Bezier Interpolation I have a Bezier curve with three shape keys as shown above. All three have the same length. The animation with shape key evaluation time from 0 to 20 (with 'Relative' unchecked) is shown below.


As you can see the curve length changes continuously during the animation. I have tried all the shape key interpolation methods (Bspline, Catmull-Rom etc). But none of them keeps the length intact. Is there a way to ensure the curve length is not modified during the interpolation? In general, it would be great if you could suggest some way to influence the behavior of the shape key interpolation.

There is this question, which I thought had the answer. But it's referring to uniform distribution of points along the curve, so it's not related.
Someone may come along and correct me.. but I think this is impossible with Shape Keys. 

Using Shape Keys, whatever the interpolation between vertex positions, the route from one to another is essentially a translation. The route that would preserve inter-vertex length has a large rotational component. The vertices have to travel along an arc around the right (possibly moving) center, not a straight line, or a curve not based on that center.

You could approximate that by using something like @moonboots' solution, and setting up a large number of linearly interpolated shape keys, (ultimately achieving a match by having one shape key per frame).