Cubic interpolation (Bezier, Hermite, Cardinal, B-Spline) written in list comprehension and vectorization, no Numpy! Used to draw trajectories between points.
Curve trajectories are all given by
$$A \times B \times C$$
$$A = \begin{bmatrix}
1 & t & t^2 & t^3
\end{bmatrix}$$
$$B \times C = \begin{bmatrix}
1 & 0 & 0 & 0 \\\
-3 & 3 & 0 & 0 \\\
3 & -6 & 3 & 0 \\\
-1 & 3 & -3 & 1
\end{bmatrix}
\begin{bmatrix}
P_1 \\\
H_1 \\\
H_2 \\\
P_2
\end{bmatrix}$$
$$B \times C = \begin{bmatrix}
1 & 0 & 0 & 0 \\\
0 & 0 & 1 & 0 \\\
-3 & 3 & -2 & -1 \\\
2 & -2 & 1 & 1
\end{bmatrix}
\begin{bmatrix}
P_1 \\\
P_2 \\\
H_1 \\\
H_2
\end{bmatrix}$$
$$B \times C = \begin{bmatrix}
0 & 1 & 0 & 0 \\\
-s & 0 & s & 0 \\\
2s & s-3 & 3-2s & -s \\\
-s & 2-s & s-2 & s
\end{bmatrix}
\begin{bmatrix}
P_1* \\\
P_2 \\\
P_3 \\\
P_4*
\end{bmatrix}$$
$$B \times C = \begin{bmatrix}
1 & 4 & 1 & 0 \\\
-3 & 0 & 3 & 0 \\\
3 & -6 & 3 & 0 \\\
-1 & 3 & -3 & 1
\end{bmatrix}
\begin{bmatrix}
H_1 \\\
H_2 \\\
H_3 \\\
H_4
\end{bmatrix}$$
$s$ is the tension, and can vary from 0 to 1. 0 is linear interpolation, 0.5 is Catmull-Rom
$P$ denotes control points that lie on the curve
$H$ denotes control points that don't lie on the curve (handles)
(*) starred denotes points that aren't interpolated
