  Several natural and artificial structures and systems are somehow optimized
for performing specific functionalities. The structure and topology of cities
is no exception, as it is critically important to ensure effective access to
the several resources as well as overall mobility. The present work addresses
the important subject of improving the plan of a given city through the
incorporation of avenues and other express ways such as bridges and tunnels.
More specifically, we start with the topology of a real city and consider the
incorporation of a express way between any two locations in the city, keeping
one location fixed and varying the angle of the other. The whole city area is
covered in this manner, which allows us to derive a respective energy surface
indicating the gain obtained regarding the average shortest path length for
each of the possible situations. These surfaces therefore provide a complete
picture of how much each city can be improved regarding minimal distances.
Quite distinct surfaces have been obtained for 18 considered European cities.
These surfaces are then characterized in terms of the number of local extrema
and respective spatial complexity, expressed in terms of a raggedness
measurement. Measurements are also obtained respectively to the geometry and
topology of the considered cities. It is shown that the shortest path gain
depends strongly on some of the considered measurements, especially lacunarity
and transitivity. Interestingly, the intricacy of the energy surfaces resulted
in relatively little correlation with the topological and geometrical
measurements.
