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apps/third_party/CRM/util/flexicubes.py

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+# 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
+from util.tables import *
+
+__all__ = [
+    'FlexiCubes'
+]
+
+
+class FlexiCubes:
+    """
+    This class implements the FlexiCubes method for extracting meshes from scalar fields. 
+    It maintains a series of lookup tables and indices to support the mesh extraction process. 
+    FlexiCubes, a differentiable variant of the Dual Marching Cubes (DMC) scheme, enhances 
+    the geometric fidelity and mesh quality of reconstructed meshes by dynamically adjusting 
+    the surface representation through gradient-based optimization.
+
+    During instantiation, the class loads DMC tables from a file and transforms them into 
+    PyTorch tensors on the specified device.
+
+    Attributes:
+        device (str): Specifies the computational device (default is "cuda").
+        dmc_table (torch.Tensor): Dual Marching Cubes (DMC) table that encodes the edges 
+            associated with each dual vertex in 256 Marching Cubes (MC) configurations.
+        num_vd_table (torch.Tensor): Table holding the number of dual vertices in each of 
+            the 256 MC configurations.
+        check_table (torch.Tensor): Table resolving ambiguity in cases C16 and C19 
+            of the DMC configurations.
+        tet_table (torch.Tensor): Lookup table used in tetrahedralizing the isosurface.
+        quad_split_1 (torch.Tensor): Indices for splitting a quad into two triangles 
+            along one diagonal.
+        quad_split_2 (torch.Tensor): Alternative indices for splitting a quad into 
+            two triangles along the other diagonal.
+        quad_split_train (torch.Tensor): Indices for splitting a quad into four triangles 
+            during training by connecting all edges to their midpoints.
+        cube_corners (torch.Tensor): Defines the positions of a standard unit cube's 
+            eight corners in 3D space, ordered starting from the origin (0,0,0), 
+            moving along the x-axis, then y-axis, and finally z-axis. 
+            Used as a blueprint for generating a voxel grid.
+        cube_corners_idx (torch.Tensor): Cube corners indexed as powers of 2, used 
+            to retrieve the case id.
+        cube_edges (torch.Tensor): Edge connections in a cube, listed in pairs. 
+            Used to retrieve edge vertices in DMC.
+        edge_dir_table (torch.Tensor): A mapping tensor that associates edge indices with 
+            their corresponding axis. For instance, edge_dir_table[0] = 0 indicates that the 
+            first edge is oriented along the x-axis. 
+        dir_faces_table (torch.Tensor): A tensor that maps the corresponding axis of shared edges 
+            across four adjacent cubes to the shared faces of these cubes. For instance, 
+            dir_faces_table[0] = [5, 4] implies that for four cubes sharing an edge along 
+            the x-axis, the first and second cubes share faces indexed as 5 and 4, respectively. 
+            This tensor is only utilized during isosurface tetrahedralization.
+        adj_pairs (torch.Tensor): 
+            A tensor containing index pairs that correspond to neighboring cubes that share the same edge.
+        qef_reg_scale (float):
+            The scaling factor applied to the regularization loss to prevent issues with singularity 
+            when solving the QEF. This parameter is only used when a 'grad_func' is specified.
+        weight_scale (float):
+            The scale of weights in FlexiCubes. Should be between 0 and 1.
+    """
+
+    def __init__(self, device="cuda", qef_reg_scale=1e-3, weight_scale=0.99):
+
+        self.device = device
+        self.dmc_table = torch.tensor(dmc_table, dtype=torch.long, device=device, requires_grad=False)
+        self.num_vd_table = torch.tensor(num_vd_table,
+                                         dtype=torch.long, device=device, requires_grad=False)
+        self.check_table = torch.tensor(
+            check_table,
+            dtype=torch.long, device=device, requires_grad=False)
+
+        self.tet_table = torch.tensor(tet_table, dtype=torch.long, device=device, requires_grad=False)
+        self.quad_split_1 = torch.tensor([0, 1, 2, 0, 2, 3], dtype=torch.long, device=device, requires_grad=False)
+        self.quad_split_2 = torch.tensor([0, 1, 3, 3, 1, 2], dtype=torch.long, device=device, requires_grad=False)
+        self.quad_split_train = torch.tensor(
+            [0, 1, 1, 2, 2, 3, 3, 0], dtype=torch.long, device=device, requires_grad=False)
+
+        self.cube_corners = torch.tensor([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [
+                                         1, 0, 1], [0, 1, 1], [1, 1, 1]], dtype=torch.float, device=device)
+        self.cube_corners_idx = torch.pow(2, torch.arange(8, requires_grad=False))
+        self.cube_edges = torch.tensor([0, 1, 1, 5, 4, 5, 0, 4, 2, 3, 3, 7, 6, 7, 2, 6,
+                                       2, 0, 3, 1, 7, 5, 6, 4], dtype=torch.long, device=device, requires_grad=False)
+
+        self.edge_dir_table = torch.tensor([0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 1, 1],
+                                           dtype=torch.long, device=device)
+        self.dir_faces_table = torch.tensor([
+            [[5, 4], [3, 2], [4, 5], [2, 3]],
+            [[5, 4], [1, 0], [4, 5], [0, 1]],
+            [[3, 2], [1, 0], [2, 3], [0, 1]]
+        ], dtype=torch.long, device=device)
+        self.adj_pairs = torch.tensor([0, 1, 1, 3, 3, 2, 2, 0], dtype=torch.long, device=device)
+        self.qef_reg_scale = qef_reg_scale
+        self.weight_scale = weight_scale
+
+    def construct_voxel_grid(self, res):
+        """
+        Generates a voxel grid based on the specified resolution.
+
+        Args:
+            res (int or list[int]): The resolution of the voxel grid. If an integer
+                is provided, it is used for all three dimensions. If a list or tuple 
+                of 3 integers is provided, they define the resolution for the x, 
+                y, and z dimensions respectively.
+
+        Returns:
+            (torch.Tensor, torch.Tensor): Returns the vertices and the indices of the 
+                cube corners (index into vertices) of the constructed voxel grid. 
+                The vertices are centered at the origin, with the length of each 
+                dimension in the grid being one.
+        """
+        base_cube_f = torch.arange(8).to(self.device)
+        if isinstance(res, int):
+            res = (res, res, res)
+        voxel_grid_template = torch.ones(res, device=self.device)
+
+        res = torch.tensor([res], dtype=torch.float, device=self.device)
+        coords = torch.nonzero(voxel_grid_template).float() / res  # N, 3
+        verts = (self.cube_corners.unsqueeze(0) / res + coords.unsqueeze(1)).reshape(-1, 3)
+        cubes = (base_cube_f.unsqueeze(0) +
+                 torch.arange(coords.shape[0], device=self.device).unsqueeze(1) * 8).reshape(-1)
+
+        verts_rounded = torch.round(verts * 10**5) / (10**5)
+        verts_unique, inverse_indices = torch.unique(verts_rounded, dim=0, return_inverse=True)
+        cubes = inverse_indices[cubes.reshape(-1)].reshape(-1, 8)
+
+        return verts_unique - 0.5, cubes
+
+    def __call__(self, x_nx3, s_n, cube_fx8, res, beta_fx12=None, alpha_fx8=None,
+                 gamma_f=None, training=False, output_tetmesh=False, grad_func=None):
+        r"""
+        Main function for mesh extraction from scalar field using FlexiCubes. This function converts 
+        discrete signed distance fields, encoded on voxel grids and additional per-cube parameters, 
+        to triangle or tetrahedral meshes using a differentiable operation as described in 
+        `Flexible Isosurface Extraction for Gradient-Based Mesh Optimization`_. FlexiCubes enhances 
+        mesh quality and geometric fidelity by adjusting the surface representation based on gradient 
+        optimization. The output surface is differentiable with respect to the input vertex positions, 
+        scalar field values, and weight parameters.
+
+        If you intend to extract a surface mesh from a fixed Signed Distance Field without the 
+        optimization of parameters, it is suggested to provide the "grad_func" which should 
+        return the surface gradient at any given 3D position. When grad_func is provided, the process 
+        to determine the dual vertex position adapts to solve a Quadratic Error Function (QEF), as 
+        described in the `Manifold Dual Contouring`_ paper, and employs an smart splitting strategy. 
+        Please note, this approach is non-differentiable.
+
+        For more details and example usage in optimization, refer to the 
+        `Flexible Isosurface Extraction for Gradient-Based Mesh Optimization`_ SIGGRAPH 2023 paper.
+
+        Args:
+            x_nx3 (torch.Tensor): Coordinates of the voxel grid vertices, can be deformed.
+            s_n (torch.Tensor): Scalar field values at each vertex of the voxel grid. Negative values 
+                denote that the corresponding vertex resides inside the isosurface. This affects 
+                the directions of the extracted triangle faces and volume to be tetrahedralized.
+            cube_fx8 (torch.Tensor): Indices of 8 vertices for each cube in the voxel grid.
+            res (int or list[int]): The resolution of the voxel grid. If an integer is provided, it 
+                is used for all three dimensions. If a list or tuple of 3 integers is provided, they 
+                specify the resolution for the x, y, and z dimensions respectively.
+            beta_fx12 (torch.Tensor, optional): Weight parameters for the cube edges to adjust dual 
+                vertices positioning. Defaults to uniform value for all edges.
+            alpha_fx8 (torch.Tensor, optional): Weight parameters for the cube corners to adjust dual 
+                vertices positioning. Defaults to uniform value for all vertices.
+            gamma_f (torch.Tensor, optional): Weight parameters to control the splitting of 
+                quadrilaterals into triangles. Defaults to uniform value for all cubes.
+            training (bool, optional): If set to True, applies differentiable quad splitting for 
+                training. Defaults to False.
+            output_tetmesh (bool, optional): If set to True, outputs a tetrahedral mesh, otherwise, 
+                outputs a triangular mesh. Defaults to False.
+            grad_func (callable, optional): A function to compute the surface gradient at specified 
+                3D positions (input: Nx3 positions). The function should return gradients as an Nx3 
+                tensor. If None, the original FlexiCubes algorithm is utilized. Defaults to None.
+
+        Returns:
+            (torch.Tensor, torch.LongTensor, torch.Tensor): Tuple containing:
+                - Vertices for the extracted triangular/tetrahedral mesh.
+                - Faces for the extracted triangular/tetrahedral mesh.
+                - Regularizer L_dev, computed per dual vertex.
+
+        .. _Flexible Isosurface Extraction for Gradient-Based Mesh Optimization:
+            https://research.nvidia.com/labs/toronto-ai/flexicubes/
+        .. _Manifold Dual Contouring:
+            https://people.engr.tamu.edu/schaefer/research/dualsimp_tvcg.pdf
+        """
+
+        surf_cubes, occ_fx8 = self._identify_surf_cubes(s_n, cube_fx8)
+        if surf_cubes.sum() == 0:
+            return torch.zeros(
+                (0, 3),
+                device=self.device), torch.zeros(
+                (0, 4),
+                dtype=torch.long, device=self.device) if output_tetmesh else torch.zeros(
+                (0, 3),
+                dtype=torch.long, device=self.device), torch.zeros(
+                (0),
+                device=self.device)
+        beta_fx12, alpha_fx8, gamma_f = self._normalize_weights(beta_fx12, alpha_fx8, gamma_f, surf_cubes)
+
+        case_ids = self._get_case_id(occ_fx8, surf_cubes, res)
+
+        surf_edges, idx_map, edge_counts, surf_edges_mask = self._identify_surf_edges(s_n, cube_fx8, surf_cubes)
+
+        vd, L_dev, vd_gamma, vd_idx_map = self._compute_vd(
+            x_nx3, cube_fx8[surf_cubes], surf_edges, s_n, case_ids, beta_fx12, alpha_fx8, gamma_f, idx_map, grad_func)
+        vertices, faces, s_edges, edge_indices = self._triangulate(
+            s_n, surf_edges, vd, vd_gamma, edge_counts, idx_map, vd_idx_map, surf_edges_mask, training, grad_func)
+        if not output_tetmesh:
+            return vertices, faces, L_dev
+        else:
+            vertices, tets = self._tetrahedralize(
+                x_nx3, s_n, cube_fx8, vertices, faces, surf_edges, s_edges, vd_idx_map, case_ids, edge_indices,
+                surf_cubes, training)
+            return vertices, tets, L_dev
+
+    def _compute_reg_loss(self, vd, ue, edge_group_to_vd, vd_num_edges):
+        """
+        Regularizer L_dev as in Equation 8
+        """
+        dist = torch.norm(ue - torch.index_select(input=vd, index=edge_group_to_vd, dim=0), dim=-1)
+        mean_l2 = torch.zeros_like(vd[:, 0])
+        mean_l2 = (mean_l2).index_add_(0, edge_group_to_vd, dist) / vd_num_edges.squeeze(1).float()
+        mad = (dist - torch.index_select(input=mean_l2, index=edge_group_to_vd, dim=0)).abs()
+        return mad
+
+    def _normalize_weights(self, beta_fx12, alpha_fx8, gamma_f, surf_cubes):
+        """
+        Normalizes the given weights to be non-negative. If input weights are None, it creates and returns a set of weights of ones.
+        """
+        n_cubes = surf_cubes.shape[0]
+
+        if beta_fx12 is not None:
+            beta_fx12 = (torch.tanh(beta_fx12) * self.weight_scale + 1)
+        else:
+            beta_fx12 = torch.ones((n_cubes, 12), dtype=torch.float, device=self.device)
+
+        if alpha_fx8 is not None:
+            alpha_fx8 = (torch.tanh(alpha_fx8) * self.weight_scale + 1)
+        else:
+            alpha_fx8 = torch.ones((n_cubes, 8), dtype=torch.float, device=self.device)
+
+        if gamma_f is not None:
+            gamma_f = torch.sigmoid(gamma_f) * self.weight_scale + (1 - self.weight_scale)/2
+        else:
+            gamma_f = torch.ones((n_cubes), dtype=torch.float, device=self.device)
+
+        return beta_fx12[surf_cubes], alpha_fx8[surf_cubes], gamma_f[surf_cubes]
+
+    @torch.no_grad()
+    def _get_case_id(self, occ_fx8, surf_cubes, res):
+        """
+        Obtains the ID of topology cases based on cell corner occupancy. This function resolves the 
+        ambiguity in the Dual Marching Cubes (DMC) configurations as described in Section 1.3 of the 
+        supplementary material. It should be noted that this function assumes a regular grid.
+        """
+        case_ids = (occ_fx8[surf_cubes] * self.cube_corners_idx.to(self.device).unsqueeze(0)).sum(-1)
+
+        problem_config = self.check_table.to(self.device)[case_ids]
+        to_check = problem_config[..., 0] == 1
+        problem_config = problem_config[to_check]
+        if not isinstance(res, (list, tuple)):
+            res = [res, res, res]
+
+        # The 'problematic_configs' only contain configurations for surface cubes. Next, we construct a 3D array,
+        # 'problem_config_full', to store configurations for all cubes (with default config for non-surface cubes).
+        # This allows efficient checking on adjacent cubes.
+        problem_config_full = torch.zeros(list(res) + [5], device=self.device, dtype=torch.long)
+        vol_idx = torch.nonzero(problem_config_full[..., 0] == 0)  # N, 3
+        vol_idx_problem = vol_idx[surf_cubes][to_check]
+        problem_config_full[vol_idx_problem[..., 0], vol_idx_problem[..., 1], vol_idx_problem[..., 2]] = problem_config
+        vol_idx_problem_adj = vol_idx_problem + problem_config[..., 1:4]
+
+        within_range = (
+            vol_idx_problem_adj[..., 0] >= 0) & (
+            vol_idx_problem_adj[..., 0] < res[0]) & (
+            vol_idx_problem_adj[..., 1] >= 0) & (
+            vol_idx_problem_adj[..., 1] < res[1]) & (
+            vol_idx_problem_adj[..., 2] >= 0) & (
+            vol_idx_problem_adj[..., 2] < res[2])
+
+        vol_idx_problem = vol_idx_problem[within_range]
+        vol_idx_problem_adj = vol_idx_problem_adj[within_range]
+        problem_config = problem_config[within_range]
+        problem_config_adj = problem_config_full[vol_idx_problem_adj[..., 0],
+                                                 vol_idx_problem_adj[..., 1], vol_idx_problem_adj[..., 2]]
+        # If two cubes with cases C16 and C19 share an ambiguous face, both cases are inverted.
+        to_invert = (problem_config_adj[..., 0] == 1)
+        idx = torch.arange(case_ids.shape[0], device=self.device)[to_check][within_range][to_invert]
+        case_ids.index_put_((idx,), problem_config[to_invert][..., -1])
+        return case_ids
+
+    @torch.no_grad()
+    def _identify_surf_edges(self, s_n, cube_fx8, surf_cubes):
+        """
+        Identifies grid edges that intersect with the underlying surface by checking for opposite signs. As each edge 
+        can be shared by multiple cubes, this function also assigns a unique index to each surface-intersecting edge 
+        and marks the cube edges with this index.
+        """
+        occ_n = s_n < 0
+        all_edges = cube_fx8[surf_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) == 1
+
+        surf_edges_mask = mask_edges[_idx_map]
+        counts = counts[_idx_map]
+
+        mapping = torch.ones((unique_edges.shape[0]), dtype=torch.long, device=cube_fx8.device) * -1
+        mapping[mask_edges] = torch.arange(mask_edges.sum(), device=cube_fx8.device)
+        # Shaped as [number of cubes x 12 edges per cube]. This is later used to map a cube edge to the unique index
+        # for a surface-intersecting edge. Non-surface-intersecting edges are marked with -1.
+        idx_map = mapping[_idx_map]
+        surf_edges = unique_edges[mask_edges]
+        return surf_edges, idx_map, counts, surf_edges_mask
+
+    @torch.no_grad()
+    def _identify_surf_cubes(self, s_n, cube_fx8):
+        """
+        Identifies grid cubes that intersect with the underlying surface by checking if the signs at 
+        all corners are not identical.
+        """
+        occ_n = s_n < 0
+        occ_fx8 = occ_n[cube_fx8.reshape(-1)].reshape(-1, 8)
+        _occ_sum = torch.sum(occ_fx8, -1)
+        surf_cubes = (_occ_sum > 0) & (_occ_sum < 8)
+        return surf_cubes, occ_fx8
+
+    def _linear_interp(self, edges_weight, edges_x):
+        """
+        Computes the location of zero-crossings on 'edges_x' using linear interpolation with 'edges_weight'.
+        """
+        edge_dim = edges_weight.dim() - 2
+        assert edges_weight.shape[edge_dim] == 2
+        edges_weight = torch.cat([torch.index_select(input=edges_weight, index=torch.tensor(1, device=self.device), dim=edge_dim), -
+                                 torch.index_select(input=edges_weight, index=torch.tensor(0, device=self.device), dim=edge_dim)], edge_dim)
+        denominator = edges_weight.sum(edge_dim)
+        ue = (edges_x * edges_weight).sum(edge_dim) / denominator
+        return ue
+
+    def _solve_vd_QEF(self, p_bxnx3, norm_bxnx3, c_bx3=None):
+        p_bxnx3 = p_bxnx3.reshape(-1, 7, 3)
+        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

apps/third_party/CRM/util/flexicubes_geometry.py

@@ -0,0 +1,116 @@
+# Copyright (c) 2022, 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
+from util.flexicubes import FlexiCubes # replace later
+# from dmtet import sdf_reg_loss_batch
+import torch.nn.functional as F
+
+def get_center_boundary_index(grid_res, device):
+    v = torch.zeros((grid_res + 1, grid_res + 1, grid_res + 1), dtype=torch.bool, device=device)
+    v[grid_res // 2 + 1, grid_res // 2 + 1, grid_res // 2 + 1] = True
+    center_indices = torch.nonzero(v.reshape(-1))
+
+    v[grid_res // 2 + 1, grid_res // 2 + 1, grid_res // 2 + 1] = False
+    v[:2, ...] = True
+    v[-2:, ...] = True
+    v[:, :2, ...] = True
+    v[:, -2:, ...] = True
+    v[:, :, :2] = True
+    v[:, :, -2:] = True
+    boundary_indices = torch.nonzero(v.reshape(-1))
+    return center_indices, boundary_indices
+
+###############################################################################
+#  Geometry interface
+###############################################################################
+class FlexiCubesGeometry(object):
+    def __init__(
+            self, grid_res=64, scale=2.0, device='cuda', renderer=None,
+            render_type='neural_render', args=None):
+        super(FlexiCubesGeometry, self).__init__()
+        self.grid_res = grid_res
+        self.device = device
+        self.args = args
+        self.fc = FlexiCubes(device, weight_scale=0.5)
+        self.verts, self.indices = self.fc.construct_voxel_grid(grid_res)
+        if isinstance(scale, list):
+            self.verts[:, 0] = self.verts[:, 0] * scale[0]
+            self.verts[:, 1] = self.verts[:, 1] * scale[1]
+            self.verts[:, 2] = self.verts[:, 2] * scale[1]
+        else:
+            self.verts = self.verts * scale
+            
+        all_edges = self.indices[:, self.fc.cube_edges].reshape(-1, 2)
+        self.all_edges = torch.unique(all_edges, dim=0)
+
+        # Parameters used for fix boundary sdf
+        self.center_indices, self.boundary_indices = get_center_boundary_index(self.grid_res, device)
+        self.renderer = renderer
+        self.render_type = render_type
+
+    def getAABB(self):
+        return torch.min(self.verts, dim=0).values, torch.max(self.verts, dim=0).values
+
+    def get_mesh(self, v_deformed_nx3, sdf_n, weight_n=None, with_uv=False, indices=None, is_training=False):
+        if indices is None:
+            indices = self.indices
+
+        verts, faces, v_reg_loss = self.fc(v_deformed_nx3, sdf_n, indices, self.grid_res,
+                                            beta_fx12=weight_n[:, :12], alpha_fx8=weight_n[:, 12:20],
+                                            gamma_f=weight_n[:, 20], training=is_training
+                                            )
+        return verts, faces, v_reg_loss
+
+
+    def render_mesh(self, mesh_v_nx3, mesh_f_fx3, camera_mv_bx4x4, resolution=256, hierarchical_mask=False):
+        return_value = dict()
+        if self.render_type == 'neural_render':
+            tex_pos, mask, hard_mask, rast, v_pos_clip, mask_pyramid, depth = self.renderer.render_mesh(
+                mesh_v_nx3.unsqueeze(dim=0),
+                mesh_f_fx3.int(),
+                camera_mv_bx4x4,
+                mesh_v_nx3.unsqueeze(dim=0),
+                resolution=resolution,
+                device=self.device,
+                hierarchical_mask=hierarchical_mask
+            )
+
+            return_value['tex_pos'] = tex_pos
+            return_value['mask'] = mask
+            return_value['hard_mask'] = hard_mask
+            return_value['rast'] = rast
+            return_value['v_pos_clip'] = v_pos_clip
+            return_value['mask_pyramid'] = mask_pyramid
+            return_value['depth'] = depth
+        else:
+            raise NotImplementedError
+
+        return return_value
+
+    def render(self, v_deformed_bxnx3=None, sdf_bxn=None, camera_mv_bxnviewx4x4=None, resolution=256):
+        # Here I assume a batch of meshes (can be different mesh and geometry), for the other shapes, the batch is 1
+        v_list = []
+        f_list = []
+        n_batch = v_deformed_bxnx3.shape[0]
+        all_render_output = []
+        for i_batch in range(n_batch):
+            verts_nx3, faces_fx3 = self.get_mesh(v_deformed_bxnx3[i_batch], sdf_bxn[i_batch])
+            v_list.append(verts_nx3)
+            f_list.append(faces_fx3)
+            render_output = self.render_mesh(verts_nx3, faces_fx3, camera_mv_bxnviewx4x4[i_batch], resolution)
+            all_render_output.append(render_output)
+
+        # Concatenate all render output
+        return_keys = all_render_output[0].keys()
+        return_value = dict()
+        for k in return_keys:
+            value = [v[k] for v in all_render_output]
+            return_value[k] = value
+            # We can do concatenation outside of the render
+        return return_value

apps/third_party/CRM/util/renderer.py

@@ -0,0 +1,49 @@
+
+import torch
+import torch.nn as nn
+import nvdiffrast.torch as dr
+from util.flexicubes_geometry import FlexiCubesGeometry
+
+class Renderer(nn.Module):
+    def __init__(self, tet_grid_size, camera_angle_num, scale, geo_type):
+        super().__init__()
+
+        self.tet_grid_size = tet_grid_size
+        self.camera_angle_num = camera_angle_num
+        self.scale = scale
+        self.geo_type = geo_type
+        self.glctx = dr.RasterizeCudaContext()
+
+        if self.geo_type == "flex":
+            self.flexicubes = FlexiCubesGeometry(grid_res = self.tet_grid_size)   
+
+    def forward(self, data, sdf, deform, verts, tets, training=False, weight = None):
+
+        results = {}
+
+        deform = torch.tanh(deform) / self.tet_grid_size * self.scale / 0.95
+        if self.geo_type == "flex":
+            deform = deform *0.5
+
+            v_deformed = verts + deform
+
+            verts_list = []
+            faces_list = []
+            reg_list = []
+            n_shape = verts.shape[0]
+            for i in range(n_shape): 
+                verts_i, faces_i, reg_i = self.flexicubes.get_mesh(v_deformed[i], sdf[i].squeeze(dim=-1),
+                with_uv=False, indices=tets, weight_n=weight[i], is_training=training)
+
+                verts_list.append(verts_i)
+                faces_list.append(faces_i)
+                reg_list.append(reg_i)       
+            verts = verts_list
+            faces = faces_list
+
+            flexicubes_surface_reg = torch.cat(reg_list).mean()
+            flexicubes_weight_reg = (weight ** 2).mean()
+            results["flex_surf_loss"] = flexicubes_surface_reg
+            results["flex_weight_loss"] = flexicubes_weight_reg
+
+        return results, verts, faces

apps/third_party/CRM/util/tables.py

@@ -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]],
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+[[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]],
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+[[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]],
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+[[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]
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+[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]
+]

apps/third_party/CRM/util/utils.py

@@ -0,0 +1,194 @@
+import numpy as np
+import torch
+import random
+
+
+# Reworked so this matches gluPerspective / glm::perspective, using fovy
+def perspective(fovx=0.7854, aspect=1.0, n=0.1, f=1000.0, device=None):
+    # y = np.tan(fovy / 2)
+    x = np.tan(fovx / 2)
+    return torch.tensor([[1/x,         0,            0,              0],
+                         [  0, -aspect/x,            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)
+
+
+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)
+
+
+def rotate_z(a, device=None):
+    s, c = np.sin(a), np.cos(a)
+    return torch.tensor([[c, -s, 0, 0],
+                         [s,  c, 0, 0],
+                         [0,  0, 1, 0],
+                         [0,  0, 0, 1]], dtype=torch.float32, device=device)
+
+@torch.no_grad()
+def batch_random_rotation_translation(b, t, device=None):
+    m = np.random.normal(size=[b, 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=2, keepdims=True)
+    m = np.pad(m, [[0, 0], [0, 1], [0, 1]], mode='constant')
+    m[:, 3, 3] = 1.0
+    m[:, :3, 3] = np.random.uniform(-t, t, size=[b, 3])
+    return torch.tensor(m, 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)
+
+
+@torch.no_grad()
+def random_rotation(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.array([0,0,0]).astype(np.float32)
+    return torch.tensor(m, dtype=torch.float32, device=device)
+
+
+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-20) -> 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-20) -> torch.Tensor:
+    return x / length(x, eps)
+
+
+def lr_schedule(iter, warmup_iter, scheduler_decay):
+    if iter < warmup_iter:
+        return iter / warmup_iter
+    return max(0.0, 10 ** (
+            -(iter - warmup_iter) * scheduler_decay)) 
+
+
+def trans_depth(depth):
+    depth = depth[0].detach().cpu().numpy()
+    valid = depth > 0
+    depth[valid] -= depth[valid].min()
+    depth[valid] = ((depth[valid] / depth[valid].max()) * 255)
+    return depth.astype('uint8')
+
+
+def nan_to_num(input, nan=0.0, posinf=None, neginf=None, *, out=None):
+    assert isinstance(input, torch.Tensor)
+    if posinf is None:
+        posinf = torch.finfo(input.dtype).max
+    if neginf is None:
+        neginf = torch.finfo(input.dtype).min
+    assert nan == 0
+    return torch.clamp(input.unsqueeze(0).nansum(0), min=neginf, max=posinf, out=out)
+
+
+def load_item(filepath):
+    with open(filepath, 'r') as f:
+        items = [name.strip() for name in f.readlines()]
+    return set(items)
+
+def load_prompt(filepath):
+    uuid2prompt = {}
+    with open(filepath, 'r') as f:
+        for line in f.readlines():
+            list_line = line.split(',')
+            uuid2prompt[list_line[0]] = ','.join(list_line[1:]).strip()
+    return uuid2prompt
+
+def resize_and_center_image(image_tensor, scale=0.95, c = 0, shift = 0, rgb=False, aug_shift = 0):
+    if scale == 1:
+        return image_tensor
+    B, C, H, W = image_tensor.shape
+    new_H, new_W = int(H * scale), int(W * scale)
+    resized_image = torch.nn.functional.interpolate(image_tensor, size=(new_H, new_W), mode='bilinear', align_corners=False).squeeze(0)
+    background = torch.zeros_like(image_tensor) + c
+    start_y, start_x = (H - new_H) // 2, (W - new_W) // 2
+    if shift == 0:
+        background[:, :, start_y:start_y + new_H, start_x:start_x + new_W] = resized_image
+    else:
+        for i in range(B):
+            randx = random.randint(-shift, shift)
+            randy = random.randint(-shift, shift)   
+            if rgb == True:
+                if i == 0 or i==2 or i==4:
+                    randx = 0
+                    randy = 0 
+            background[i, :, start_y+randy:start_y + new_H+randy, start_x+randx:start_x + new_W+randx] = resized_image[i]
+    if aug_shift == 0:
+        return background  
+    for i in range(B):
+        for j in range(C):
+            background[i, j, :, :] += (random.random() - 0.5)*2 * aug_shift / 255
+    return background 
+                               
+def get_tri(triview_color, dim = 1, blender=True, c = 0, scale=0.95, shift = 0, fix = False, rgb=False, aug_shift = 0):
+    # triview_color: [6,C,H,W]
+    # rgb is useful when shift is not 0
+    triview_color = resize_and_center_image(triview_color, scale=scale, c = c, shift=shift,rgb=rgb, aug_shift = aug_shift)
+    if blender is False:
+        triview_color0 = torch.rot90(triview_color[0],k=2,dims=[1,2])
+        triview_color1 = torch.rot90(triview_color[4],k=1,dims=[1,2]).flip(2).flip(1)
+        triview_color2 = torch.rot90(triview_color[5],k=1,dims=[1,2]).flip(2)
+        triview_color3 = torch.rot90(triview_color[3],k=2,dims=[1,2]).flip(2)
+        triview_color4 = torch.rot90(triview_color[1],k=3,dims=[1,2]).flip(1)
+        triview_color5 = torch.rot90(triview_color[2],k=3,dims=[1,2]).flip(1).flip(2)
+    else:
+        triview_color0 = torch.rot90(triview_color[2],k=2,dims=[1,2])
+        triview_color1 = torch.rot90(triview_color[4],k=0,dims=[1,2]).flip(2).flip(1)
+        triview_color2 = torch.rot90(torch.rot90(triview_color[0],k=3,dims=[1,2]).flip(2), k=2,dims=[1,2])
+        triview_color3 = torch.rot90(torch.rot90(triview_color[5],k=2,dims=[1,2]).flip(2), k=2,dims=[1,2])
+        triview_color4 = torch.rot90(triview_color[1],k=2,dims=[1,2]).flip(1).flip(1).flip(2)
+        triview_color5 = torch.rot90(triview_color[3],k=1,dims=[1,2]).flip(1).flip(2)
+        if fix == True:
+            triview_color0[1] = triview_color0[1] * 0
+            triview_color0[2] = triview_color0[2] * 0
+            triview_color3[1] = triview_color3[1] * 0
+            triview_color3[2] = triview_color3[2] * 0
+
+            triview_color1[0] = triview_color1[0] * 0
+            triview_color1[1] = triview_color1[1] * 0
+            triview_color4[0] = triview_color4[0] * 0
+            triview_color4[1] = triview_color4[1] * 0
+
+            triview_color2[0] = triview_color2[0] * 0
+            triview_color2[2] = triview_color2[2] * 0
+            triview_color5[0] = triview_color5[0] * 0
+            triview_color5[2] = triview_color5[2] * 0
+    color_tensor1_gt = torch.cat((triview_color0, triview_color1, triview_color2), dim=2)
+    color_tensor2_gt = torch.cat((triview_color3, triview_color4, triview_color5), dim=2)
+    color_tensor_gt = torch.cat((color_tensor1_gt, color_tensor2_gt), dim = dim)
+    return color_tensor_gt
+