implicit-known-traj

[Peter230655]

I played around will Hilly Race, but I set the racecourse like this:
In the range -250 < point < 1250 I picked 15 points at random, say
xx = np.linspace(-250, 1250, 15)
yy = np.cumsum(np.random uniform(-35, 35, 15))
then I set w = np.UnivariateSpline(xx, yy, k = a)
Then,
x_meas = np.linspace(-250, 1250, 3001)
theta = np.atan(w(x_meas, 1))
dtheadx = np.atan(w(meas, 2))
all else like before

I found this:
The larger a ( 1 <= k <= 5 is allowed) the faster the convergence.
So, smoothness of dtheadx seems to help convergence,

[moorepants]

Thanks. This will be helpful for @Neville-N to know for his research problem.

[Peter230655]

For different k the interpolations may look quite different in my somewhat artificial example. So probably good to look at the interpolations for different k. In Hilly Race for k >= 4 dthetadx is continuously differentiable.