  We explore the properties of nuclear pasta appearing in supernova matter,
i.e., matter at finite temperature with a fixed proton fraction. The pasta
phases with a series of geometric shapes are studied using the compressible
liquid-drop (CLD) model, where nuclear matter separates into a dense liquid
phase of nucleons and a dilute gas phase of nucleons and $\alpha$ particles.
The equilibrium conditions for two coexisting phases are derived by
minimization of the total free energy including the surface and Coulomb
contributions, which are clearly different from the Gibbs conditions for phase
equilibrium due to the finite-size effects. Compared to the results considering
only spherical nuclei, the inclusion of pasta phases can delay the transition
to uniform matter and enlarge the region of nonuniform matter in the phase
diagram. The thermodynamic quantities obtained in the present calculation with
the CLD model are consistent with those in the realistic equation of state
table for astrophysical simulations using the Thomas--Fermi approximation. It
is found that the density ranges of various pasta shapes depend on both the
temperature $T$ and the proton fraction $Y_p$. Furthermore, the nuclear
symmetry energy and its density dependence may play crucial roles in
determining the properties of pasta phases. Our results suggest that the pasta
phase diagram is most sensitively dependent on the symmetry energy slope $L$
especially in the low-$Y_p$ and high-$T$ region.
