def forward(self, cam2world_matrix, intrinsics, resolution):
        """
        Create batches of rays and return origins and directions.

        cam2world_matrix: (N, 4, 4)
        intrinsics: (N, 3, 3)
        resolution: int

        ray_origins: (N, M, 3)
        ray_dirs: (N, M, 2)
        """
        N, M = cam2world_matrix.shape[0], resolution**2
        cam_locs_world = cam2world_matrix[:, :3, 3]
        fx = intrinsics[:, 0, 0]
        fy = intrinsics[:, 1, 1]
        cx = intrinsics[:, 0, 2]
        cy = intrinsics[:, 1, 2]
        sk = intrinsics[:, 0, 1]

        uv = torch.stack(torch.meshgrid(torch.arange(resolution, dtype=torch.float32, device=cam2world_matrix.device), torch.arange(resolution, dtype=torch.float32, device=cam2world_matrix.device), indexing='ij')) * (1./resolution) + (0.5/resolution)
        uv = uv.flip(0).reshape(2, -1).transpose(1, 0)
        uv = uv.unsqueeze(0).repeat(cam2world_matrix.shape[0], 1, 1)

        x_cam = uv[:, :, 0].view(N, -1)
        y_cam = uv[:, :, 1].view(N, -1)
        z_cam = torch.ones((N, M), device=cam2world_matrix.device)

        x_lift = (x_cam - cx.unsqueeze(-1) + cy.unsqueeze(-1)*sk.unsqueeze(-1)/fy.unsqueeze(-1) - sk.unsqueeze(-1)*y_cam/fy.unsqueeze(-1)) / fx.unsqueeze(-1) * z_cam
        y_lift = (y_cam - cy.unsqueeze(-1)) / fy.unsqueeze(-1) * z_cam

        cam_rel_points = torch.stack((x_lift, y_lift, z_cam, torch.ones_like(z_cam)), dim=-1)

        world_rel_points = torch.bmm(cam2world_matrix, cam_rel_points.permute(0, 2, 1)).permute(0, 2, 1)[:, :, :3]

        ray_dirs = world_rel_points - cam_locs_world[:, None, :]
        ray_dirs = torch.nn.functional.normalize(ray_dirs, dim=2)

        ray_origins = cam_locs_world.unsqueeze(1).repeat(1, ray_dirs.shape[1], 1)

        return ray_origins, ray_dirs

        Create batches of rays and return origins and directions.

        cam2world_matrix: (N, 4, 4)
        intrinsics: (N, 3, 3)
        resolution: int

        ray_origins: (N, M, 3)
        ray_dirs: (N, M, 2)
        
training/volumetric_rendering/ray_sampler.py