Say the 4 control points of a cubic Bezier curve are $A, B, C, D$. If the 2 end points ($A, D$) and their tangents ($\vec{a}, \vec{d}$) are already fixed, i.e. $C, D$ can only move along 2 rays: $A+p\vec{a}$ and $D-q\vec{d}$, then how should I find the pair of values $p, q$ so that the max curvature can be minimized?
I recognized there have already been a bunch of questions related to Bezier curve curvature extrema. I just wonder under this specific constraint whether there exists a viable solution.