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I have 3 cubic Bézier curves with different control points:

  1. https://cubic-bezier.com/#.17,.8,.77,1 enter image description here
  2. https://cubic-bezier.com/#.18,.59,.5,1 enter image description here
  3. https://cubic-bezier.com/#.12,.41,.41,1 enter image description here

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?

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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.

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  • $\begingroup$ 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) ? $\endgroup$ – zhangxaochen Jul 8 at 1:55
  • $\begingroup$ When P1 and P2 are moved to new locations (and P0 and P3 are fixed), the curve will have a new shape. This new shape will have a certain deviation to the original shape and such deviations cannot be reduced as you don't have any other control points that you can change. $\endgroup$ – fang Jul 9 at 1:22

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