def unproject_depth_frame(depth, intrinsics, extrinsics):
    import numpy as np

    height, width = depth.shape
    x, y = np.meshgrid(
        np.arange(width, dtype=np.float32),
        np.arange(height, dtype=np.float32),
    )
    pixels = np.stack((x, y, np.ones_like(x)), axis=-1).reshape(-1, 3)
    rays = (np.linalg.inv(intrinsics) @ pixels.T).T
    camera_points = rays * depth.reshape(-1, 1)
    camera_points = np.column_stack(
        (camera_points, np.ones(camera_points.shape[0], dtype=np.float32))
    )
    world_to_camera = np.eye(4, dtype=np.float32)
    world_to_camera[: extrinsics.shape[0], :4] = extrinsics
    world_points = (np.linalg.inv(world_to_camera) @ camera_points.T).T
    return world_points[:, :3].reshape(height, width, 3)


def unproject_camera_depth(depth, intrinsics):
    import numpy as np

    height, width = depth.shape
    x, y = np.meshgrid(
        np.arange(width, dtype=np.float32),
        np.arange(height, dtype=np.float32),
    )
    pixels = np.stack((x, y, np.ones_like(x)), axis=-1).reshape(-1, 3)
    rays = (np.linalg.inv(intrinsics) @ pixels.T).T
    return (rays * depth.reshape(-1, 1)).reshape(height, width, 3)