Constructing splines from truncated signatures
Constructing splines from truncated signatures
Consider piecewise polynomial paths in the plane that have one quadratic and one linear piece, and parallel tangent vectors at the control point. There are 5 parameters involved, which agrees with the dimension of the associated signature variety. Here, this is just the step 3 free nilpotent Lie group. For a generic element of the Lie group, there are two complex points in the fiber, with real points corresponding to path reconstructions. Adjust the signature values below to see how they change the paths.
