  Context. Observations reveal that shocks can be driven by fast coronal mass
ejections (CMEs) and play essential roles in particle accelerations. A critical
ratio, $\delta$, derived from a shock standoff distance normalized by the
radius of curvature (ROC) of a CME, allows us to estimate shock and ambient
coronal parameters. However, true ROCs of CMEs are difficult to measure due to
observed projection effects.
  Aims. We investigate the formation mechanism of a shock driven by an
aspherical CME without evident lateral expansion. Through three-dimensional
(3D) reconstructions without a priori assumptions of the object morphology, we
estimate two principal ROCs of the CME surface and demonstrate how the
difference between two principal ROCs of the CME affects the estimate of the
coronal physical parameters.
  Methods. The CME was observed by the Sun Earth Connection Coronal and
Heliospheric Investigation (SECCHI) instruments and the Large Angle and
Spectrometric Coronagraph (LASCO). We used the mask-fitting method to obtain
the irregular 3D shape of the CME and reconstructed the shock surface using the
bow-shock model. Through smoothings with fifth-order polynomial functions and
Monte Carlo simulations, we calculated the ROCs at the CME nose.
  Results. We find that (1) the maximal ROC is 2-4 times the minimal ROC of the
CME. A significant difference between the CME ROCs implies that the assumption
of one ROC of an aspherical CME could cause over-/under- estimations of the
shock and coronal parameters. (2) The shock nose obeys the bow-shock formation
mechanism, considering the constant standoff distance and the similar speed
between the shock and CME around the nose. (3) With a more precise $\delta$
calculated via 3D ROCs in space, we derive corona parameters at high latitudes
of about -50$^{\circ}$, including the Alfv{\'e}n speed and the coronal magnetic
field strength.
