Psurface is a C++ library that handles piecewise linear bijections between
triangulated surfaces. These surfaces can be of arbitrary shape and need not
even be manifolds.

There are two main uses for psurface. When doing adaptive finite element
simulations on grids with parametrized boundaries, psurface can store the
parametrization. Boundary parametrizations are practically mappings from the
coarse grid boundary to the actual boundary, and if that actual boundary is a
triangulated surface then psurface can handle it. This is implemented, for
example, in the dune-grid module of Dune.