Found this site:
web.cs.wpi.edu/~matt/courses/cs5 … eform.html
So I tried reproducing the same effect on Synfig:
freeform-deform.sif (41.5 KB)
There’s still an issue that makes the deformed shape not follow the bezier as closely as it should.
If you want to play with it you can edit (and animate) the P0, P1, P2 (to control the deformation bezier) and the point0, point1, point2, point3 (to control the shape being deformed, ie. two straight lines).
The magenta circles represent the original shape, the green circles the deformation bezier and the orange circles the result deformed shape. The other circles represent various intermediate steps, you can enable them if you want to see a bit of the inner workings.