  Persistence diagram (PD) bundles, a generalization of vineyards, were
introduced as a way to study the persistent homology of a set of filtrations
parameterized by a topological space $B$. In this paper, we present an
algorithm for computing piecewise-linear PD bundles, a wide class that includes
many of the PD bundles that one may encounter in practice. Full details are
given for the case in which $B$ is a triangulated surface, and we outline the
generalization to higher dimensions and other cases.
