The angular resolution of any vertex in a drawing
is the smallest angle formed
by its adjacent edges.
When the edges are drawn as curved arcs it is measured with regards
to the tangent at that vertex.
A vertex has perfect angular resolution if its angular resolution
is *360/d* where *d* is the degree of the vertex.

Rather than judge the angular resolution of each drawing
precisely and thus
require precise positions, the judges shall use a visual comparison
with emphasis foremost on angular resolution particularly the
worst-case deviation of the angular resolution from the perfect
angular resolution value.
However, other standard aesthetic criteria still remain.
In particular, if the graph is planar (Category A),
it **must** be drawn without crossings.
If there are crossings (Category B) then the angular resolution
at the crossings will also be taken into consideration.
In addition, the graph
should use a reasonably small grid area.
The vertices do not have to be on an integer grid but the
vertex resolution,
the ratio between the distance of the closest two vertices and
the farthest two vertices, should still remain relatively low.
Both graphs are highly symmetric so any exploitation of that
feature will also be taken into consideration.

Unlike the challenge, the scoring is still subjective, simply with a more focused consideration. Thus, a planar graph drawn with perfect angular resolution but having crossings and using exponential grid area would likely lose to one having less than perfect angular resolution but without crossings and in a quadratic grid space.

**Category A: straight-line planar**

The first (undirected) graph is planar. The drawing should be drawn in the plane, without crossings, and using only straight-line edges. Whereas many bad examples of angular resolution use sequences of nested triangles, this graph contains only two nested triangles and their removal creates a collection of outerplanar graphs.

The data can be obtained here.**Category B: curved drawings**

The second (undirected) graph is not planar. The drawing, again in the plane, can have as many crossings as necessary but the angles of the crossings will also be taken into consideration. In addition, the drawings can use curved arcs. There can be as many bends as needed but during judging both the number of bends and smoothness of the bends will be taken into consideration and weighed against the gain in overall angular resolution.

The 15-node, 45-edge graph in LCF notation is`1^15 4^15 6^15`.

It can be downloaded here.

The graphs are given in a simple adjacency list format.
The first line contains the numbers, N and M, of vertices and edges
respectively.
The remaining N lines each represent a single vertex
and its adjacencies.
The first number on the line is the vertex number (0 to N-1).
The remaining numbers correspond to vertices adjacent to the vertex.
Thus, the line `2 1 3 6` means that node 2 is adjacent
to nodes 1, 3, and 6.