Given a set of points, we want to model the general trend of the points by finding a smooth curve that fits the dataset. This is actually what we do in machine learning.

Problem Formulation

Given . estimate for any point such that .


2 ways to go about interpolation:

When there are very few points (<6), we do Polynomial Interpolation

However, then, when there are lots of points, your 1 function might be of degree too high and it won’t be as smooth anymore. Therefore, a better strategy is to use Piecewise Interpolation

There also is another category of interpolation called Hermite Interpolation, where we want to set the derivatives at control points.

Polynomial Interpolation

If we have 5 points, we can find a polynomial of degree 4 passing through these points.

We use the equation below:

Now, it looks very complicated at first, but we can calculate the finite differences very easily. Use the triangular table:

Interpolation in Python

There’s logic for interpolating racing lines.

I need to reference both the TUFTM, and some implementation that the guys at F1TENTH did.

But there’s this Scipy function for interpolation:

class_Β scipy.interpolate.interp1d(_x_,Β _y_, ...)