  We present sweeping line graphs, a generalization of $\Theta$-graphs. We show
that these graphs are spanners of the complete graph, as well as of the
visibility graph when line segment constraints or polygonal obstacles are
considered. Our proofs use general inductive arguments to make the step to the
constrained setting. These same arguments could apply to other spanner
constructions in the unconstrained setting, removing the need to find separate
proofs that they are spanning in the constrained and polygonal obstacle
settings.
