Large error between distance travelled along center line and distance actually travelled about nuscenes-devkit HOT 3 CLOSED

def plot_curve_parameter_VS_distance_travelled(lane):
    """
    If the parameterization is the arclength parameterization, then the result
    is the line y=x.
    """
    pose = arcline_path_utils.pose_at_length(lane[0],1e-6)
    position = np.array(pose[:2])
    ts = np.linspace(1e-6,166,1000)
    distances = []
    for t in ts:
        next_pose = arcline_path_utils.pose_at_length(lane[0],t)
        next_position = np.array(next_pose[:2])
        distances.append(np.linalg.norm(next_position-position))
        position = next_position
    cum_distances = np.cumsum(distances)
    _,ax = plt.subplots()
    ax.set_aspect('equal')
    ax.plot(ts,cum_distances)
    print(ts[-5:])
    print(cum_distances[-5:])

def check_project_pose_to_lane(lane,current_pose,final_pose):
    resolution_meters=0.01
    my_current_arclength = find_arclength_of_normal_proj(current_pose[:2],lane)
    _,current_arclength = arcline_path_utils.project_pose_to_lane(current_pose
                                                            ,lane
                                                            ,resolution_meters)
    _,final_arclength = arcline_path_utils.project_pose_to_lane(final_pose
                                                        ,lane
                                                        ,resolution_meters)
    my_final_arclength = find_arclength_of_normal_proj(final_pose[:2],lane)
    print(np.abs(current_arclength-my_current_arclength))
    print(np.abs(final_arclength-my_final_arclength))

def find_arclength_of_normal_proj(position,lane):
    N = 10000
    positions = np.full((N,2),np.nan)
    ts = np.linspace(1e-6,166,N)
    for i, t in enumerate(ts):
        positions[i] = arcline_path_utils.pose_at_length(lane[0],t)[:2]
    idx = np.argmin(np.linalg.norm(positions - position,axis=1))
    return ts[idx]