nerf/renderer.py

import os
import math
import cv2
import trimesh
import numpy as np

import torch
import torch.nn as nn
import torch.nn.functional as F

import mcubes
import raymarching
from .utils import custom_meshgrid, safe_normalize

def sample_pdf(bins, weights, n_samples, det=False):
    # This implementation is from NeRF
    # bins: [B, T], old_z_vals
    # weights: [B, T - 1], bin weights.
    # return: [B, n_samples], new_z_vals

    # Get pdf
    weights = weights + 1e-5  # prevent nans
    pdf = weights / torch.sum(weights, -1, keepdim=True)
    cdf = torch.cumsum(pdf, -1)
    cdf = torch.cat([torch.zeros_like(cdf[..., :1]), cdf], -1)
    # Take uniform samples
    if det:
        u = torch.linspace(0. + 0.5 / n_samples, 1. - 0.5 / n_samples, steps=n_samples).to(weights.device)
        u = u.expand(list(cdf.shape[:-1]) + [n_samples])
    else:
        u = torch.rand(list(cdf.shape[:-1]) + [n_samples]).to(weights.device)

    # Invert CDF
    u = u.contiguous()
    inds = torch.searchsorted(cdf, u, right=True)
    below = torch.max(torch.zeros_like(inds - 1), inds - 1)
    above = torch.min((cdf.shape[-1] - 1) * torch.ones_like(inds), inds)
    inds_g = torch.stack([below, above], -1)  # (B, n_samples, 2)

    matched_shape = [inds_g.shape[0], inds_g.shape[1], cdf.shape[-1]]
    cdf_g = torch.gather(cdf.unsqueeze(1).expand(matched_shape), 2, inds_g)
    bins_g = torch.gather(bins.unsqueeze(1).expand(matched_shape), 2, inds_g)

    denom = (cdf_g[..., 1] - cdf_g[..., 0])
    denom = torch.where(denom < 1e-5, torch.ones_like(denom), denom)
    t = (u - cdf_g[..., 0]) / denom
    samples = bins_g[..., 0] + t * (bins_g[..., 1] - bins_g[..., 0])

    return samples


def plot_pointcloud(pc, color=None):
    # pc: [N, 3]
    # color: [N, 3/4]
    print('[visualize points]', pc.shape, pc.dtype, pc.min(0), pc.max(0))
    pc = trimesh.PointCloud(pc, color)
    # axis
    axes = trimesh.creation.axis(axis_length=4)
    # sphere
    sphere = trimesh.creation.icosphere(radius=1)
    trimesh.Scene([pc, axes, sphere]).show()


class NeRFRenderer(nn.Module):
    def __init__(self, opt):
        super().__init__()

        self.opt = opt
        self.bound = opt.bound
        self.cascade = 1 + math.ceil(math.log2(opt.bound))
        self.grid_size = 128
        self.cuda_ray = opt.cuda_ray
        self.min_near = opt.min_near
        self.density_thresh = opt.density_thresh
        self.bg_radius = opt.bg_radius

        # prepare aabb with a 6D tensor (xmin, ymin, zmin, xmax, ymax, zmax)
        # NOTE: aabb (can be rectangular) is only used to generate points, we still rely on bound (always cubic) to calculate density grid and hashing.
        aabb_train = torch.FloatTensor([-opt.bound, -opt.bound, -opt.bound, opt.bound, opt.bound, opt.bound])
        aabb_infer = aabb_train.clone()
        self.register_buffer('aabb_train', aabb_train)
        self.register_buffer('aabb_infer', aabb_infer)

        # extra state for cuda raymarching
        if self.cuda_ray:
            # density grid
            density_grid = torch.zeros([self.cascade, self.grid_size ** 3]) # [CAS, H * H * H]
            density_bitfield = torch.zeros(self.cascade * self.grid_size ** 3 // 8, dtype=torch.uint8) # [CAS * H * H * H // 8]
            self.register_buffer('density_grid', density_grid)
            self.register_buffer('density_bitfield', density_bitfield)
            self.mean_density = 0
            self.iter_density = 0
            # step counter
            step_counter = torch.zeros(16, 2, dtype=torch.int32) # 16 is hardcoded for averaging...
            self.register_buffer('step_counter', step_counter)
            self.mean_count = 0
            self.local_step = 0

    
    def forward(self, x, d):
        raise NotImplementedError()

    def density(self, x):
        raise NotImplementedError()

    def color(self, x, d, mask=None, **kwargs):
        raise NotImplementedError()

    def reset_extra_state(self):
        if not self.cuda_ray:
            return 
        # density grid
        self.density_grid.zero_()
        self.mean_density = 0
        self.iter_density = 0
        # step counter
        self.step_counter.zero_()
        self.mean_count = 0
        self.local_step = 0

    @torch.no_grad()
    def export_mesh(self, path, resolution=None, S=128):

        if resolution is None:
            resolution = self.grid_size

        density_thresh = min(self.mean_density, self.density_thresh)

        sigmas = np.zeros([resolution, resolution, resolution], dtype=np.float32)

        # query
        X = torch.linspace(-1, 1, resolution).split(S)
        Y = torch.linspace(-1, 1, resolution).split(S)
        Z = torch.linspace(-1, 1, resolution).split(S)

        for xi, xs in enumerate(X):
            for yi, ys in enumerate(Y):
                for zi, zs in enumerate(Z):
                    xx, yy, zz = custom_meshgrid(xs, ys, zs)
                    pts = torch.cat([xx.reshape(-1, 1), yy.reshape(-1, 1), zz.reshape(-1, 1)], dim=-1) # [S, 3]
                    val = self.density(pts.to(self.density_bitfield.device))
                    sigmas[xi * S: xi * S + len(xs), yi * S: yi * S + len(ys), zi * S: zi * S + len(zs)] = val['sigma'].reshape(len(xs), len(ys), len(zs)).detach().cpu().numpy() # [S, 1] --> [x, y, z]

        vertices, triangles = mcubes.marching_cubes(sigmas, density_thresh)

        vertices = vertices / (resolution - 1.0) * 2 - 1
        vertices = vertices.astype(np.float32)
        triangles = triangles.astype(np.int32)

        v = torch.from_numpy(vertices).to(self.density_bitfield.device)
        f = torch.from_numpy(triangles).int().to(self.density_bitfield.device)

        # mesh = trimesh.Trimesh(vertices, triangles, process=False) # important, process=True leads to seg fault...
        # mesh.export(os.path.join(path, f'mesh.ply'))

        # texture?
        def _export(v, f, h0=2048, w0=2048, ssaa=1, name=''):
            # v, f: torch Tensor
            device = v.device
            v_np = v.cpu().numpy() # [N, 3]
            f_np = f.cpu().numpy() # [M, 3]

            print(f'[INFO] running xatlas to unwrap UVs for mesh: v={v_np.shape} f={f_np.shape}')

            # unwrap uvs
            import xatlas
            import nvdiffrast.torch as dr
            from sklearn.neighbors import NearestNeighbors
            from scipy.ndimage import binary_dilation, binary_erosion

            glctx = dr.RasterizeCudaContext()

            atlas = xatlas.Atlas()
            atlas.add_mesh(v_np, f_np)
            chart_options = xatlas.ChartOptions()
            chart_options.max_iterations = 0 # disable merge_chart for faster unwrap...
            atlas.generate(chart_options=chart_options)
            vmapping, ft_np, vt_np = atlas[0] # [N], [M, 3], [N, 2]

            # vmapping, ft_np, vt_np = xatlas.parametrize(v_np, f_np) # [N], [M, 3], [N, 2]

            vt = torch.from_numpy(vt_np.astype(np.float32)).float().to(device)
            ft = torch.from_numpy(ft_np.astype(np.int64)).int().to(device)

            # render uv maps
            uv = vt * 2.0 - 1.0 # uvs to range [-1, 1]
            uv = torch.cat((uv, torch.zeros_like(uv[..., :1]), torch.ones_like(uv[..., :1])), dim=-1) # [N, 4]

            if ssaa > 1:
                h = int(h0 * ssaa)
                w = int(w0 * ssaa)
            else:
                h, w = h0, w0

            rast, _ = dr.rasterize(glctx, uv.unsqueeze(0), ft, (h, w)) # [1, h, w, 4]
            xyzs, _ = dr.interpolate(v.unsqueeze(0), rast, f) # [1, h, w, 3]
            mask, _ = dr.interpolate(torch.ones_like(v[:, :1]).unsqueeze(0), rast, f) # [1, h, w, 1]

            # masked query 
            xyzs = xyzs.view(-1, 3)
            mask = (mask > 0).view(-1)
            
            sigmas = torch.zeros(h * w, device=device, dtype=torch.float32)
            feats = torch.zeros(h * w, 3, device=device, dtype=torch.float32)

            if mask.any():
                xyzs = xyzs[mask] # [M, 3]

                # batched inference to avoid OOM
                all_sigmas = []
                all_feats = []
                head = 0
                while head < xyzs.shape[0]:
                    tail = min(head + 640000, xyzs.shape[0])
                    results_ = self.density(xyzs[head:tail])
                    all_sigmas.append(results_['sigma'].float())
                    all_feats.append(results_['albedo'].float())
                    head += 640000

                sigmas[mask] = torch.cat(all_sigmas, dim=0)
                feats[mask] = torch.cat(all_feats, dim=0)
            
            sigmas = sigmas.view(h, w, 1)
            feats = feats.view(h, w, -1)
            mask = mask.view(h, w)

            ### alpha mask
            # deltas = 2 * np.sqrt(3) / 1024
            # alphas = 1 - torch.exp(-sigmas * deltas)
            # alphas_mask = alphas > 0.5
            # feats = feats * alphas_mask

            # quantize [0.0, 1.0] to [0, 255]
            feats = feats.cpu().numpy()
            feats = (feats * 255).astype(np.uint8)

            # alphas = alphas.cpu().numpy()
            # alphas = (alphas * 255).astype(np.uint8)

            ### NN search as an antialiasing ...
            mask = mask.cpu().numpy()

            inpaint_region = binary_dilation(mask, iterations=3)
            inpaint_region[mask] = 0

            search_region = mask.copy()
            not_search_region = binary_erosion(search_region, iterations=2)
            search_region[not_search_region] = 0

            search_coords = np.stack(np.nonzero(search_region), axis=-1)
            inpaint_coords = np.stack(np.nonzero(inpaint_region), axis=-1)

            knn = NearestNeighbors(n_neighbors=1, algorithm='kd_tree').fit(search_coords)
            _, indices = knn.kneighbors(inpaint_coords)

            feats[tuple(inpaint_coords.T)] = feats[tuple(search_coords[indices[:, 0]].T)]

            # do ssaa after the NN search, in numpy
            feats = cv2.cvtColor(feats, cv2.COLOR_RGB2BGR)

            if ssaa > 1:
                # alphas = cv2.resize(alphas, (w0, h0), interpolation=cv2.INTER_NEAREST)
                feats = cv2.resize(feats, (w0, h0), interpolation=cv2.INTER_LINEAR)

            # cv2.imwrite(os.path.join(path, f'alpha.png'), alphas)
            cv2.imwrite(os.path.join(path, f'{name}albedo.png'), feats)

            # save obj (v, vt, f /)
            obj_file = os.path.join(path, f'{name}mesh.obj')
            mtl_file = os.path.join(path, f'{name}mesh.mtl')

            print(f'[INFO] writing obj mesh to {obj_file}')
            with open(obj_file, "w") as fp:
                fp.write(f'mtllib {name}mesh.mtl \n')
                
                print(f'[INFO] writing vertices {v_np.shape}')
                for v in v_np:
                    fp.write(f'v {v[0]} {v[1]} {v[2]} \n')
            
                print(f'[INFO] writing vertices texture coords {vt_np.shape}')
                for v in vt_np:
                    fp.write(f'vt {v[0]} {1 - v[1]} \n') 

                print(f'[INFO] writing faces {f_np.shape}')
                fp.write(f'usemtl mat0 \n')
                for i in range(len(f_np)):
                    fp.write(f"f {f_np[i, 0] + 1}/{ft_np[i, 0] + 1} {f_np[i, 1] + 1}/{ft_np[i, 1] + 1} {f_np[i, 2] + 1}/{ft_np[i, 2] + 1} \n")

            with open(mtl_file, "w") as fp:
                fp.write(f'newmtl mat0 \n')
                fp.write(f'Ka 1.000000 1.000000 1.000000 \n')
                fp.write(f'Kd 1.000000 1.000000 1.000000 \n')
                fp.write(f'Ks 0.000000 0.000000 0.000000 \n')
                fp.write(f'Tr 1.000000 \n')
                fp.write(f'illum 1 \n')
                fp.write(f'Ns 0.000000 \n')
                fp.write(f'map_Kd {name}albedo.png \n')

        _export(v, f)

    def run(self, rays_o, rays_d, num_steps=128, upsample_steps=128, light_d=None, ambient_ratio=1.0, shading='albedo', bg_color=None, perturb=False, **kwargs):
        # rays_o, rays_d: [B, N, 3], assumes B == 1
        # bg_color: [BN, 3] in range [0, 1]
        # return: image: [B, N, 3], depth: [B, N]

        prefix = rays_o.shape[:-1]
        rays_o = rays_o.contiguous().view(-1, 3)
        rays_d = rays_d.contiguous().view(-1, 3)

        N = rays_o.shape[0] # N = B * N, in fact
        device = rays_o.device

        results = {}

        # choose aabb
        aabb = self.aabb_train if self.training else self.aabb_infer

        # sample steps
        nears, fars = raymarching.near_far_from_aabb(rays_o, rays_d, aabb, self.min_near)
        nears.unsqueeze_(-1)
        fars.unsqueeze_(-1)

        # random sample light_d if not provided
        if light_d is None:
            # gaussian noise around the ray origin, so the light always face the view dir (avoid dark face)
            light_d = (rays_o[0] + torch.randn(3, device=device, dtype=torch.float))
            light_d = safe_normalize(light_d)

        #print(f'nears = {nears.min().item()} ~ {nears.max().item()}, fars = {fars.min().item()} ~ {fars.max().item()}')

        z_vals = torch.linspace(0.0, 1.0, num_steps, device=device).unsqueeze(0) # [1, T]
        z_vals = z_vals.expand((N, num_steps)) # [N, T]
        z_vals = nears + (fars - nears) * z_vals # [N, T], in [nears, fars]

        # perturb z_vals
        sample_dist = (fars - nears) / num_steps
        if perturb:
            z_vals = z_vals + (torch.rand(z_vals.shape, device=device) - 0.5) * sample_dist
            #z_vals = z_vals.clamp(nears, fars) # avoid out of bounds xyzs.

        # generate xyzs
        xyzs = rays_o.unsqueeze(-2) + rays_d.unsqueeze(-2) * z_vals.unsqueeze(-1) # [N, 1, 3] * [N, T, 1] -> [N, T, 3]
        xyzs = torch.min(torch.max(xyzs, aabb[:3]), aabb[3:]) # a manual clip.

        #plot_pointcloud(xyzs.reshape(-1, 3).detach().cpu().numpy())

        # query SDF and RGB
        density_outputs = self.density(xyzs.reshape(-1, 3))

        #sigmas = density_outputs['sigma'].view(N, num_steps) # [N, T]
        for k, v in density_outputs.items():
            density_outputs[k] = v.view(N, num_steps, -1)

        # upsample z_vals (nerf-like)
        if upsample_steps > 0:
            with torch.no_grad():

                deltas = z_vals[..., 1:] - z_vals[..., :-1] # [N, T-1]
                deltas = torch.cat([deltas, sample_dist * torch.ones_like(deltas[..., :1])], dim=-1)

                alphas = 1 - torch.exp(-deltas * density_outputs['sigma'].squeeze(-1)) # [N, T]
                alphas_shifted = torch.cat([torch.ones_like(alphas[..., :1]), 1 - alphas + 1e-15], dim=-1) # [N, T+1]
                weights = alphas * torch.cumprod(alphas_shifted, dim=-1)[..., :-1] # [N, T]

                # sample new z_vals
                z_vals_mid = (z_vals[..., :-1] + 0.5 * deltas[..., :-1]) # [N, T-1]
                new_z_vals = sample_pdf(z_vals_mid, weights[:, 1:-1], upsample_steps, det=not self.training).detach() # [N, t]

                new_xyzs = rays_o.unsqueeze(-2) + rays_d.unsqueeze(-2) * new_z_vals.unsqueeze(-1) # [N, 1, 3] * [N, t, 1] -> [N, t, 3]
                new_xyzs = torch.min(torch.max(new_xyzs, aabb[:3]), aabb[3:]) # a manual clip.

            # only forward new points to save computation
            new_density_outputs = self.density(new_xyzs.reshape(-1, 3))
            #new_sigmas = new_density_outputs['sigma'].view(N, upsample_steps) # [N, t]
            for k, v in new_density_outputs.items():
                new_density_outputs[k] = v.view(N, upsample_steps, -1)

            # re-order
            z_vals = torch.cat([z_vals, new_z_vals], dim=1) # [N, T+t]
            z_vals, z_index = torch.sort(z_vals, dim=1)

            xyzs = torch.cat([xyzs, new_xyzs], dim=1) # [N, T+t, 3]
            xyzs = torch.gather(xyzs, dim=1, index=z_index.unsqueeze(-1).expand_as(xyzs))

            for k in density_outputs:
                tmp_output = torch.cat([density_outputs[k], new_density_outputs[k]], dim=1)
                density_outputs[k] = torch.gather(tmp_output, dim=1, index=z_index.unsqueeze(-1).expand_as(tmp_output))

        deltas = z_vals[..., 1:] - z_vals[..., :-1] # [N, T+t-1]
        deltas = torch.cat([deltas, sample_dist * torch.ones_like(deltas[..., :1])], dim=-1)
        alphas = 1 - torch.exp(-deltas * density_outputs['sigma'].squeeze(-1)) # [N, T+t]
        alphas_shifted = torch.cat([torch.ones_like(alphas[..., :1]), 1 - alphas + 1e-15], dim=-1) # [N, T+t+1]
        weights = alphas * torch.cumprod(alphas_shifted, dim=-1)[..., :-1] # [N, T+t]

        dirs = rays_d.view(-1, 1, 3).expand_as(xyzs)
        for k, v in density_outputs.items():
            density_outputs[k] = v.view(-1, v.shape[-1])

        sigmas, rgbs, normals = self(xyzs.reshape(-1, 3), dirs.reshape(-1, 3), light_d, ratio=ambient_ratio, shading=shading)
        rgbs = rgbs.view(N, -1, 3) # [N, T+t, 3]

        #print(xyzs.shape, 'valid_rgb:', mask.sum().item())
        # orientation loss
        if normals is not None:
            normals = normals.view(N, -1, 3)
            # print(weights.shape, normals.shape, dirs.shape)
            loss_orient = weights.detach() * (normals * dirs).sum(-1).clamp(min=0) ** 2
            results['loss_orient'] = loss_orient.mean()

        # calculate weight_sum (mask)
        weights_sum = weights.sum(dim=-1) # [N]
        
        # calculate depth 
        ori_z_vals = ((z_vals - nears) / (fars - nears)).clamp(0, 1)
        depth = torch.sum(weights * ori_z_vals, dim=-1)

        # calculate color
        image = torch.sum(weights.unsqueeze(-1) * rgbs, dim=-2) # [N, 3], in [0, 1]

        # mix background color
        if self.bg_radius > 0:
            # use the bg model to calculate bg_color
            # sph = raymarching.sph_from_ray(rays_o, rays_d, self.bg_radius) # [N, 2] in [-1, 1]
            bg_color = self.background(rays_d.reshape(-1, 3)) # [N, 3]
        elif bg_color is None:
            bg_color = 1
            
        image = image + (1 - weights_sum).unsqueeze(-1) * bg_color

        image = image.view(*prefix, 3)
        depth = depth.view(*prefix)

        mask = (nears < fars).reshape(*prefix)

        results['image'] = image
        results['depth'] = depth
        results['weights_sum'] = weights_sum
        results['mask'] = mask

        return results


    def run_cuda(self, rays_o, rays_d, dt_gamma=0, light_d=None, ambient_ratio=1.0, shading='albedo', bg_color=None, perturb=False, force_all_rays=False, max_steps=1024, T_thresh=1e-4, **kwargs):
        # rays_o, rays_d: [B, N, 3], assumes B == 1
        # return: image: [B, N, 3], depth: [B, N]

        prefix = rays_o.shape[:-1]
        rays_o = rays_o.contiguous().view(-1, 3)
        rays_d = rays_d.contiguous().view(-1, 3)

        N = rays_o.shape[0] # N = B * N, in fact
        device = rays_o.device

        # pre-calculate near far
        nears, fars = raymarching.near_far_from_aabb(rays_o, rays_d, self.aabb_train if self.training else self.aabb_infer)

        # random sample light_d if not provided
        if light_d is None:
            # gaussian noise around the ray origin, so the light always face the view dir (avoid dark face)
            light_d = (rays_o[0] + torch.randn(3, device=device, dtype=torch.float))
            light_d = safe_normalize(light_d)

        results = {}

        if self.training:
            # setup counter
            counter = self.step_counter[self.local_step % 16]
            counter.zero_() # set to 0
            self.local_step += 1

            xyzs, dirs, deltas, rays = raymarching.march_rays_train(rays_o, rays_d, self.bound, self.density_bitfield, self.cascade, self.grid_size, nears, fars, counter, self.mean_count, perturb, 128, force_all_rays, dt_gamma, max_steps)

            #plot_pointcloud(xyzs.reshape(-1, 3).detach().cpu().numpy())
            
            sigmas, rgbs, normals = self(xyzs, dirs, light_d, ratio=ambient_ratio, shading=shading)

            #print(f'valid RGB query ratio: {mask.sum().item() / mask.shape[0]} (total = {mask.sum().item()})')

            weights_sum, depth, image = raymarching.composite_rays_train(sigmas, rgbs, deltas, rays, T_thresh)

            # orientation loss
            if normals is not None:
                weights = 1 - torch.exp(-sigmas)
                loss_orient = weights.detach() * (normals * dirs).sum(-1).clamp(min=0) ** 2
                results['loss_orient'] = loss_orient.mean()

        else:
           
            # allocate outputs 
            dtype = torch.float32
            
            weights_sum = torch.zeros(N, dtype=dtype, device=device)
            depth = torch.zeros(N, dtype=dtype, device=device)
            image = torch.zeros(N, 3, dtype=dtype, device=device)
            
            n_alive = N
            rays_alive = torch.arange(n_alive, dtype=torch.int32, device=device) # [N]
            rays_t = nears.clone() # [N]

            step = 0
            
            while step < max_steps: # hard coded max step

                # count alive rays 
                n_alive = rays_alive.shape[0]

                # exit loop
                if n_alive <= 0:
                    break

                # decide compact_steps
                n_step = max(min(N // n_alive, 8), 1)

                xyzs, dirs, deltas = raymarching.march_rays(n_alive, n_step, rays_alive, rays_t, rays_o, rays_d, self.bound, self.density_bitfield, self.cascade, self.grid_size, nears, fars, 128, perturb if step == 0 else False, dt_gamma, max_steps)

                sigmas, rgbs, normals = self(xyzs, dirs, light_d, ratio=ambient_ratio, shading=shading)

                raymarching.composite_rays(n_alive, n_step, rays_alive, rays_t, sigmas, rgbs, deltas, weights_sum, depth, image, T_thresh)

                rays_alive = rays_alive[rays_alive >= 0]
                #print(f'step = {step}, n_step = {n_step}, n_alive = {n_alive}, xyzs: {xyzs.shape}')

                step += n_step

        # mix background color
        if self.bg_radius > 0:
            
            # use the bg model to calculate bg_color
            # sph = raymarching.sph_from_ray(rays_o, rays_d, self.bg_radius) # [N, 2] in [-1, 1]
            bg_color = self.background(rays_d) # [N, 3]

        elif bg_color is None:
            bg_color = 1

        image = image + (1 - weights_sum).unsqueeze(-1) * bg_color
        image = image.view(*prefix, 3)

        depth = torch.clamp(depth - nears, min=0) / (fars - nears)
        depth = depth.view(*prefix)

        weights_sum = weights_sum.reshape(*prefix)

        mask = (nears < fars).reshape(*prefix)

        results['image'] = image
        results['depth'] = depth
        results['weights_sum'] = weights_sum
        results['mask'] = mask

        return results


    @torch.no_grad()
    def update_extra_state(self, decay=0.95, S=128):
        # call before each epoch to update extra states.

        if not self.cuda_ray:
            return 
        
        ### update density grid
        tmp_grid = - torch.ones_like(self.density_grid)
        
        X = torch.arange(self.grid_size, dtype=torch.int32, device=self.density_bitfield.device).split(S)
        Y = torch.arange(self.grid_size, dtype=torch.int32, device=self.density_bitfield.device).split(S)
        Z = torch.arange(self.grid_size, dtype=torch.int32, device=self.density_bitfield.device).split(S)

        for xs in X:
            for ys in Y:
                for zs in Z:
                    
                    # construct points
                    xx, yy, zz = custom_meshgrid(xs, ys, zs)
                    coords = torch.cat([xx.reshape(-1, 1), yy.reshape(-1, 1), zz.reshape(-1, 1)], dim=-1) # [N, 3], in [0, 128)
                    indices = raymarching.morton3D(coords).long() # [N]
                    xyzs = 2 * coords.float() / (self.grid_size - 1) - 1 # [N, 3] in [-1, 1]

                    # cascading
                    for cas in range(self.cascade):
                        bound = min(2 ** cas, self.bound)
                        half_grid_size = bound / self.grid_size
                        # scale to current cascade's resolution
                        cas_xyzs = xyzs * (bound - half_grid_size)
                        # add noise in [-hgs, hgs]
                        cas_xyzs += (torch.rand_like(cas_xyzs) * 2 - 1) * half_grid_size
                        # query density
                        sigmas = self.density(cas_xyzs)['sigma'].reshape(-1).detach()
                        # assign 
                        tmp_grid[cas, indices] = sigmas
        
        # ema update
        valid_mask = self.density_grid >= 0
        self.density_grid[valid_mask] = torch.maximum(self.density_grid[valid_mask] * decay, tmp_grid[valid_mask])
        self.mean_density = torch.mean(self.density_grid[valid_mask]).item()
        self.iter_density += 1

        # convert to bitfield
        density_thresh = min(self.mean_density, self.density_thresh)
        self.density_bitfield = raymarching.packbits(self.density_grid, density_thresh, self.density_bitfield)

        ### update step counter
        total_step = min(16, self.local_step)
        if total_step > 0:
            self.mean_count = int(self.step_counter[:total_step, 0].sum().item() / total_step)
        self.local_step = 0

        # print(f'[density grid] min={self.density_grid.min().item():.4f}, max={self.density_grid.max().item():.4f}, mean={self.mean_density:.4f}, occ_rate={(self.density_grid > density_thresh).sum() / (128**3 * self.cascade):.3f} | [step counter] mean={self.mean_count}')


    def render(self, rays_o, rays_d, staged=False, max_ray_batch=4096, **kwargs):
        # rays_o, rays_d: [B, N, 3], assumes B == 1
        # return: pred_rgb: [B, N, 3]

        if self.cuda_ray:
            _run = self.run_cuda
        else:
            _run = self.run

        B, N = rays_o.shape[:2]
        device = rays_o.device

        # never stage when cuda_ray
        if staged and not self.cuda_ray:
            depth = torch.empty((B, N), device=device)
            image = torch.empty((B, N, 3), device=device)
            weights_sum = torch.empty((B, N), device=device)

            for b in range(B):
                head = 0
                while head < N:
                    tail = min(head + max_ray_batch, N)
                    results_ = _run(rays_o[b:b+1, head:tail], rays_d[b:b+1, head:tail], **kwargs)
                    depth[b:b+1, head:tail] = results_['depth']
                    weights_sum[b:b+1, head:tail] = results_['weights_sum']
                    image[b:b+1, head:tail] = results_['image']
                    head += max_ray_batch
            
            results = {}
            results['depth'] = depth
            results['image'] = image
            results['weights_sum'] = weights_sum

        else:
            results = _run(rays_o, rays_d, **kwargs)

        return results