  We study the geometry of bifurcation sets of generic unfoldings of
$D_4^\pm$-functions. Taking blow-ups, we show each of the bifurcation sets of
$D_4^\pm$-functions admit a parametrization as a surface in $R^3$. Using this
parametrization, we investigate the behavior of the Gaussian curvature and the
principal curvatures. Furthermore, we investigate the number of ridge curves
and subparabolic curves near their singular point.
