  An algorithm is given for explicitly computing Penrose diagrams for
spacetimes of the form $ds^2 = -f(r)\, dt^2 + f(r)^{-1} \, dr^2 + r^2 \,
d\Omega^2$. The resulting diagram coordinates are shown to extend the metric
continuously and nondegenerately across an arbitrary number of horizons. The
method is extended to include piecewise approximations to dynamically evolving
spacetimes using a standard hypersurface junction procedure. Examples generated
by an implementation of the algorithm are shown for standard and new cases. In
the appendix, this algorithm is compared to existing methods.
