Little Bird tells me one DOSNAE need them iterations

The explanations on JSI and the subsequent links from there to Wiki are quite enlightening. Unfortunately, I cannot get the Examples there to work. Probably something that's not supported by Android Chrome, like SVG. I don't know.

I have a nice Apache Server with PHP and GD. Did some things in it before...

Bezier Variations

First thing I did was a canvas with some points and a visualization of the reduction ('viz'). Has been online for 2 weeks now, and it's a bit boring. After a couple of them, I've seen enough.

The Power of Bezier however, is not the Single Curve, but the combination of some Curves.

The original version is still there somewhere, every now and then. You'll see the Points that determine the Curve, sequence numbers and all. And an orange dot at the center of the points.

But mostly, there will be more than one set of points.

Sometimes (35%) they're totally free. Which is nice.

Single Point Connection

When they connect, the Magic happens. Which is even nicer. Quite some strong results, often with very sharp edges where two curves meet.

These Combinations have a more transparent viz.

Mirror Connection

And then one notices that there is something peculiar with connections. If the second point of the next curve is the mirror of the penultimate from the prev, the resulting curve smoothens!

Here I've completely vaporized the viz.

FAQ

What happened to your promise that we would be able to drag them points around?

Flushed it. Best riddance ever!