  Characterizing the local structural evolution is an essential step in
understanding the nature of glass transition. In this work, we probe the
evolution of Voronoi cell geometry in simple glass models, and find that the
individual particle cages deform anisotropically in supercooled liquid and
isotropically in glass. We introduce an anisotropy parameter $k$ for each
Voronoi cell, which mean value exhibits a sharp change at the mode-coupling
glass transition $\phi_\mathrm{c}$. Moreover, a power law of packing fraction
$\phi\propto q_1^{-d}$ is discovered in the liquid regime with $d>D$, in
contrast to $d=D$ in the glass regime, where $q_1$ is the first peak position
of structure factor, and $D$ is the space dimension. This power law is
explained by the change of $k$. The active motions in supercooled liquid are
spatially correlated with long axes rather than short axes of Voronoi cells. In
addition, the dynamic slowing down approaching the glass transition can be well
characterized through a modified free volume model based on $k$. These findings
reveal that the nonagnostic structural parameter $k$ determines glassy dynamics
and is effective in identifying the structure-dynamics correlations and the
glass transition.
