I wanted to generate a cubic bezier spline which connects specified points with constraints on the first and second derivatives of the cubic spline (with first and second derivatives less than some constant). I am generating the control points of the bezier curve by following this tutorial
How do I select control points such that the first and second derivatives are already constrained?
If your (cubic) Bezier curve has control points $A,B,C,D$, then, at $t=0$, the first derivative is $\tfrac13(B-A)$, and the second derivative is $\tfrac16\bigl[(C-B)-(B-A)\bigr]$. Similarly, at $t=1$, the first derivative is $\tfrac13(D-C)$, and the second derivative is $\tfrac16\bigl[(C-B)-(D-C)\bigr]$. So, you have to constrain the lengths of these vectors.