# How to move the control points of the cubic Bézier curve, to keep the curve invariant?

I have 3 cubic Bézier curves with different control points:

They look similar to each other. Assuming the anchor points $$P_0=(0, 0)$$, $$P_3=(1, 1)$$ are static, Is there a way to move $$P_1$$, $$P_2$$ while keeping the curve invariant?

A cubic Bezier curve is defined by the 4 control points. Any change to any control point will result in a different curve. So, moving $$P_1$$ or $$P_2$$ while keeping $$P_0$$ and $$P_3$$ unchanged will still change the curve.
• My original question is edited, there is one more Q: if invariant is impossible, how to keep the deformation as little as possible (while moving $P_1$, $P_2$ around) ? – zhangxaochen Jul 8 at 1:55