  An emanation graph of grade $k$ on a set of points is a plane spanner made by
shooting $2^{k+1}$ equally spaced rays from each point, where the shorter rays
stop the longer ones upon collision. The collision points are the Steiner
points of the spanner. Emanation graphs of grade one were studied by Mondal and
Nachmanson in the context of network visualization. They proved that the
spanning ratio of such a graph is bounded by $(2+\sqrt{2})\approx 3.414$. We
improve this upper bound to $\sqrt{10} \approx 3.162$ and show this to be
tight, i.e., there exist emanation graphs with spanning ratio $\sqrt{10}$. We
show that for every fixed $k$, the emanation graphs of grade $k$ are constant
spanners, where the constant factor depends on $k$.
  An emanation graph of grade two may have twice the number of edges compared
to grade one graphs. Hence we introduce a heuristic method for simplifying
them.
  In particular, we compare simplified emanation graphs against Shewchuk's
constrained Delaunay triangulations on both synthetic and real-life datasets.
Our experimental results reveal that the simplified emanation graphs outperform
constrained Delaunay triangulations in common quality measures (e.g., edge
count, angular resolution, average degree, total edge length) while maintaining
a comparable spanning ratio and Steiner point count.
