, 2).sum(-1) == 2
|
||||
mask = mask_edges[_idx_map]
|
||||
counts = counts[_idx_map]
|
||||
mapping = torch.ones((unique_edges.shape[0]), dtype=torch.long, device=self.device) * -1
|
||||
mapping[mask_edges] = torch.arange(mask_edges.sum(), device=self.device)
|
||||
idx_map = mapping[_idx_map]
|
||||
|
||||
group_mask = (counts == 4) & mask
|
||||
group = idx_map.reshape(-1)[group_mask]
|
||||
edge_indices, indices = torch.sort(group)
|
||||
cube_idx = torch.arange((_idx_map.shape[0] // 12), dtype=torch.long,
|
||||
device=self.device).unsqueeze(1).expand(-1, 12).reshape(-1)[group_mask]
|
||||
edge_idx = torch.arange((12), dtype=torch.long, device=self.device).unsqueeze(
|
||||
0).expand(_idx_map.shape[0] // 12, -1).reshape(-1)[group_mask]
|
||||
# Identify the face shared by the adjacent cells.
|
||||
cube_idx_4 = cube_idx[indices].reshape(-1, 4)
|
||||
edge_dir = self.edge_dir_table[edge_idx[indices]].reshape(-1, 4)[..., 0]
|
||||
shared_faces_4x2 = self.dir_faces_table[edge_dir].reshape(-1)
|
||||
cube_idx_4x2 = cube_idx_4[:, self.adj_pairs].reshape(-1)
|
||||
# Identify an edge of the face with different signs and
|
||||
# select the mesh vertex corresponding to the identified edge.
|
||||
case_ids_expand = torch.ones((surface_n_inside_cubes).sum(), dtype=torch.long, device=x_nx3.device) * 255
|
||||
case_ids_expand[surf_cubes] = case_ids
|
||||
cases = case_ids_expand[cube_idx_4x2]
|
||||
quad_edge = edge_center_vertex_idx[cube_idx_4x2, self.tet_table[cases, shared_faces_4x2]].reshape(-1, 2)
|
||||
mask = (quad_edge == -1).sum(-1) == 0
|
||||
inside_edge = mapping_inside_verts[unique_edges[mask_edges][edge_indices].reshape(-1)].reshape(-1, 2)
|
||||
tets_inside = torch.cat([quad_edge, inside_edge], -1)[mask]
|
||||
|
||||
tets = torch.cat([tets_surface, tets_inside])
|
||||
vertices = torch.cat([vertices, inside_verts, inside_cubes_center])
|
||||
return vertices, tets
|
||||
@@ -0,0 +1,95 @@
|
||||
# Copyright (c) 2023, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
|
||||
#
|
||||
# NVIDIA CORPORATION & AFFILIATES and its licensors retain all intellectual property
|
||||
# and proprietary rights in and to this software, related documentation
|
||||
# and any modifications thereto. Any use, reproduction, disclosure or
|
||||
# distribution of this software and related documentation without an express
|
||||
# license agreement from NVIDIA CORPORATION & AFFILIATES is strictly prohibited.
|
||||
import torch
|
||||
import torch_scatter
|
||||
|
||||
###############################################################################
|
||||
# Pytorch implementation of the developability regularizer introduced in paper
|
||||
# "Developability of Triangle Meshes" by Stein et al.
|
||||
###############################################################################
|
||||
def mesh_developable_reg(mesh):
|
||||
|
||||
verts = mesh.vertices
|
||||
tris = mesh.faces
|
||||
|
||||
device = verts.device
|
||||
V = verts.shape[0]
|
||||
F = tris.shape[0]
|
||||
|
||||
POS_EPS = 1e-6
|
||||
REL_EPS = 1e-6
|
||||
|
||||
def normalize(vecs):
|
||||
return vecs / (torch.linalg.norm(vecs, dim=-1, keepdim=True) + POS_EPS)
|
||||
|
||||
tri_pos = verts[tris]
|
||||
|
||||
vert_normal_covariance_sum = torch.zeros((V, 9), device=device)
|
||||
vert_area = torch.zeros(V, device=device)
|
||||
vert_degree = torch.zeros(V, dtype=torch.int32, device=device)
|
||||
|
||||
for iC in range(3): # loop over three corners of each triangle
|
||||
|
||||
# gather tri verts
|
||||
pRoot = tri_pos[:, iC, :]
|
||||
pA = tri_pos[:, (iC + 1) % 3, :]
|
||||
pB = tri_pos[:, (iC + 2) % 3, :]
|
||||
|
||||
# compute the corner angle & normal
|
||||
vA = pA - pRoot
|
||||
vAn = normalize(vA)
|
||||
vB = pB - pRoot
|
||||
vBn = normalize(vB)
|
||||
area_normal = torch.linalg.cross(vA, vB, dim=-1)
|
||||
face_area = 0.5 * torch.linalg.norm(area_normal, dim=-1)
|
||||
normal = normalize(area_normal)
|
||||
corner_angle = torch.acos(torch.clamp(torch.sum(vAn * vBn, dim=-1), min=-1., max=1.))
|
||||
|
||||
# add up the contribution to the covariance matrix
|
||||
outer = normal[:, :, None] @ normal[:, None, :]
|
||||
contrib = corner_angle[:, None] * outer.reshape(-1, 9)
|
||||
|
||||
# scatter the result to the appropriate matrices
|
||||
vert_normal_covariance_sum = torch_scatter.scatter_add(src=contrib,
|
||||
index=tris[:, iC],
|
||||
dim=-2,
|
||||
out=vert_normal_covariance_sum)
|
||||
|
||||
vert_area = torch_scatter.scatter_add(src=face_area / 3.,
|
||||
index=tris[:, iC],
|
||||
dim=-1,
|
||||
out=vert_area)
|
||||
|
||||
vert_degree = torch_scatter.scatter_add(src=torch.ones(F, dtype=torch.int32, device=device),
|
||||
index=tris[:, iC],
|
||||
dim=-1,
|
||||
out=vert_degree)
|
||||
|
||||
# The energy is the smallest eigenvalue of the outer-product matrix
|
||||
vert_normal_covariance_sum = vert_normal_covariance_sum.reshape(
|
||||
-1, 3, 3) # reshape to a batch of matrices
|
||||
vert_normal_covariance_sum = vert_normal_covariance_sum + torch.eye(
|
||||
3, device=device)[None, :, :] * REL_EPS
|
||||
|
||||
min_eigvals = torch.min(torch.linalg.eigvals(vert_normal_covariance_sum).abs(), dim=-1).values
|
||||
|
||||
# Mask out degree-3 vertices
|
||||
vert_area = torch.where(vert_degree == 3, torch.tensor(0, dtype=vert_area.dtype,device=vert_area.device), vert_area)
|
||||
|
||||
# Adjust the vertex area weighting so it is unit-less, and 1 on average
|
||||
vert_area = vert_area * (V / torch.sum(vert_area, dim=-1, keepdim=True))
|
||||
|
||||
return vert_area * min_eigvals
|
||||
|
||||
def sdf_reg_loss(sdf, all_edges):
|
||||
sdf_f1x6x2 = sdf[all_edges.reshape(-1)].reshape(-1,2)
|
||||
mask = torch.sign(sdf_f1x6x2[...,0]) != torch.sign(sdf_f1x6x2[...,1])
|
||||
sdf_f1x6x2 = sdf_f1x6x2[mask]
|
||||
sdf_diff = torch.nn.functional.binary_cross_entropy_with_logits(sdf_f1x6x2[...,0], (sdf_f1x6x2[...,1] > 0).float()) + \
|
||||
torch.nn.functional.binary_cross_entropy_with_logits(sdf_f1x6x2[...,1], (sdf_f1x6x2[...,0] > 0).float())
|
||||
return sdf_diff
|
||||
@@ -0,0 +1,791 @@
|
||||
# Copyright (c) 2023, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
|
||||
#
|
||||
# NVIDIA CORPORATION & AFFILIATES and its licensors retain all intellectual property
|
||||
# and proprietary rights in and to this software, related documentation
|
||||
# and any modifications thereto. Any use, reproduction, disclosure or
|
||||
# distribution of this software and related documentation without an express
|
||||
# license agreement from NVIDIA CORPORATION & AFFILIATES is strictly prohibited.
|
||||
dmc_table = [
|
||||
[[-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 8, 9, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [4, 7, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 7, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [4, 5, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 5, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 5, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 7, 8, 9, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 5, 7, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 5, 7, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 5, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 8, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 8, 9, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 7, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [4, 7, 8, -1, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 7, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 8, 11, -1, -1, -1], [4, 5, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 5, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 5, 8, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 7, 8, 9, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 5, 7, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 5, 7, 8, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 5, 7, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 9, 10, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 8, 9, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 7, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 9, 10, -1, -1, -1], [4, 7, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 7, 9, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [4, 5, 9, -1, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 5, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 5, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 7, 8, 9, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 5, 7, 9, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 5, 7, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 5, 7, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 8, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 9, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[8, 9, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [1, 3, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 7, 10, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 9, 10, 11, -1, -1], [4, 7, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 9, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [1, 3, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 8, 10, 11, -1, -1], [4, 5, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 5, 10, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 8, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 7, 8, 9, -1, -1, -1], [1, 3, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 5, 7, 9, 10, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 5, 7, 8, 10, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 7, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 8, 9, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 6, 8, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 6, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [4, 6, 8, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 6, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [4, 5, 9, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 5, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 5, 8, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 6, 8, 9, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 5, 6, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 5, 6, 8, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 5, 6, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 6, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 6, 7, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [2, 3, 6, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 6, 7, 8, 9, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 6, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 6, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [2, 3, 4, 6, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 6, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [2, 3, 6, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 6, 7, 8, -1, -1], [4, 5, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 5, -1, -1, -1], [2, 3, 6, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 5, 6, 7, 8], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 5, 6, 8, 9, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 5, 6, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 2, 3, 5, 6, 8], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 5, 6, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 10, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 9, 10, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 8, 9, 10, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 6, 8, 11, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 6, 11, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 9, 10, -1, -1, -1], [4, 6, 8, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 6, 9, 10, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [4, 5, 9, -1, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 5, 10, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 5, 8, 10, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 6, 8, 9, 11, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 5, 6, 9, 11, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 5, 6, 8, 10, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 5, 6, 10, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 6, 7, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 6, 7, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 6, 7, 9, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[6, 7, 8, 9, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 6, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 6, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 6, 8, 9, 10], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 6, 9, 10, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [1, 3, 6, 7, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 6, 7, 8, 10, -1], [4, 5, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 5, 6, 7, 10], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 6, 7, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 5, 6, 8, 9, 10], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 5, 6, 9, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 8, 9, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 7, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [4, 7, 8, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 7, 9, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 6, 9, 10, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [4, 6, 9, 10, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 6, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 6, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[6, 7, 8, 9, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 6, 7, 9, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 6, 7, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 6, 7, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 11, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 8, 11, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 8, 9, 11, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 7, 11, -1, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [4, 7, 8, -1, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [5, 6, 10, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 7, 9, 11, -1], [5, 6, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 6, 9, 10, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 8, 11, -1, -1, -1], [4, 6, 9, 10, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 6, 10, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 6, 8, 10, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[6, 7, 8, 9, 10, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 6, 7, 9, 10, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 6, 7, 8, 10, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 6, 7, 10, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 5, 6, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [1, 2, 5, 6, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 5, 6, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 5, 6, 8, 9, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [1, 2, 5, 6, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 7, -1, -1, -1], [1, 2, 5, 6, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 5, 6, 9, -1, -1], [4, 7, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 5, 6, 7, 9], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 6, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [1, 2, 4, 6, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 6, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 6, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 6, 7, 8, 9, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 2, 3, 6, 7, 9], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 6, 7, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 6, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 5, 6, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 5, 6, 8, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 5, 6, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 6, 8, 9, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [1, 3, 5, 6, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 5, 6, 7, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 5, 6, 9, 11, -1], [4, 7, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 6, 7, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 6, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 6, 8, 9, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 6, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 6, 8, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 6, 7, 8, 9, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 6, 7, 8, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[6, 7, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 7, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [5, 7, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [5, 7, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 8, 9, -1, -1, -1], [5, 7, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 8, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 5, 10, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [4, 5, 8, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 5, 9, 10, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 9, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [4, 7, 9, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 7, 10, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 7, 8, 10, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[8, 9, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 9, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 8, 10, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 10, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 5, 7, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 5, 7, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [2, 3, 5, 7, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 5, 7, 8, 9, 10], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 5, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 5, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [2, 3, 4, 5, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 5, 9, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 7, 9, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 7, 8, 9, 10], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 2, 3, 4, 7, 10], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 8, 9, 10, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 9, 10, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 2, 3, 8, 10, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 10, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 5, 7, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [1, 2, 5, 7, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 5, 7, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 5, 7, 8, 9, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 5, 8, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 2, 3, 4, 5, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 5, 8, 9, 11], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 4, 7, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [1, 2, 4, 7, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 4, 7, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 4, 7, 8, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 2, 8, 9, 11, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 2, 3, 9, 11, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 2, 8, 11, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[2, 3, 11, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 5, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 5, 7, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 5, 7, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[5, 7, 8, 9, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 5, 8, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 5, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 5, 8, 9, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 5, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 4, 7, 9, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 4, 7, 8, 9, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 4, 7, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[4, 7, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[1, 3, 8, 9, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 1, 9, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[0, 3, 8, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]],
|
||||
[[-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1]]
|
||||
]
|
||||
num_vd_table = [0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2,
|
||||
2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2,
|
||||
1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 3, 2, 2, 1, 1, 1, 1,
|
||||
1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 2, 1, 3, 4, 2,
|
||||
2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2,
|
||||
3, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 2, 4, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1,
|
||||
2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1,
|
||||
1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2,
|
||||
1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
|
||||
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
|
||||
check_table = [
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 1, 0, 0, 194],
|
||||
[1, -1, 0, 0, 193],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 1, 0, 164],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, -1, 0, 161],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, 1, 152],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, 1, 145],
|
||||
[1, 0, 0, 1, 144],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, -1, 137],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 1, 0, 133],
|
||||
[1, 0, 1, 0, 132],
|
||||
[1, 1, 0, 0, 131],
|
||||
[1, 1, 0, 0, 130],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, 1, 100],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, 1, 98],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, 1, 96],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 1, 0, 88],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, -1, 0, 82],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 1, 0, 74],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 1, 0, 72],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, -1, 70],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, -1, 0, 0, 67],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, -1, 0, 0, 65],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 1, 0, 0, 56],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, -1, 0, 0, 52],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 1, 0, 0, 44],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 1, 0, 0, 40],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, -1, 38],
|
||||
[1, 0, -1, 0, 37],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, -1, 0, 33],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, -1, 0, 0, 28],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, -1, 0, 26],
|
||||
[1, 0, 0, -1, 25],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, -1, 0, 0, 20],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, -1, 0, 18],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, -1, 9],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, -1, 6],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0]
|
||||
]
|
||||
tet_table = [
|
||||
[-1, -1, -1, -1, -1, -1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 0, 0, 4, 4, -1],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[0, 4, 0, 4, 4, -1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[5, 5, 5, 5, 5, 5],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 0, 2, -1, 0, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, -1, 2, 4, 4, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 0, 2, 4, 4, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 4, 2, 4, 4, 2],
|
||||
[0, 4, 0, 4, 4, 0],
|
||||
[2, 0, 2, 0, 0, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 5, 2, 5, 5, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 0, 2, 0, 0, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 1, 1, -1, 0, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[4, 1, 1, 4, 4, 1],
|
||||
[0, 1, 1, 0, 0, 1],
|
||||
[4, 0, 0, 4, 4, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[-1, 1, 1, 4, 4, 1],
|
||||
[0, 1, 1, 4, 4, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[5, 1, 1, 5, 5, 1],
|
||||
[0, 1, 1, 0, 0, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[8, 8, 8, 8, 8, 8],
|
||||
[1, 1, 1, 4, 4, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 0, 0, 4, 4, 0],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[1, 1, 1, 4, 4, 1],
|
||||
[0, 4, 0, 4, 4, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[1, 1, 1, 5, 5, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[5, 5, 5, 5, 5, 5],
|
||||
[6, 6, 6, 6, 6, 6],
|
||||
[6, -1, 0, 6, 0, 6],
|
||||
[6, 0, 0, 6, 0, 6],
|
||||
[6, 1, 1, 6, 1, 6],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 0, 0, 4, 4, 4],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[6, 4, -1, 6, 4, 6],
|
||||
[6, 4, 0, 6, 4, 6],
|
||||
[6, 0, 0, 6, 0, 6],
|
||||
[6, 1, 1, 6, 1, 6],
|
||||
[5, 5, 5, 5, 5, 5],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 0, 2, 2, 0, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 0, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 4, 2, 2, 4, 2],
|
||||
[0, 4, 0, 4, 4, 0],
|
||||
[2, 0, 2, 2, 0, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[6, 1, 1, 6, -1, 6],
|
||||
[6, 1, 1, 6, 0, 6],
|
||||
[6, 0, 0, 6, 0, 6],
|
||||
[6, 2, 2, 6, 2, 6],
|
||||
[4, 1, 1, 4, 4, 1],
|
||||
[0, 1, 1, 0, 0, 1],
|
||||
[4, 0, 0, 4, 4, 4],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[6, 1, 1, 6, 4, 6],
|
||||
[6, 1, 1, 6, 4, 6],
|
||||
[6, 0, 0, 6, 0, 6],
|
||||
[6, 2, 2, 6, 2, 6],
|
||||
[5, 1, 1, 5, 5, 1],
|
||||
[0, 1, 1, 0, 0, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[6, 6, 6, 6, 6, 6],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[1, 1, 1, 1, 4, 1],
|
||||
[0, 4, 0, 4, 4, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 5, 0, 5, 0, 5],
|
||||
[5, 5, 5, 5, 5, 5],
|
||||
[5, 5, 5, 5, 5, 5],
|
||||
[0, 5, 0, 5, 0, 5],
|
||||
[-1, 5, 0, 5, 0, 5],
|
||||
[1, 5, 1, 5, 1, 5],
|
||||
[4, 5, -1, 5, 4, 5],
|
||||
[0, 5, 0, 5, 0, 5],
|
||||
[4, 5, 0, 5, 4, 5],
|
||||
[1, 5, 1, 5, 1, 5],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[0, 4, 0, 4, 4, 4],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[6, 6, 6, 6, 6, 6],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 5, 2, 5, -1, 5],
|
||||
[0, 5, 0, 5, 0, 5],
|
||||
[2, 5, 2, 5, 0, 5],
|
||||
[1, 5, 1, 5, 1, 5],
|
||||
[2, 5, 2, 5, 4, 5],
|
||||
[0, 5, 0, 5, 0, 5],
|
||||
[2, 5, 2, 5, 4, 5],
|
||||
[1, 5, 1, 5, 1, 5],
|
||||
[2, 4, 2, 4, 4, 2],
|
||||
[0, 4, 0, 4, 4, 4],
|
||||
[2, 0, 2, 0, 0, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 6, 2, 6, 6, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 0, 2, 0, 0, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 1, 1, 1, 0, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[4, 1, 1, 1, 4, 1],
|
||||
[0, 1, 1, 1, 0, 1],
|
||||
[4, 0, 0, 4, 4, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[5, 5, 5, 5, 5, 5],
|
||||
[1, 1, 1, 1, 4, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 0, 0, 4, 4, 0],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[6, 0, 0, 6, 0, 6],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[6, 6, 6, 6, 6, 6],
|
||||
[5, 5, 5, 5, 5, 5],
|
||||
[5, 5, 0, 5, 0, 5],
|
||||
[5, 5, 0, 5, 0, 5],
|
||||
[5, 5, 1, 5, 1, 5],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 4, 0, 4, 4, 4],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[4, 4, 0, 4, 4, 4],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[8, 8, 8, 8, 8, 8],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 0, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 1, 1, 4, 4, 1],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[1, 1, 1, 1, 0, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 4, 2, 4, 4, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[2, 2, 2, 2, 2, 2],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[5, 5, 5, 5, 5, 5],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[4, 4, 4, 4, 4, 4],
|
||||
[1, 1, 1, 1, 1, 1],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[12, 12, 12, 12, 12, 12]
|
||||
]
|
||||
@@ -0,0 +1,93 @@
|
||||
# Copyright (c) 2023, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
|
||||
#
|
||||
# NVIDIA CORPORATION & AFFILIATES and its licensors retain all intellectual property
|
||||
# and proprietary rights in and to this software, related documentation
|
||||
# and any modifications thereto. Any use, reproduction, disclosure or
|
||||
# distribution of this software and related documentation without an express
|
||||
# license agreement from NVIDIA CORPORATION & AFFILIATES is strictly prohibited.
|
||||
import numpy as np
|
||||
import torch
|
||||
import nvdiffrast.torch as dr
|
||||
|
||||
###############################################################################
|
||||
# Functions adapted from https://github.com/NVlabs/nvdiffrec
|
||||
###############################################################################
|
||||
|
||||
def dot(x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
|
||||
return torch.sum(x*y, -1, keepdim=True)
|
||||
|
||||
def length(x: torch.Tensor, eps: float =1e-8) -> torch.Tensor:
|
||||
return torch.sqrt(torch.clamp(dot(x,x), min=eps)) # Clamp to avoid nan gradients because grad(sqrt(0)) = NaN
|
||||
|
||||
def safe_normalize(x: torch.Tensor, eps: float =1e-8) -> torch.Tensor:
|
||||
return x / length(x, eps)
|
||||
|
||||
def perspective(fovy=0.7854, aspect=1.0, n=0.1, f=1000.0, device=None):
|
||||
y = np.tan(fovy / 2)
|
||||
return torch.tensor([[1/(y*aspect), 0, 0, 0],
|
||||
[ 0, 1/-y, 0, 0],
|
||||
[ 0, 0, -(f+n)/(f-n), -(2*f*n)/(f-n)],
|
||||
[ 0, 0, -1, 0]], dtype=torch.float32, device=device)
|
||||
|
||||
def translate(x, y, z, device=None):
|
||||
return torch.tensor([[1, 0, 0, x],
|
||||
[0, 1, 0, y],
|
||||
[0, 0, 1, z],
|
||||
[0, 0, 0, 1]], dtype=torch.float32, device=device)
|
||||
|
||||
@torch.no_grad()
|
||||
def random_rotation_translation(t, device=None):
|
||||
m = np.random.normal(size=[3, 3])
|
||||
m[1] = np.cross(m[0], m[2])
|
||||
m[2] = np.cross(m[0], m[1])
|
||||
m = m / np.linalg.norm(m, axis=1, keepdims=True)
|
||||
m = np.pad(m, [[0, 1], [0, 1]], mode='constant')
|
||||
m[3, 3] = 1.0
|
||||
m[:3, 3] = np.random.uniform(-t, t, size=[3])
|
||||
return torch.tensor(m, dtype=torch.float32, device=device)
|
||||
|
||||
def rotate_x(a, device=None):
|
||||
s, c = np.sin(a), np.cos(a)
|
||||
return torch.tensor([[1, 0, 0, 0],
|
||||
[0, c, s, 0],
|
||||
[0, -s, c, 0],
|
||||
[0, 0, 0, 1]], dtype=torch.float32, device=device)
|
||||
|
||||
def rotate_y(a, device=None):
|
||||
s, c = np.sin(a), np.cos(a)
|
||||
return torch.tensor([[ c, 0, s, 0],
|
||||
[ 0, 1, 0, 0],
|
||||
[-s, 0, c, 0],
|
||||
[ 0, 0, 0, 1]], dtype=torch.float32, device=device)
|
||||
|
||||
class SimpleMesh:
|
||||
def __init__(self, vertices, faces):
|
||||
self.vertices = vertices
|
||||
self.faces = faces
|
||||
|
||||
def auto_normals(self):
|
||||
v0 = self.vertices[self.faces[:, 0], :]
|
||||
v1 = self.vertices[self.faces[:, 1], :]
|
||||
v2 = self.vertices[self.faces[:, 2], :]
|
||||
nrm = safe_normalize(torch.cross(v1 - v0, v2 - v0, dim=-1))
|
||||
self.nrm = nrm
|
||||
|
||||
def xfm_points(points, matrix):
|
||||
'''Transform points.
|
||||
Args:
|
||||
points: Tensor containing 3D points with shape [minibatch_size, num_vertices, 3] or [1, num_vertices, 3]
|
||||
matrix: A 4x4 transform matrix with shape [minibatch_size, 4, 4]
|
||||
use_python: Use PyTorch's torch.matmul (for validation)
|
||||
Returns:
|
||||
Transformed points in homogeneous 4D with shape [minibatch_size, num_vertices, 4].
|
||||
'''
|
||||
out = torch.matmul(
|
||||
torch.nn.functional.pad(points, pad=(0, 1), mode='constant', value=1.0), torch.transpose(matrix, 1, 2))
|
||||
if torch.is_anomaly_enabled():
|
||||
assert torch.all(torch.isfinite(out)), "Output of xfm_points contains inf or NaN"
|
||||
return out
|
||||
|
||||
def interpolate(attr, rast, attr_idx, rast_db=None):
|
||||
return dr.interpolate(
|
||||
attr, rast, attr_idx, rast_db=rast_db,
|
||||
diff_attrs=None if rast_db is None else 'all')
|
||||
Reference in New Issue
Block a user