[shaftway]

Try this link: https://blog.richardekwonye.com/bezier-curves

The animations make it very intuitive to understand what's happening. Once you get that it's trivial to turn that into a parametric formula (`x(t)` and `y(t)`, not `f(x)`) to calculate all the points along the curve.

Start by understanding quadratic beziers, they're pretty straightforward. Then when you move to cubic ones realize that it's just adding one more level of interpolation.

The hurdle for me was realizing that it's impossible to calculate the corresponding y position given the x position for all 2d curves, because there may be multiple y positions. Instead think of it as little steps that get you from the beginning to the end.