[kowdermeister]

I give them a big kudos for adding lots of illustrations, it's vital to have good visual representation for math concepts.

> Evaluating the curve's equation for values of tt going from 0 to 1, is sort of the same as walking along the curve. It is important to understand that tt is a scalar but that the result of the equation for any tt contained in the range [0:1] is a position in 3D space (for 3D curves, and obviously a 2D point for 2D curves). In other words, if we need to visualise a parametric curve, all we have to do is to evaluate the curve's equation for increasing values of tt at some regular positions (it doesn't have to be though), and connecting the resulting positions in space to create a polygonal path (as illustrated in figure 5).

Unfortunately this is the language that you should avoid if you want to explain these concepts for beginners. Too technical, too rigid, too dry. I sort of understand what it says, but it could be done in much simpler way. I'd put it this way:

"We have a function that describes the bezier curve. If you call that function with the P1-4 parameters you will receive X,Y (or Z if you do 3D) coordinates that you can easily plot and connect with straight lines. You also need to specify how many segments you want to receive, this will be resolution of the curve."

Or something like this. Better explained ( betterexplained.com/calculus/ ) does a good job at this and I recently recently rediscovered Kirupa, I love his tutorials: https://www.kirupa.com/html5/animating_with_easing_functions...