another (simpler) inflection calculation

[kanou-h]

We can calculate the inflection of a cubic Bezier curve defined by (P0, P1, P2, P3) without aligning it:

Define vector variables
V0 = P1 - P0, V1 = P2 - P1, V2 = P3 - P2,
A0 = V1 - V0, A1 = V2 - V1
and cross product P×Q as
cross(P, Q) = P.x * Q.y - P.y * Q.x,
then the coefficients of quadratic equation
a * t*t + b * t + c = 0
can be expressed as
a = cross(A1, A0),
c = cross(V1, V0),
b = cross(V2, V0) - 2 * c.