def mtpv(pmrel, u1max, i1max, title='', projection='', ax=0):
    """create a line or surface plot with voltage and mtpv curve"""
    w1 = pmrel.w2_imax_umax(i1max, u1max)
    nsamples = 20
    if projection == '3d':
        nsamples = 50

    iqmax, idmax = pmrel.iqdmax(i1max)
    iqmin, idmin = pmrel.iqdmin(i1max)
    id = np.linspace(idmin, idmax, nsamples)
    iq = np.linspace(iqmin, iqmax, nsamples)
    u1_iqd = np.array(
        [[np.linalg.norm(pmrel.uqd(w1, iqx, idx))/np.sqrt(2)
          for idx in id] for iqx in iq])
    u1 = np.mean(u1_iqd)
    imtpv = np.array([pmrel.mtpv(wx, u1, i1max)
                      for wx in np.linspace(w1, 20*w1, nsamples)]).T

    if projection == '3d':
        torque_iqd = np.array(
            [[pmrel.torque_iqd(x, y)
              for y in id] for x in iq])
        ax = idq_torque(id, iq, torque_iqd, ax)
        ax.plot(imtpv[1], imtpv[0], imtpv[2],
                color='red', linewidth=2)
    else:
        if ax == 0:
            ax = plt.gca()
        ax.set_aspect('equal')
        x, y = np.meshgrid(id, iq)
        CS = ax.contour(x, y, u1_iqd, 4, colors='b')  # linestyles='dashed')
        ax.clabel(CS, fmt='%d', inline=1)

        ax.plot(imtpv[1], imtpv[0],
                color='red', linewidth=2,
                label='MTPV: {0:5.0f} Nm'.format(np.max(imtpv[2])))
        # beta = np.arctan2(imtpv[1][0], imtpv[0][0])
        # b = np.linspace(beta, 0)
        # ax.plot(np.sqrt(2)*i1max*np.sin(b), np.sqrt(2)*i1max*np.cos(b), 'r-')

        ax.grid()
        ax.legend()
    ax.set_xlabel('Id/A')
    ax.set_ylabel('Iq/A')
    if title:
        ax.set_title(title)