Bezier curve inflection points

Adrian Colomitchi wrote me an email about an article I wrote. It turns out that I was wrong about the inflection point section. I was trying to figure out what Timo meant by “loop tips”, and I figured it could be an inflection point.

So here’s how Adrian describes inflection points:

If you drive or ride a bicycle: inflection points will happen when you switch your direction from left-to-right or vice-versa.
The inflexion points have 0-curvature (and infinite radius)… for an instant you travel straight (because you are switching the direction).
By contrast, the tip points will have maximum curvature.

Here’s how the inflection points should actually look like (screenshots taken from Adrian’s site):

A Bezier curve with no inflection points:
Bezier curve with no inflection points

A Bezier curve with one inflection point:
Bezier curve with one inflection point

A Bezier curve with two inflection points:
Bezier curve with two inflection points

You can find out more about inflection points on a cubic Bezier curve on Adrian’s website.

If you have anything to add about inflection points (or Bezier curves), comment below.