### Bezier curve information

How many segments, and which ones, do we need to cut a Bezier curve into, in order for us to create an offset-curve
simply by scaling the sections? In order to answer that question, we need to know where the Bezier inflects -- i.e. where its
curvature changes direction in some interesting way. This is actually fairly simply checked, by looking at the first (blue) and
second (red) derivatives of the Bezier curve function:

*f*_{x}(t) = (1-t)³·x_{0} + (1-t)²·t·x_{1} + (1-t)·t²·x_{2} + t³·x_{3}

*f*_{y}(t) = (1-t)³·y_{0} + (1-t)²·t·y_{1} + (1-t)·t²·y_{2} + t³·y_{3}

Every root for *f '(t)* and *f "(t)* (for *t* inside the range <0,1>) indicates an inflection point in the original
curve. Let's math: everwhere a blue or red line crosses the *t*-axis, that's a point of interest.