  Let G be a Lie group endowed with a bi-invariant pseudo-Riemannian metric.
Then the moduli space of flat connections on a principal G-bundle, P\to \Sigma,
over a compact oriented surface, \Sigma, carries a Poisson structure. If we
trivialize P over a finite number of points on the boundary of \Sigma, then the
moduli space carries a quasi-Poisson structure instead. Our first result is to
describe this quasi-Poisson structure in terms of an intersection form on the
fundamental groupoid of the surface, generalizing results of Massuyeau and
Turaev.
  Our second result is to extend this framework to quilted surfaces, i.e.
surfaces where the structure group varies from region to region and a reduction
(or relation) of structure occurs along the borders of the regions, extending
results of the second author.
  We describe the Poisson structure on the moduli space for a quilted surface
in terms of an operation on spin networks, i.e. graphs immersed in the surface
which are endowed with some additional data on their edges and vertices. This
extends the results of various authors.
