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# Path Complexity or Driving Skills

### [1] Evaluating Path Complexity

We regard a vehicle path that includes frequent turns to be “more complex” than a straight-line path. MotionLab possesses an equation that quantitatively evaluates the complexity of a given path. Let us take two slalom sample paths, A+B-C+D-E- and A+B-C+D-E+; MathMind computes each of their complexity in a single number, which we call path complexity or motion complexity. (We already discussed these sample motions in Path Classes and Their Symbolic Representation [2].) A path with a larger path complexity means the path is more complicated.

A user inputs
“A+B-C+D-E-”
for this Slalom motion.

The Motion Complexity field reports
1.0114 at the end.

A user inputs
“A+B-C+D-E+”
for this Slalom motion.

The Motion Complexity field reports
1.0887 at the end.

We intuitively expect that the former path class “A+B-C+D-E-” is less complex than the latter “A+B-C+D-E+.” This intuition is confirmed by the path complexity numbers shown in the demonstrations.

### [2] Evaluating Driving Skills

The same equation used for complexity evaluation can assess a driver’s driving skills as well. In this case, we call the number the driving-skill index:

A user drives a car using mouse clicks
in Math Mind motion 8.1 Driving Skills.

In this performance, Math Mind returns
a driving-skill index of 2.3928.

A smaller index means a better skill.

If this user tests the same Driving Skills program again, he or she will obtain a different motion-skill index.

Motions created by a novice driver may contain unnecessary windings; the driving-skill index reports the result quantitatively. Any vehicle can install this driving-skill-evaluating capacity, not only in self-driving cars. This equation has a wide variety of potential applications. A driver can check his or her skills as a reference, and the index would indicate how much a driver’s skills have improved. This capacity can also be used to compare the performances of two self-driving algorithms.